Chiral and topological superconductivity in isospin polarized multilayer graphene

Authors: Max Geier, Margarita Davydova, Liang Fu

Published: Tue, 24 Sep 2024 00:00:00 -0400

arXiv:2409.13829v1 Announce Type: new Abstract: A microscopic mechanism for chiral superconductivity from Coulomb repulsion is proposed for spin- and valley-polarized state of rhombohedral multilayer graphene. The superconducting state occurs at low density, has chiral $p$-wave pairing symmetry, and exhibits highest $T_c$ close to a Lifshitz transition from annular to simply-connected Fermi sea. This Lifshitz transition also marks a topological phase transition from a trivial to a topological superconducting phase hosting Majorana fermions. The chirality of the superconducting order parameter is selected by the chirality of the valley-polarized Bloch electrons. Our results are in reasonable agreement with observations in a recent experiment on tetralayer graphene [arXiv:2408.15233]

Topological frequency conversion in rhombohedral multilayer graphene

Authors: Étienne Lantagne-Hurtubise, Iliya Esin, Gil Refael, and Frederik Nathan

Published: 2024-09-20T10:00:00+00:00

Author(s): Étienne Lantagne-Hurtubise, Iliya Esin, Gil Refael, and Frederik Nathan

We show that rhombohedral multilayer graphene supports topological frequency conversion, whereby a fraction of electrons transfer energy between two monochromatic light sources at a quantized rate. The pristine nature and gate tunability of these materials, along with a Berry curvature that directly…

[Phys. Rev. B 110, L100305] Published Fri Sep 20, 2024

Sliding-dependent electronic structures of alternating-twist tetralayer graphene

Authors: Kyungjin Shin, Jiseon Shin, Yoonsung Lee, Hongki Min, and Jeil Jung

Published: 2024-09-17T10:00:00+00:00

Author(s): Kyungjin Shin, Jiseon Shin, Yoonsung Lee, Hongki Min, and Jeil Jung

Unlike twisted bilayer graphene (TBG), the electronic structures of alternating-twist tetralayer graphene (ATTG) vary with sliding between layers. Here, the authors model the system as two vertically stacked equal twist angle TBG layers. They specifically explore how three sliding geometries (AA, AB, and SP) affect its electronic and optical properties, including valley Chern numbers. The results of optical conductivity and self-consistent Hartree band structures provide deeper insights into ATTG with various sliding configurations and offer potential experimental fingerprints.

[Phys. Rev. B 110, 115136] Published Tue Sep 17, 2024

Self-consistent theory of fractional quantum anomalous Hall states in rhombohedral graphene

Authors: Ke Huang, Xiao Li, Sankar Das Sarma, and Fan Zhang

Published: 2024-09-24T10:00:00+00:00

Author(s): Ke Huang, Xiao Li, Sankar Das Sarma, and Fan Zhang

The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In parti…

[Phys. Rev. B 110, 115146] Published Tue Sep 24, 2024

Sliding-dependent electronic structures of alternating-twist tetralayer graphene

Authors: Kyungjin Shin, Jiseon Shin, Yoonsung Lee, Hongki Min, Jeil Jung

Published: Mon, 30 Sep 2024 00:00:00 -0400

arXiv:2406.11527v2 Announce Type: replace Abstract: We study the electronic structure of alternating-twist tetralayer graphene, especially near its magic angle $\theta = 1.75^\circ$, for different AA, AB, and SP sliding geometries at their middle interface that divides two twisted bilayer graphenes. This sliding dependence is shown for the bandwidths, band gaps, and $K$-valley Chern numbers of the lowest-energy valence and conduction bands as a function of twist angle and interlayer potential difference. Our analysis reveals that the AA sliding is most favorable for narrow bands and gaps, and the AB sliding is most prone to developing finite valley Chern numbers. We further analyze the linear longitudinal optical absorptions as a function of photon energy and the absorption map in the moir\'{e} Brillouin zone for specific transition energies. A self-consistent Hartree calculation reveals that the AA system's electronic structure is the most sensitive to variations in carrier density.

Author Correction: Intervalley coherence and intrinsic spin–orbit coupling in rhombohedral trilayer graphene

Authors: Trevor Arp, Owen Sheekey, Haoxin Zhou, C. L. Tschirhart, Caitlin L. Patterson, H. M. Yoo, Ludwig Holleis, Evgeny Redekop, Grigory Babikyan, Tian Xie, Jiewen Xiao, Yaar Vituri, Tobias Holder, Takashi Taniguchi, Kenji Watanabe, Martin E. Huber, Erez Berg, Andrea F. Young

Published: 2024-10-08

Nature Physics, Published online: 08 October 2024; doi:10.1038/s41567-024-02689-5

Author Correction: Intervalley coherence and intrinsic spin–orbit coupling in rhombohedral trilayer graphene

Chiral superconductivity from parent Chern band and its non-Abelian generalization

Authors: Yan-Qi Wang, Zhi-Qiang Gao, Hui Yang

Published: Thu, 10 Oct 2024 00:00:00 -0400

arXiv:2410.05384v1 Announce Type: new Abstract: We propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetra-layer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose-Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose-Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multi-layer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. We argue that a chiral spin liquid phase can emerge in the vicinity of the chiral superconductor phase of the composite fermion, i.e., the non-Abelian Moore-Read quantum Hall phase. Our work suggests rhombohedral multi-layer graphene as a potential platform for rich correlated topological phases.

Bilayer Graphene on hexagonal Boron Nitride and the Family of quantum MetaMaterial

Authors: Takuya Iwasaki, Yoshifumi Morita

Published: Thu, 10 Oct 2024 00:00:00 -0400

arXiv:2410.05649v1 Announce Type: new Abstract: We report on the fabrication and characterization of dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Due to the moire effect, the hBN/BLG superlattice harbors an energy gap at the charge neutral point (CNP) and the satellites even without a perpendicular electric field. In BLG, moreover, the application of a perpendicular electric field tunes the energy gap, which contrasts with the single-layer graphene (SLG) and is linked to the family of rhombohedral multilayer graphene. Therefore, the hBN/BLG superlattice is accompanied with non-trivial energy-band topology and a narrow energy band with van Hove singularities. By the dual gating, systematic engineering of the energy-band structure can be performed and the carrier concentration is fine-tunable. This review is an extended version of the talk based on ref. [1], which is also a supplementary to the ref. T. Iwasaki, Y. Morita, K. Watanabe, T. Taniguchi, Phys. Rev. B106, 165134 (2022) and Phys. Rev. B109, 075409 (2024). The data show the universality and diversity in the physics of the hBN/BLG superlattices.

Snell's law in multirefringent systems

Authors: J\'ozsef Cserti, \'Aron Holl\'o, L\'aszl\'o Oroszl\'any

Published: Thu, 17 Oct 2024 00:00:00 -0400

arXiv:2410.12410v1 Announce Type: new Abstract: In anisotropic crystals, Maxwell's equations permit only birefringence for the propagation of light. Notwithstanding, multirefringent systems comprising more than two propagating modes exist, such as in electron optics and photonic crystals. It has been demonstrated that in such systems, the propagation of waves in the short wavelength limit results in the formation of anomalous caustics. To calculate these caustic curves, we generalized Snell's law valid for reflection and refraction in multirefringent systems possessing more than one propagating mode. The emergence of anomalous caustics in the wave function patterns obtained from rigorous quantum mechanical calculations in electron-optical systems is confirmed. These calculations were performed on electron scattering from circularly gated potential regions applied to multilayer rhombohedral graphene. Our results may generate further work to explore more complex phenomena in multirefringent systems.

Self-consistent theory for the fractional quantum anomalous Hall effect in rhombohedral pentalayer graphene

Authors: Ke Huang, Xiao Li, Sankar Das Sarma, Fan Zhang

Published: Fri, 18 Oct 2024 00:00:00 -0400

arXiv:2407.08661v2 Announce Type: replace Abstract: The fractional quantum anomalous Hall (FQAH) effect in rhombohedral pentalayer graphene (PLG) has attracted significant attention due to its potential for observing exotic quantum states. In this work, we present a self-consistent Hartree-Fock theory for the FQAH effect in rhombohedral PLG. In particular, we focus on the convergence of the Hartree-Fock calculation with various reference fields and discuss the stability of the FQAH states in PLG. We show that the so-called charge neutrality scheme provides an unambiguous result for the Hartree-Fock calculation, as it ensures a convergence with respect to the momentum cutoff. Based on the Hartree-Fock band structure, we further carry out exact diagonalization calculations to explore the stability of the FQAH states in PLG. Our work provides an improved and unified (minimal) theoretical framework to understand the FQAH effect in rhombohedral PLG and paves the way for future experimental and theoretical studies.

Correlated topological flat bands in rhombohedral graphite

Authors: Hongyun ZhangQian LiMichael G. ScheerRenqi WangChuyi TuoNianlong ZouWanying ChenJiaheng LiXuanxi CaiChanghua BaoMing-Rui LiKe DengKenji WatanabeTakashi TaniguchiMao YePeizhe TangYong XuPu YuJose AvilaPavel DudinJonathan D. DenlingerHong YaoBiao LianWenhui DuanShuyun ZhouaState Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of ChinabDepartment of Physics, Princeton University, Princeton, NJ 08544cInstitute for Advanced Study, Tsinghua University, Beijing 100084, People’s Republic of ChinadResearch Center for Functional Materials, National Institute for Materials Science, Tsukuba 305-0044, JapaneInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, JapanfShanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, People’s Republic of ChinagSchool of Materials Science and Engineering, Beihang University, Beijing 100191, People’s Republic of ChinahMax Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg 22761, GermanyiFrontier Science Center for Quantum Information, Beijing 100084, People’s Republic of ChinajSynchrotron SOLEIL, L’Orme des Merisiers, Gif sur Yvette Cedex 91192, FrancekAdvanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Published: 2024-10-16T07:00:00Z

Proceedings of the National Academy of Sciences, Volume 121, Issue 43, October 2024.

A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order

Authors: Patrick H. Wilhelm, Andreas M. L\"auchli, Mathias S. Scheurer

Published: Wed, 23 Oct 2024 00:00:00 -0400

arXiv:2406.09505v2 Announce Type: replace Abstract: Motivated by recent experiments on correlated van der Waals materials, including twisted and rhombohedral graphene and twisted WSe$_2$, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an extensive non-trivial ground state manifold within the band filling range $0 < \nu < 1$ and introduce a general principle, the ''three-rule'', for combining flatband wave functions, which governs their zero-energy property on the torus geometry. Based on the structure of these wave functions, we develop a variational approach that reveals distinct phases under different perturbations: metallic behavior emerges from a finite dispersion, and superconductivity is induced by attractive Cooper channel interactions. Our approach, not reliant on the commonly applied mean-field approximations, provides an analytical expression for the macroscopic wave function of the off-diagonal long-range order correlator, attributing pairing susceptibility to the set of non-trivial zero-energy ground state wave functions. Extending to finite screening lengths and beyond the ideal limit using exact diagonalization simulations, we demonstrate the peculiar structure in the many-body wave function's coefficients to be imprinted in the low-energy spectrum of the topologically ordered Halperin spin-singlet state. Our findings also make connections to frustration-free models of non-commuting projector Hamiltonians, potentially aiding the future construction of exact ground states for various fractional fillings.

Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene

Authors: Sankar Das Sarma and Ming Xie

Published: 2024-10-22T10:00:00+00:00

Author(s): Sankar Das Sarma and Ming Xie

A recent experiment in pentalayer graphene/hBN moiré superlattices uncovered a surprising new phase, with integer quantization at fractional fillings, emerging at lower temperatures than the previously observed FQAHE states. Through theoretical analysis of the transport data, the authors establish here that this low-temperature phase is likely a disorder-induced localized insulating phase, and that the transition between this phase and the higher temperature FQAHE phase is a crossover phenomenon driven by the competition between interaction and disorder energy scales.

[Phys. Rev. B 110, 155148] Published Tue Oct 22, 2024

Topological frequency conversion in rhombohedral multilayer graphene

Authors: \'Etienne Lantagne-Hurtubise, Iliya Esin, Gil Refael, Frederik Nathan

Published: Fri, 25 Oct 2024 00:00:00 -0400

arXiv:2403.09935v2 Announce Type: replace Abstract: We show that rhombohedral multilayer graphene supports topological frequency conversion, whereby a fraction of electrons transfer energy between two monochromatic light sources at a quantized rate. The pristine nature and gate tunability of these materials, along with a Berry curvature that directly couples to electric fields, make them ideal platforms for the experimental realization of topological frequency conversion. Among the rhombohedral family, we find that Bernal bilayer graphene appears most promising for THz-scale applications due to lower dissipation. We discuss strategies to circumvent cancellations between the two valleys of graphene and to minimize dissipative losses using commensurate frequencies, thus opening a potential pathway for net amplification.

Thermal crossover from a Chern insulator to a fractional Chern insulator in pentalayer graphene

Authors: Sankar Das Sarma, Ming Xie

Published: Fri, 01 Nov 2024 00:00:00 -0400

arXiv:2408.10931v3 Announce Type: replace Abstract: By theoretically analyzing the recent temperature dependent transport data in pentalayer graphene [Lu et al., arXiv:2408.10203], we establish that the experimentally observed transition from low-temperature quantum anomalous Hall effect to higher-temperature fractional quantum anomalous Hall effect is a crossover phenomenon arising from the competition between interaction and disorder energy scales, with the likely zero temperature ground state of the system being either a localized insulator or a Chern insulator with a quantized anomalous Hall effect. In particular, the intriguing suppression of FQAHE in favor of QAHE with decreasing temperature is explained as arising from the low-temperature localization of the carriers where disorder overcomes the interaction effects. We provide a detailed analysis of the data in support of the crossover scenario.

Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra-layer graphen

Authors: Hui Yang, Ya-Hui Zhang

Published: Wed, 06 Nov 2024 00:00:00 -0500

arXiv:2411.02503v1 Announce Type: new Abstract: We performed a random phase approximation (RPA) calculation for a spin-valley polarized model of the rhombohedral tetra-layer graphene to study the possibility of chiral superconductor from the Kohn-Luttinger mechanism. We included the realistic band structure and form factor in our calculation and solved the self-consistent equation numerically by sampling 20,000 points in the momentum space at a given temperature. Around the Van-Hove singularity (VHS), we find p-ip pairing with Chern number switching from $C=-1$ to $C=0$ through a gap closing at $\mathbf k=(0,0)$ (defined relative to $\mathbf K$). Although the superconductor is generically fully gapped at low temperature, we find Bogoliubov Fermi surface at temperature just below mean field $T_c$. Besides, through calculation of the free energy, we conclude that the optimal Cooper pair momentum $\mathbf Q$ is generically finite and can be as large as $0.1 k_F$. We dub the $\mathbf Q\neq 0$ phase as an incommensurate Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconductor to distinguish it from the $\mathbf Q=0$ phase. Compared to the $\mathbf Q=0$ phase, our incommensurate $\mathbf Q$ phase is a nematic superconductor if it is in the Fulde-Ferrell(FF) phase or exhibts charge density wave (CDW) if it is in the Larkin-Ovchinnikov (LO) phase. Our work demonstrates the rhombohedral tetra-layer graphene as a wonderful platform to explore Majorana zero-mode, FFLO physics and Bogoliubov fermi surface within one single platform.

Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra-layer graphene

Authors: Hui Yang, Ya-Hui Zhang

Published: Thu, 07 Nov 2024 00:00:00 -0500

arXiv:2411.02503v2 Announce Type: replace Abstract: We performed a random phase approximation (RPA) calculation for a spin-valley polarized model of the rhombohedral tetra-layer graphene to study the possibility of chiral superconductor from the Kohn-Luttinger mechanism. We included the realistic band structure and form factor in our calculation and solved the self-consistent equation numerically by sampling 20,000 points in the momentum space at a given temperature. Around the Van-Hove singularity (VHS), we find p-ip pairing with Chern number switching from $C=-1$ to $C=0$ through a gap closing at $\mathbf k=(0,0)$ (defined relative to $\mathbf K$). Although the superconductor is generically fully gapped at low temperature, we find Bogoliubov Fermi surface at temperature just below mean field $T_c$. Besides, through calculation of the free energy, we conclude that the optimal Cooper pair momentum $\mathbf Q$ is generically finite and can be as large as $0.1 k_F$. We dub the $\mathbf Q\neq 0$ phase as an incommensurate Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconductor to distinguish it from the $\mathbf Q=0$ phase. Compared to the $\mathbf Q=0$ phase, our incommensurate $\mathbf Q$ phase is a nematic superconductor if it is in the Fulde-Ferrell(FF) phase or exhibts charge density wave (CDW) if it is in the Larkin-Ovchinnikov (LO) phase. Our work demonstrates the rhombohedral tetra-layer graphene as a wonderful platform to explore Majorana zero-mode, FFLO physics and Bogoliubov fermi surface within one single platform.

New classes of quantum anomalous Hall crystals in multilayer graphene

Authors: Boran Zhou, Ya-Hui Zhang

Published: Fri, 08 Nov 2024 00:00:00 -0500

arXiv:2411.04174v1 Announce Type: new Abstract: The recent experimental observation of quantum anomalous Hall (QAH) effects in the rhombohedrally stacked pentalayer graphene has motivated theoretical discussions on the possibility of quantum anomalous Hall crystal (QAHC), a topological version of Wigner crystal. Conventionally Wigner crystal was assumed to have a period $a_{\text{crystal}}=1/\sqrt{n}$ locked to the density $n$. In this work we propose new types of topological Wigner crystals labeled as QAHC-$z$ with period $a_{\text{crystal}}=\sqrt{z/n}$. In rhombohedrally stacked graphene aligned with hexagon boron nitride~(hBN), we find parameter regimes where QAHC-2 and QAHC-3 have lower energy than the conventional QAHC-1 at total filling $\nu=1$ per moir\'e unit cell. These states all have total Chern number $C_\mathrm{tot}=1$ and are consistent with the QAH effect observed in the experiments. The larger period QAHC states have better kinetic energy due to the unique Mexican-hat dispersion of the pentalayer graphene, which can compensate for the loss in the interaction energy. Unlike QAHC-1, QAHC-2 and QAHC-3 also break the moir\'e translation symmetry and are sharply distinct from a moir\'e band insulator. We also briefly discuss the competition between integer QAHC and fractional QAHC states at filling $\nu=2/3$. Besides, we notice the importance of the moir\'e potential. A larger moir\'e potential can greatly change the phase diagram and even favors a QAHC-1 ansatz with $C=2$ Chern band.

Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene

Authors: Ammon Fischer, Lennart Klebl, Dante M. Kennes, Tim O. Wehling

Published: Tue, 12 Nov 2024 00:00:00 -0500

arXiv:2407.02576v2 Announce Type: replace Abstract: We derive a minimal low-energy model for Bernal bilayer graphene and related rhombohedral graphene multilayers at low electronic densities by constructing Wannier orbitals defined in real-space supercells of the original primitive cell. Starting from an ab-initio electronic structure theory comprising the atomic carbon $p_z$-orbitals, momentum locality of the Fermi surface pockets around $K,K'$ is circumvented by backfolding the $\pi$-bands to the concomitant mini-Brillouin zone of the supercell, reminiscent of their (twisted) moir\'e counterparts. The supercell Wannier functions reproduce the spectral weight and Berry curvature of the microscopic model and offer an intuitive real-space picture of the emergent physics at low electronic densities being shaped by flavor-polarized wave packets with mesoscopic extent. By projecting an orbital-resolved, dual-gated Coulomb interaction to the effective Wannier basis, we find that the low-energy physics of Bernal bilayer graphene is governed by weak electron-electron interactions. Our study bridges between existing continuum theories and ab-initio studies of small Fermi pocket systems like rhombohedral graphene stacks by providing a symmetric lattice description of their low-energy physics.

Suppression of symmetry-breaking correlated insulators in a rhombohedral trilayer graphene superlattice

Authors: No author

Published: Mon, 11 Nov 2024 00:00:00 +0000

Correlated topological flat bands in rhombohedral graphite

Authors: Hongyun Zhang, Qian Li, Michael G. Scheer, Renqi Wang, Chuyi Tuo, Nianlong Zou, Wanying Chen, Jiaheng Li, Xuanxi Cai, Changhua Bao, Ming-Rui Li, Ke Deng, Kenji Watanabe, Takashi Taniguchi, Mao Ye, Peizhe Tang, Yong Xu, Pu Yu, Jose Avila, Pavel Dudin, Jonathan D. Denlinger, Hong Yao, Biao Lian, Wenhui Duan, Shuyun Zhou

Published: Wed, 13 Nov 2024 00:00:00 -0500

arXiv:2411.07906v1 Announce Type: new Abstract: Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger (SSH) model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon {\it in situ} electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a new platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model

Authors: Tomohiro Soejima (副島智大), Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker

Published: 2024-11-12T10:00:00+00:00

Author(s): Tomohiro Soejima (副島智大), Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker

Anomalous Hall crystals (AHCs) form a new phase of matter with spontaneous crystallization and quantized Hall response. It has been invoked to explain a recent experiment on rhombohedral pentalayer graphene, but a simple conceptual understanding of its existence has been lacking. Here, the authors propose a simple three-patch model that captures how quantum mechanical exchange interactions can stabilize the AHC phase, and apply it to analyze the phenomenology of rhombohedral pentalayer graphene.

[Phys. Rev. B 110, 205124] Published Tue Nov 12, 2024

Theory of Quantum Anomalous Hall Phases in Pentalayer Rhombohedral Graphene Moiré Structures

Authors: Zhihuan Dong, Adarsh S. Patri, and T. Senthil

Published: 2024-11-12T10:00:00+00:00

Author(s): Zhihuan Dong, Adarsh S. Patri, and T. Senthil

Remarkable recent experiments on the moiré structure formed by pentalayer rhombohedral graphene aligned with a hexagonal boron nitride substrate report the discovery of a zero field fractional quantum Hall effect. These “(fractional) quantum anomalous Hall” [(F)QAH] phases occur for one sign of a pe…

[Phys. Rev. Lett. 133, 206502] Published Tue Nov 12, 2024

Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Authors: Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Tomohiro Soejima (副島智大), Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker

Published: 2024-11-12T10:00:00+00:00

Author(s): Junkai Dong (董焌锴), Taige Wang, Tianle Wang, Tomohiro Soejima (副島智大), Michael P. Zaletel, Ashvin Vishwanath, and Daniel E. Parker

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattic…

[Phys. Rev. Lett. 133, 206503] Published Tue Nov 12, 2024

Fractional Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene in the Moiréless Limit

Authors: Boran Zhou, Hui Yang, and Ya-Hui Zhang

Published: 2024-11-12T10:00:00+00:00

Author(s): Boran Zhou, Hui Yang, and Ya-Hui Zhang

The standard theoretical framework for fractional quantum anomalous Hall (FQAH) effect assumes an isolated flat Chern band in the single particle level. In this Letter, we challenge this paradigm for the FQAH effect recently observed in pentalayer rhombohedrally stacked graphene aligned with hexagon…

[Phys. Rev. Lett. 133, 206504] Published Tue Nov 12, 2024

Efficient prediction of superlattice and anomalous miniband topology from quantum geometry

Authors: Valentin Cr\'epel, Jennifer Cano

Published: Thu, 14 Nov 2024 00:00:00 -0500

arXiv:2406.17843v2 Announce Type: replace Abstract: Two dimensional materials subject to long-wavelength modulations have emerged as novel platforms to study topological and correlated quantum phases. In this article, we develop a versatile and computationally inexpensive method to predict the topological properties of materials subjected to a superlattice potential by combining degenerate perturbation theory with the method of symmetry indicators. In the absence of electronic interactions, our analysis provides a systematic rule to find the Chern number of the superlattice-induced miniband starting from the harmonics of the applied potential and a few material-specific coefficients. Our method also applies to anomalous (interaction-generated) bands, for which we derive an efficient algorithm to determine all Chern numbers compatible with a self-consistent solution to the Hartree-Fock equations. Our approach gives a microscopic understanding of the quantum anomalous Hall insulators recently observed in rhombohedral graphene multilayers.

Chiral superconductivity from parent Chern band and its non-Abelian generalization

Authors: Yan-Qi Wang, Zhi-Qiang Gao, Hui Yang

Published: Thu, 14 Nov 2024 00:00:00 -0500

arXiv:2410.05384v2 Announce Type: replace Abstract: We propose a minimal model starting from a parent Chern band with quartic dispersion that can describe the spin-valley polarized electrons in rhombohedral tetra-layer graphene. The interplay between repulsive and attractive interactions on top of that parent Chern band is studied. We conduct standard self-consistent mean-field calculations, and find a rich phase diagram that consists of metal, quantum anomalous Hall crystal, chiral topological superconductor, as well as trivial gapped Bose-Einstein condensate. In particular, there exists a topological phase transition from the chiral superconductor to the Bose-Einstein condensate at zero temperature. Motivated by the recent experimental and theoretical studies of composite Fermi liquid in rhombohedral stacked multi-layer graphene, we further generalize the physical electron model to its composite fermion counterpart based on a field theory analysis. The chiral superconductor phase of the composite fermion becomes the non-Abelian Moore-Read quantum Hall phase. We argue that a chiral (pseudo-)spin liquid phase can emerge in the vicinity of this Moore-Read quantum Hall phase. Our work suggests rhombohedral multi-layer graphene as a potential platform for rich correlated topological phases.

Layer-dependent evolution of electronic structures and correlations in rhombohedral multilayer graphene

Authors: Yang Zhang, Yue-Ying Zhou, Shihao Zhang, Hao Cai, Ling-Hui Tong, Wei-Yu Liao, Ruo-Jue Zou, Si-Min Xue, Yuan Tian, Tongtong Chen, Qiwei Tian, Chen Zhang, Yiliu Wang, Xuming Zou, Xingqiang Liu, Yuanyuan Hu, Ya-Ning Ren, Li Zhang, Lijie Zhang, Wen-Xiao Wang, Lin He, Lei Liao, Zhihui Qin, Long-Jing Yin

Published: 2024-11-13

Nature Nanotechnology, Published online: 13 November 2024; doi:10.1038/s41565-024-01822-y

By using scanning tunnelling microscopy and spectroscopy, researchers observe layer-dependent electronic correlations in rhombohedral graphene multilayers at 77 K, revealing the layer-enhanced low-energy flat bands and interlayer interactions.

Theory of anomalous Hall effect from screened vortex charge in a phase disordered superconductor

Authors: Jay D. Sau, Shuyang Wang

Published: Fri, 15 Nov 2024 00:00:00 -0500

arXiv:2411.08969v1 Announce Type: new Abstract: Motivated by recent experiments showing evidence for chiral superconductivity in an anomalous Hall phase of tetralayer graphene, we study the relation between the normal state anomalous Hall conductivity and that in the phase disordered state above the critical temperature of the superconductor. By a numerical calculation of superconductivity in an anomalous Hall metal, we find that a difference in vortex and antivortex charge is determined by the Fermi surface Berry phase. Combining this with the vortex dynamics in a back-ground supercurrent leads to a Hall response in the phase disordered state of the superconductor that is close to the normal state anomalous Hall response. However, using a gauge-invariant superconducting response framework, we find that while vortex charge is screened by interactions, the screening charge, after a time-delay, reappears in the longitudinal current. Thus, the dc Hall conductivity in this phase, instead of matching the screened vortex charge, matches the ac Hall conductance in the superconducting and normal phase, which are similar.

Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry

Authors: Ammar Jahin, Shi-Zeng Lin

Published: Fri, 15 Nov 2024 00:00:00 -0500

arXiv:2411.09664v1 Announce Type: new Abstract: We study the effect of the electron wavefunction on Kohn-Luttinger superconductivity. The role of the wavefunction is encoded in a complex form factor describing the topology and geometry of the bands. We show that the electron wavefunction significantly impacts the superconducting transition temperature and superconducting order parameter. We illustrate this using the lowest Landau level form factor and find exponential enhancement of $T_c$ for the resulting topological superconductor. We find that the ideal band geometry, which favors a fractional Chern insulator in the flat band limit, has an optimal $T_c$. Finally, we apply this understanding to a model relevant to rhombohedral graphene multilayers and unravel the importance of the band geometry for achieving robust superconductivity.

Layer-dependent evolution of electronic structures and correlations in rhombohedral multilayer graphene

Authors: Yang Zhang, Yue-Ying Zhou, Shihao Zhang, Hao Cai, Ling-Hui Tong, Yuan Tian, Tongtong Chen, Qiwei Tian, Chen Zhang, Yiliu Wang, Xuming Zou, Xingqiang Liu, Yuanyuan Hu, Ya-Ning Ren, Li Zhang, Lijie Zhang, Wen-Xiao Wang, Lin He, Lei Liao, Zhihui Qin, Long-Jing Yin

Published: Fri, 15 Nov 2024 00:00:00 -0500

arXiv:2312.13637v2 Announce Type: replace Abstract: The recent discovery of superconductivity and magnetism in trilayer rhombohedral graphene (RG) establishes an ideal, untwisted platform to study strong correlation electronic phenomena. However, the correlated effects in multilayer RG have received limited attention, and, particularly, the evolution of the correlations with increasing layer number remains an unresolved question. Here, we show the observation of layer-dependent electronic structures and correlations, under surprising liquid nitrogen temperature, in RG multilayers from 3 to 9 layers by using scanning tunneling microscopy and spectroscopy. We explicitly determine layer-enhanced low-energy flat bands and interlayer coupling strengths. The former directly demonstrates the further flattening of low-energy bands in thicker RG, and the latter indicates the presence of varying interlayer interactions in RG multilayers. Moreover, we find significant splittings of the flat bands, ranging from ~50-80 meV, at 77 K when they are partially filled, indicating the emergence of interaction-induced strongly correlated states. Particularly, the strength of the correlated states is notably enhanced in thicker RG and reaches its maximum in the six-layer, validating directly theoretical predictions and establishing abundant new candidates for strongly correlated systems. Our results provide valuable insights into the layer dependence of the electronic properties in RG and demonstrate it as a suitable system for investigating robust and highly accessible correlated phases.

Stability of anomalous Hall crystals in multilayer rhombohedral graphene

Authors: Zhihuan Dong, Adarsh S. Patri, and T. Senthil

Published: 2024-11-14T10:00:00+00:00

Author(s): Zhihuan Dong, Adarsh S. Patri, and T. Senthil

Amidst recent burning interest in quantum anomalous Hall phenomena in pentalayer graphene, the authors provide here an elegant understanding for existing numerical mean field results. Beyond mean field, the authors propose the picture of “moiré-enabled Hall crystals”, emphasizing the crucial role of a moiré potential even when weak. The authors provide a connection between electronic crystals and the superconducting Little-Parks effect to explicitly demonstrate the quantization of Chern number associated with spontaneous crystalline order, analogous to quantization of vorticity in a superconducting ring under a background magnetic field.

[Phys. Rev. B 110, 205130] Published Thu Nov 14, 2024

Entropy-Enhanced Fractional Quantum Anomalous Hall Effect

Authors: Gal Shavit

Published: Mon, 18 Nov 2024 00:00:00 -0500

arXiv:2409.02997v2 Announce Type: replace Abstract: Strongly interacting electrons in a topologically non trivial band may form exotic phases of matter. An especially intriguing example of which is the fractional quantum anomalous Hall phase, recently discovered in twisted transition metal dichalcogenides and in moir\'e graphene multilayers. However, it has been shown to be destabilized in certain filling factors at sub-100 mK temperatures in pentalayer graphene, in favor of a novel integer quantum anomalous Hall phase [Z. Lu et al., arXiv:2408.10203 ]. We propose that the culprit stabilizing the fractional phase at higher temperatures is its rich edge state structure. Possessing a multiplicity of chiral modes on its edge, the fractional phase has lower free energy at higher temperatures due to the excess edge modes entropy. We make distinct predictions under this scenario, including the system-size dependency of the fractional phase entropic enhancement, and how the phase boundaries change as a function of temperature.

Visualizing incommensurate inter-valley coherent states in rhombohedral trilayer graphene

Authors: Yiwen Liu, Ambikesh Gupta, Youngjoon Choi, Yaar Vituri, Hari Stoyanov, Jiewen Xiao, Yanzhen Wang, Haibiao Zhou, Barun Barick, Takashi Taniguchi, Kenji Watanabe, Binghai Yan, Erez Berg, Andrea F. Young, Haim Beidenkopf, Nurit Avraham

Published: Tue, 19 Nov 2024 00:00:00 -0500

arXiv:2411.11163v1 Announce Type: new Abstract: ABC-stacked rhombohedral graphene multilayers exhibit a wide variety of electronic ground states characterized by broken isospin symmetry and superconductivity. Recently, indirect evidence of inter-valley coherent (IVC) order has been reported in rhombohedral trilayer graphene (RTG), with possible implications for the origin of superconductivity. Here, we report the direct visualization of IVC order in RTG using scanning tunneling microscopy and spectroscopy. Tuning the chemical potential through the Van Hove singularity near the edge of the valence band, we observe a cascade of phase transitions associated with the formation of half- and quarter-metal states. IVC phases, distinguished by an enlarged real space unit cell, are directly imaged near both the high- and low-density boundaries of the half-metal phase. At high hole density, we precisely reconstruct the IVC band structure through quasiparticle interference. Intriguingly, the charge density modulations reveal a C3-symmetric incommensurate IVC order that agrees with the recent prediction of an IVC-crystal phase. Our findings demonstrate that IVC phases are a widespread symmetry-broken ground state within graphene systems.

Thickness-dependent Topological Phases and Flat Bands in Rhombohedral Multilayer Graphene

Authors: H. B. Xiao, C. Chen, X. Sui, S. H. Zhang, M. Z. Sun, H. Gao, Q. Jiang, Q. Li, L. X. Yang, M. Ye, F. Y. Zhu, M. X. Wang, J. P. Liu, Z. B. Zhang, Z. J. Wang, Y. L. Chen, K. H. Liu, Z. K. Liu

Published: Tue, 19 Nov 2024 00:00:00 -0500

arXiv:2411.11359v1 Announce Type: new Abstract: Rhombohedral multilayer graphene has emerged as an extraordinary platform for investigating exotic quantum states, such as superconductivity and fractional quantum anomalous Hall effects, mainly due to the existence of topological surface flatbands. Despite extensive research efforts, a systematic spectroscopic investigation on the evolution of its electronic structure from thin layers to bulk remains elusive. Using state-of-the-art angle-resolved photoemission spectroscopy with submicron spatial resolution, we directly probe and trace the thickness evolution of the topological electronic structures of rhombohedral multilayer graphene. As the layer number increases, the gapped subbands transform into the 3D Dirac nodes that spirals in the momentum space; while the flatbands are constantly observed around Fermi level, and eventually evolve into the topological drumhead surface states. This unique thickness-dependent topological phase transition can be well captured by the 3D generalization of 1D Su-Schrieffer-Heeger chain in thin layers, to the topological Dirac nodal spiral semimetal in the bulk limit. Our findings establish a solid foundation for exploring the exotic quantum phases with nontrivial topology and correlation effects in rhombohedral multilayer graphene.

Spontaneous spin superconductor state in ABCA-stacked tetralayer graphene

Authors: Shuai Li, Yuan-Hang Ren, Ao-Long Li, and Hua Jiang

Published: 2024-11-18T10:00:00+00:00

Author(s): Shuai Li, Yuan-Hang Ren, Ao-Long Li, and Hua Jiang

We theoretically demonstrate a spontaneous spin superconductor (SC) state in ABCA-stacked tetralayer graphene, under sequential effects of electron-electron (e-e) and electron-hole (e-h) interactions. First of all, we examine the ferromagnetic (FM) exchange instability and phase diagram of the syste…

[Phys. Rev. B 110, 174512] Published Mon Nov 18, 2024

Promoting and imaging intervalley coherent order in rhombohedral tetralayer graphene on MoS2

Authors: Wei-Yu Liao, Wen-Xiao Wang, Shihao Zhang, Yang Zhang, Ling-Hui Tong, Wenjia Zhang, Hao Cai, Yuan Tian, Yuanyuan Hu, Li Zhang, Lijie Zhang, Zhihui Qin, Long-Jing Yin

Published: Fri, 22 Nov 2024 00:00:00 -0500

arXiv:2411.14113v1 Announce Type: new Abstract: Multilayer rhombohedral graphene (RG) has recently emerged as a new, structurally simple flat-band system, which facilitates the exploration of interaction-driven correlation states with highly ordered electron arrangements. Despite a variety of many-body order behaviors observed in RG by transport measurements, the direct microscopic visualization of such correlated phases in real space is still lacking. Here, we show the discovery of a robust intervalley coherent order, a long-predicted ground state in RG, at 77 K in tetralayer RG placed on MoS2 via imaging atomic-scale spatial reconstruction of wave functions for correlated states. By using scanning tunnelling microscopy, we observe spectroscopic signatures of electronic correlations at partially filled flat bands, where distinct splitting appears. At ~60% and ~70% fillings of the flat bands, we visualize atomic-scale reconstruction patterns with a 3 x 3 supercell on graphene lattice at liquid nitrogen temperature, which indicates a robust intervalley coherent phase of the interacting electrons. The 3 x 3 pattern is observed in MoS2-supported RG, while it is absent in hBN-based ones under the same experimental conditions, suggesting the significant influence of spin-orbit proximity effect. Our results provide microscopic insights into the correlated phases in tetralayer RG and highlight the significant potential for realizing highly accessible collective phenomena through Van der Waals proximity.

Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene

Authors: Ammon Fischer, Lennart Klebl, Dante M. Kennes, and Tim O. Wehling

Published: 2024-11-22T10:00:00+00:00

Author(s): Ammon Fischer, Lennart Klebl, Dante M. Kennes, and Tim O. Wehling

The authors derive here a minimal low-energy model for Bernal bilayer graphene and related rhombohedral graphene multilayers at low electronic densities. They construct valley-polarized Wannier orbitals defined in real-space supercells of the original primitive cell. By projecting realistic Coulomb interactions to the supercell Wannier basis, the authors demonstrate that Bernal bilayer graphene is in the weakly coupled regime. The resulting low-energy lattice models for rhombohedral graphene stacks pave the way for unbiased characterization of many-body phases in multilayer graphene.

[Phys. Rev. B 110, L201113] Published Fri Nov 22, 2024

Interplay between topology and correlations in the second moir\'e band of twisted bilayer MoTe2

Authors: Fan Xu, Xumin Chang, Jiayong Xiao, Yixin Zhang, Feng Liu, Zheng Sun, Ning Mao, Nikolai Peshcherenko, Jiayi Li, Kenji Watanabe, Takashi Taniguchi, Bingbing Tong, Li Lu, Jinfeng Jia, Dong Qian, Zhiwen Shi, Yang Zhang, Xiaoxue Liu, Shengwei Jiang, Tingxin Li

Published: Wed, 04 Dec 2024 00:00:00 -0500

arXiv:2406.09687v2 Announce Type: replace Abstract: Topological flat bands formed in two-dimensional lattice systems offer unique opportunity to study the fractional phases of matter in the absence of an external magnetic field. Celebrated examples include fractional quantum anomalous Hall (FQAH) effects and fractional topological insulators. Recently, FQAH effects have been experimentally realized in both the twisted bilayer MoTe2 (tMoTe2) system and the rhombohedral stacked multilayer graphene/hBN moir\'e systems. To date, experimental studies mainly focus on the first moir\'e flat band, except a very recent work that studied novel transport properties in higher moir\'e bands of a 2.1{\deg} tMoTe2 device. Here, we present the systematical transport study of approximately 3{\deg} tMoTe2 devices, especially for the second moir\'e band. At {\nu} = -2 and -4, time-reversal-symmetric single and double quantum spin Hall states formed, consistent with the previous observation in 2.1{\deg} tMoTe2 device. On the other hand, we observed ferromagnetism in the second moir\'e band, and a Chern insulator state driven by out-of-plane magnetic fields at {\nu} = -3. At {\nu} = -2.2 to -2.7, finite temperature resistivity minimum with 1/T scaling at low temperatures, and large out-of-plane negative magnetoresistance have been observed. Applying out-of-plane electric field can induce quantum phase transitions at both integer and fractional filling factors. Our studies pave the way for realizing tunable topological states and other unexpected magnetic phases beyond the first moir\'e flat band based on twisted MoTe2 platform.

Competing magnetic states on the surface of multilayer ABC-stacked graphene

Authors: Lauro B. Braz, Tanay Nag, and Annica M. Black-Schaffer

Published: 2024-12-03T10:00:00+00:00

Author(s): Lauro B. Braz, Tanay Nag, and Annica M. Black-Schaffer

The discovery of novel magnetic phases on the surface of rhombohedral graphene multilayers presents exciting potential for novel physics. Here, the authors demonstrate that the topological surface states of ABC-stacked graphite host competing magnetic states arising from intravalley and intervalley electron scattering. Electron-electron interactions generate incommensurate magnetic states with notably long spin-spin relaxation times at charge neutrality. These findings suggest that rhombohedral graphite likely hosts a plethora of different magnetic states.

[Phys. Rev. B 110, L241401] Published Tue Dec 03, 2024

Berry Phase Dynamics of Sliding Electron Crystals

Authors: Yongxin Zeng, Andrew J. Millis

Published: Thu, 05 Dec 2024 00:00:00 -0500

arXiv:2412.03399v1 Announce Type: new Abstract: Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a non-vanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system's nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean non-invariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

Spontaneous emergence of straintronics effects and striped stacking domains in untwisted three-layer epitaxial graphene

Authors: Martin RejhonNitika ParasharLorenzo SchellackMykhailo ShestopalovJan KuncElisa RiedoaTandon School of Engineering, Chemical and Biomolecular Engineering, New York University, Brooklyn, NY 11201bFaculty of Mathematics and Physics, Institute of Physics, Charles University, Prague 2 CZ-121 16, Czech Republic

Published: 2024-12-04T08:00:00Z

Proceedings of the National Academy of Sciences, Volume 121, Issue 50, December 2024.
SignificanceThe self-organized emergence of ABA and ABC stacking domains in a three-layer epitaxial graphene system grown on SiC is observed using conductive AFM. These domains self-assemble without the need of expert mechanical twisting and alignment, as ...

Ideal Chern bands with strong short-range repulsion: Applications to correlated metals, superconductivity, and topological order

Authors: Patrick H. Wilhelm, Andreas M. Läuchli, and Mathias S. Scheurer

Published: 2024-12-05T10:00:00+00:00

Author(s): Patrick H. Wilhelm, Andreas M. Läuchli, and Mathias S. Scheurer

Motivated by recent experiments on correlated van der Waals materials, including twisted and rhombohedral graphene and twisted ${\mathrm{WSe}}_{2}$, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We…

[Phys. Rev. Research 6, 043240] Published Thu Dec 05, 2024

Extended quantum anomalous Hall effect in moiré structures: Phase transitions and transport

Authors: Adarsh S. Patri, Zhihuan Dong, and T. Senthil

Published: 2024-12-06T10:00:00+00:00

Author(s): Adarsh S. Patri, Zhihuan Dong, and T. Senthil

Recent experiments on multilayer rhombohedral graphene have unearthed a number of interesting phenomena in the regime where integer and fractional quantum anomalous Hall phenomena were previously reported. Specifically, at low temperature ($T$) and low applied currents, an “extended” integer quantum…

[Phys. Rev. B 110, 245115] Published Fri Dec 06, 2024

Real-space study of zero-field correlation in tetralayer rhombohedral graphene

Authors: Yufeng Liu, Zonglin Li, Shudan Jiang, Min Li, Yu Gu, Kai Liu, Qia Shen, Liang Liu, Xiaoxue Liu, Dandan Guan, Yaoyi Li, Hao Zheng, Canhua Liu, Kenji Watanabe, Takashi Taniguchi, Jinfeng Jia, Tingxin Li, Guorui Chen, Jianpeng Liu, Can Li, Zhiwen Shi, Shiyong Wang

Published: Tue, 10 Dec 2024 00:00:00 -0500

arXiv:2412.06476v1 Announce Type: new Abstract: Rhombohedral graphene (RG) has emerged as a promising platform for exploring exotic quantum phenomena, such as quantum magnetism, unconventional superconductivity, and fractional quantum anomalous Hall effects. Despite its potential, atomic-scale investigations of RG remain limited, hindering a detailed microscopic understanding of the origins of these correlated states. In this study, we employ scanning probe microscopy and spectroscopy to probe the intrinsic electronic states in trilayer and tetralayer RG. We identify a correlated insulating state with a 17 meV gap at the charge neutrality point in tetralayer RG, which is absent in the trilayer configuration. This gap is suppressed by applying a perpendicular magnetic field or doping the charge carrier density and does not exhibit inter-valley coherence patterns. We attribute this phenomenon to a symmetry-broken layer antiferromagnetic state, characterized by ferrimagnetic ordering in the outermost layers and antiferromagnetic coupling between them. To further investigate this magnetic correlated state, we conduct local scattering experiments. Within the correlated regime, a bound state emerges around a non-magnetic impurity but is absent near magnetic impurities, suggesting that non-magnetic doping induces a spin texture in the ferrimagnetic surface layers. Outside the correlated regime, Friedel oscillations are observed, allowing precise determination of the band dispersion in tetralayer RG. These findings provide atomic-scale evidences of zero-field correlations in RG and may be extended to study other exotic phases in RG.

Electronic properties of stacking faults in Bernal graphite

Authors: Patrick Johansen Sarsfield, Sergey Slizovskiy, Mikito Koshino, Vladimir Fal'ko

Published: Tue, 10 Dec 2024 00:00:00 -0500

arXiv:2412.06665v1 Announce Type: new Abstract: Using the tight-binding model of graphite, incorporating all Slonczewski-Weiss-McClure parameters, we compute the spectrum of two-dimensional states of electrons bound to a stacking fault in Bernal graphite. We find that those bands retain characteristic features of the low-energy bands of a rhombohedral graphene trilayer, which actually represents the lattice structure the fault. Based on the self-consistent analysis of charge and potential distribution across the fault layers, we determine the shape of the Fermi contour for the 2D band, which has the form of three pockets with a hole-like conic dispersion and Dirac points above the Fermi level. The computed frequency of Shubnikov-de Haas oscillations and the cyclotron mass of the fault-bound charge carriers (at the Fermi level) are sufficiently different from the corresponding bulk values in graphite, making such stacking faults identifiable by quantum transport and cyclotron resonance measurements.

Competing magnetic states on the surface of multilayer ABC-stacked graphene

Authors: Lauro B. Braz, Tanay Nag, Annica M. Black-Schaffer

Published: Tue, 10 Dec 2024 00:00:00 -0500

arXiv:2401.16345v2 Announce Type: replace Abstract: We study interaction-mediated magnetism on the surface of ABC-multilayer graphene driven by its zero-energy topological flat bands. Using the random-phase approximation we treat onsite Hubbard repulsion and find multiple competing magnetic states, due to both intra- and inter-valley scattering, with the latter causing an enlarged magnetic unit cell. At half-filling and when the Hubbard repulsion is weak, we observe two different ferromagnetic orders. Once the Hubbard repulsion becomes more realistic, new ferrimagnetic orders arise with distinct incommensurate intra- or inter-valley scattering vectors depending on interaction strength and doping, leading to a multitude of competing magnetic states.

Evolution of topological Dirac-line semimetal phases in a three-dimensional acoustic rhombohedral graphite

Authors: Hua-Shan Lai, Cheng He, and Yan-Feng Chen

Published: 2024-12-09T10:00:00+00:00

Author(s): Hua-Shan Lai, Cheng He, and Yan-Feng Chen

Rhombohedral graphite (RG), composed of ABC-stacked graphene layers, is a typical topological semimetal that hosts intricate configurations of Dirac lines (nodal lines), predominantly influenced by interlayer hopping. However, the fabrication of stable RG with strong interlayer coupling remains chal…

[Phys. Rev. B 110, 224104] Published Mon Dec 09, 2024

Chiral finite-momentum superconductivity in the tetralayer graphene

Authors: Qiong Qin, Congjun Wu

Published: Wed, 11 Dec 2024 00:00:00 -0500

arXiv:2412.07145v1 Announce Type: new Abstract: Motivated by the recent discovery of superconductivity in tetralayer graphene, we investigate the pairing mechanism arising from density-density interactions within the random phase approximation. This approach successfully highlights the dominance of chiral $p$-wave pairing between electrons with the same spin and valley at low electron densities, while also predicting the superconducting range in agreement with experimental findings. Furthermore, we examine the characteristics of distinct superconducting regions: SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations, whereas SC4 displays nematic zero-momentum superconductivity, with its transition temperature constrained by the pairing strength. Additionally, we delve into the exotic features of chiral finite-momentum superconductivity, underscoring its potential significance for realizing a charge-4e exotic metal with time-reversal symmetry.

Relativistic Mott transition in strongly correlated artificial graphene

Authors: Liguo Ma, Raghav Chaturvedi, Phuong X. Nguyen, Kenji Watanabe, Takashi Taniguchi, Kin Fai Mak, Jie Shan

Published: Wed, 11 Dec 2024 00:00:00 -0500

arXiv:2412.07150v1 Announce Type: new Abstract: The realization of graphene has provided a bench-top laboratory for quantum electrodynamics. The low-energy excitations of graphene are two-dimensional massless Dirac fermions with opposite chiralities at the $\pm$K valleys of the graphene Brillouin zone. It has been speculated that the electron-electron interactions in graphene could spontaneously break the chiral symmetry to induce a finite mass for Dirac fermions, in analogue to dynamical mass generation in elementary particles. The phenomenon is also known as the relativistic Mott transition and has not been observed in pristine graphene because the interaction strength is insufficient. Here, we report the realization of strongly correlated artificial graphene and the observation of the relativistic Mott transition in twisted WSe2 tetralayers. Using magneto transport, we show that the first $\Gamma$-valley moir\'e valence band mimics the low-energy graphene band structure. At half-band filling, the system exhibits hallmarks of massless Dirac fermions, including an anomalous Landau fan originated from a $\pi$-Berry phase and a square-root density dependence of the cyclotron mass. We tune the interaction across the semimetal-insulator transition by reducing the twist angle below about 2.7 degrees. The emergent insulator is compatible with an antiferromagnetic Mott insulator. Our results open the possibility of studying strongly correlated Dirac fermions in a condensed matter system.

Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors

Authors: Benjamin A. Levitan, Yuval Oreg, Erez Berg, Mark Rudner, Ivan Iorsh

Published: Wed, 11 Dec 2024 00:00:00 -0500

arXiv:2406.08706v3 Announce Type: replace Abstract: We consider optical response in multi-band, multi-layer two-dimensional superconductors. Within a simple model, we show that linear response to AC gating can detect collective modes of the condensate, such as Leggett and clapping modes. We show how trigonal warping of the superconducting order parameter can help facilitate detection of clapping modes. Taking rhombohedral trilayer graphene as an example, we consider several possible pairing mechanisms and show that all-electronic mechanisms may produce in-gap clapping modes. These modes, if present, should be detectable in the absorption of microwaves applied via the gate electrodes, which are necessary to enable superconductivity in this and many other settings; their detection would constitute strong evidence for unconventional pairing. Last, we show that absorption at frequencies above the superconducting gap $2 |\Delta|$ also contains a wealth of information about the gap structure. Our results suggest that linear spectroscopy can be a powerful tool for the characterization of unconventional two-dimensional superconductors.

Quantum geometry and nonlinear optical responses in rhombohedral trilayer graphene

Authors: Abigail Postlewaite, Arpit Raj, Swati Chaudhary, and Gregory A. Fiete

Published: 2024-12-10T10:00:00+00:00

Author(s): Abigail Postlewaite, Arpit Raj, Swati Chaudhary, and Gregory A. Fiete

Multilayered graphene systems provide a highly tunable platform to study quantum geometric effects. Here, the authors show that the quantum geometry of electronic bands in rhombohedral trilayer graphene leads to a large shift-current response which can be tuned by applying a displacement field perpendicular to the layers. The authors compare the response with Bernal stacked bilayer graphene and find additional features arising due to the confluence of quantum geometry and the multiband nature of rhombohedral trilayer graphene.

[Phys. Rev. B 110, 245122] Published Tue Dec 10, 2024

Switchable Chern insulator, isospin competitions and charge density waves in rhombohedral graphene moire superlattices

Authors: Jian Zheng, Size Wu, Kai Liu, Bosai Lyu, Shuhan Liu, Yating Sha, Zhengxian Li, Kenji Watanabe, Takashi Taniguchi, Jinfeng Jia, Zhiwen Shi, Guorui Chen

Published: Mon, 16 Dec 2024 00:00:00 -0500

arXiv:2412.09985v1 Announce Type: new Abstract: Graphene-based moire superlattices provide a versatile platform for exploring novel correlated and topological electronic states, driven by enhanced Coulomb interactions within flat bands. The intrinsic tunability of graphene s multiple degrees of freedom enables precise control over these complex quantum phases. In this study, we observe a range of competing phases and their transitions in rhombohedrally stacked hexalayer graphene on hexagonal boron nitride (r-6G/hBN) moire superlattices. When electrons are polarized away from the moire superlattice, we firstly identify a Chern insulator with reversible Chern numbers at v = 1 (one electron per moire cell), attributed to the competition between bulk and edge magnetizations.Then, we detect transitions between three distinct insulating states at v = 2, driven by vertical displacement field D and vertical magnetic field B. These insulating phases are distinguished as spin-antiferromagnetic, spin-polarized, and valley-polarized insulators, based on their responses to parallel and perpendicular magnetic fields. When electrons are polarized toward the moire superlattice, in a device with large twist angle, insulating states appear at v = 1/3 and 2/3 at zero magnetic field, and v = 1/2 in a magnetic field. Our findings reveal a rich interplay of charge, isospin, topology and magnetic field in rhombohedral graphene moire superlattices.

Increasing flatness of surface bands of multilayer rhombohedral graphite with crystal thickness

Authors: E. J. Seifert, Erin Akyuz, Randall M. Feenstra, and Benjamin M. Hunt

Published: 2024-12-17T10:00:00+00:00

Author(s): E. J. Seifert, Erin Akyuz, Randall M. Feenstra, and Benjamin M. Hunt

Flat bands, where Coulomb repulsion dwarfs bandwidth, hold the potential to realize many correlated electron states in a material. Rhombohedral graphite (RG) hosts an intrinsic flat band near the Fermi level localized on its top and bottom surfaces, in which the density of states is predicted to inc…

[Phys. Rev. B 110, L241407] Published Tue Dec 17, 2024

Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices

Authors: Koji Kudo, Ryota Nakai, and Kentaro Nomura

Published: 2024-12-23T10:00:00+00:00

Author(s): Koji Kudo, Ryota Nakai, and Kentaro Nomura

Recent experiments on pentalayer rhombohedral graphene moiré superlattices have observed the quantum anomalous Hall effect at a moiré filling factor of $ν=1$ and various fractional values. These phenomena are attributed to a flat Chern band induced by electron-electron interactions. In this study, w…

[Phys. Rev. B 110, 245135] Published Mon Dec 23, 2024

Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions

Authors: Changpeng Lin, Samuel Ponc\'e, Francesco Macheda, Francesco Mauri, Nicola Marzari

Published: Wed, 25 Dec 2024 00:00:00 -0500

arXiv:2412.18482v1 Announce Type: new Abstract: Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending rigidity tensors of crystalline solids, leveraging interatomic force constants and long-wavelength perturbation theory. Crucially, in the long-wavelength limit, lattice vibrations induce macroscopic electric fields which further couple with the propagation of elastic waves, and a separate treatment on the long-range electrostatic interactions is thereby required to obtain elastic properties under the appropriate electrical boundary conditions. A cluster expansion of the charge density response and dielectric screening function in the long-wavelength limit has been developed to efficiently extract multipole and dielectric tensors of arbitrarily high order. We implement the proposed method in a first-principles framework and perform extensive validations on silicon, NaCl, GaAs and rhombohedral BaTiO$_3$ as well as monolayer graphene, hexagonal BN, MoS$_2$ and InSe, obtaining good to excellent agreement with other theoretical approaches and experimental measurements. Notably, we establish that multipolar interactions up to at least octupoles are necessary to obtain the accurate short-circuit elastic tensor of bulk materials, while higher orders beyond octupole interactions are required to converge the bending rigidity tensor of 2D crystals. The present approach greatly simplifies the calculations of bending rigidities and will enable the automated characterization of the mechanical properties of novel functional materials.

Substrate, temperature, and magnetic field dependence of electric polarization in mixed-stacking tetralayer graphenes

Authors: Patrick Johansen Sarsfield, Aitor Garcia-Ruiz (艾飛宇), and Vladimir I. Fal'ko

Published: 2024-12-27T10:00:00+00:00

Author(s): Patrick Johansen Sarsfield, Aitor Garcia-Ruiz (艾飛宇), and Vladimir I. Fal'ko

Polytypes of tetralayer graphene (TLG: Bernal, rhombohedral, and mixed stacking) are crystalline structures with different symmetries. Among those, mixed-stacking tetralayers lack inversion symmetry, which allows for intrinsic spontaneous out-of-plane electrical polarization, inverted in the mirror-…

[Phys. Rev. Research 6, 043324] Published Fri Dec 27, 2024

Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moir\'e superlattices

Authors: Koji Kudo, Ryota Nakai, Kentaro Nomura

Published: Mon, 30 Dec 2024 00:00:00 -0500

arXiv:2406.14354v2 Announce Type: replace Abstract: Recent experiments on pentalayer rhombohedral graphene moir\'e superlattices have observed the quantum anomalous Hall effect at moir\'e filling factor of $\nu = 1$ and various fractional values. These phenomena are attributed to a flat Chern band induced by electron-electron interactions. In this study, we demonstrate that at $\nu = 2$, many-body effects can lead to the emergence of quantum spin Hall and quantum valley Hall states, in addition to the quantum anomalous Hall state, even in the absence of spin-orbit coupling or valley-dependent potentials. These three topological states can be selectively induced by the application and manipulation of a magnetic field. Furthermore, we show that at $\nu = 3$ and $4$, the ground state can be a combination of topologically trivial and nontrivial states, unlike the cases of $\nu=1$ and 2. This contrasts with the conventional quantum Hall effect in graphene where the ground state at filling factor $\nu$ is given as the particle-hole counterpart at $4-\nu$.

Dissipation-enhanced non-reciprocal superconductivity: application to multi-valley superconductors

Authors: Sayan Banerjee, Mathias S. Scheurer

Published: Mon, 06 Jan 2025 00:00:00 -0500

arXiv:2501.01501v1 Announce Type: new Abstract: We here propose and study theoretically a non-equilibrium mechanism for the superconducting diode effect, which applies specifically to the case where time-reversal-symmetry -- a prerequisite for the diode effect -- is spontaneously broken by the superconducting electrons themselves. We employ a generalized time-dependent Ginzburg-Landau formalism to capture dissipation effects in the non-equilibrium current-carrying state via phase slips and show that the coupling of the resistive current to the symmetry-breaking order is enough to induce a diode effect. Depending on parameters, the critical current asymmetry can be sizeable, asymptotically reaching a perfect diode efficiency; the competition of symmetry-breaking order, superconducting and resistive currents gives rise to rich physics, such as current-stabilized, non-equilibrium superconducting correlations. Although our mechanism is more general, the findings are particularly relevant to twisted trilayer and rhombohedral tetralayer graphene, where the symmetry-breaking order parameter refers to the imbalance of the two valleys of the systems.

Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers

Authors: Zezhu Wei, Ang-Kun Wu, Miguel Gonçalves, and Shi-Zeng Lin

Published: 2025-01-08T10:00:00+00:00

Author(s): Zezhu Wei, Ang-Kun Wu, Miguel Gonçalves, and Shi-Zeng Lin

Puzzling transitions between an extended quantum anomalous Hall (EQAH) crystal and fractional Chern insulators (FCI) were recently observed in pentalayer graphene. This work proposes a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases. The edge velocity in FCI is smaller than that in EQAHE and can be reduced by current, both contributing to a higher entropy. Therefore, the edge entropy can drive the transition from EQAH to FCI either by temperature or current.

[Phys. Rev. B 111, 035116] Published Wed Jan 08, 2025

Switching Graphitic Polytypes in Elastically Coupled Islands

Authors: Nirmal Roy, Simon Salleh Atri, Yoav Sharaby, Noam Raab, Youngki Yeo, Watanabe Kenji, Takashi Taniguchi, Moshe Ben Shalom

Published: Tue, 14 Jan 2025 00:00:00 -0500

arXiv:2501.06817v1 Announce Type: new Abstract: Van der Waals polytypes are commensurate configurations of two-dimensional layers with discrete crystalline symmetries and distinct stacking-dependent properties. In graphitic polytypes, the different stacking arrangements of graphene sheets exhibit rich electronic phases, such as intrinsic electric polarizations, orbital magnetizations, superconductivity, and anomalous fractional Hall states. Switching between these metastable periodic configurations by controlling interlayer shifts unlocks intriguing multiferroic responses. Here, we report super-lubricant arrays of polytypes (SLAP) devices, with nanometer-scale islands of Bernal polytypes that switch into Rhombohedral crystals and vice versa under a shear force as low as 6 nano-Newtons. We assemble these four-layer SLAP structures by aligning a pair of graphene bilayers above and under circular cavities in a misaligned spacer layer. Using local current measurements, we detect the shifts between the active bilayers and reveal long-range elastic relaxations outside the cavities that enable efficient nucleation and spontaneous sliding of stacking dislocation inside the islands. We demonstrate configurable, deterministic, and robust polytype switching by confining these boundary strips in narrow cavity channels that connect the islands. Such controlled switching between elastically-coupled single-crystalline islands is appealing for novel multiferroic SlideTronic applications.

Correlation stabilized anomalous Hall crystal in bilayer graphene

Authors: Zhongqing Guo, Jianpeng Liu

Published: Tue, 14 Jan 2025 00:00:00 -0500

arXiv:2409.14658v3 Announce Type: replace Abstract: When the charge density is sufficiently low, interacting two-dimensional electron gas (2DEG) would undergo a phase transition from homogeneous Fermi liquid to an electronic crystal state, known as Wigner crystal. Besides conventional 2DEG, various topological fermionic excitations may also be realized in 2D materials. For example, ``high-order" Dirac fermions exhibiting nontrivial Berry phases may approximately characterize the low-energy excitations in rhombohedral multilayer graphene (RMG). In this work, we develop a beyond-mean-field theoretical framework to study the interacting ground states and single-particle excitations in slightly charge-doped RMG under vertical electric field. We find that transitions from Fermi liquid to trivial Wigner-crystal states would occur at critical carrier density $\sim 10^{10}\,\textrm{cm}^{-2}$ for all $n$-layer RMG (with $n=2, 3, 4, 5, 6$) which are approximately described by $n$-order Dirac-fermion models. Most saliently, using a more realistic modeling of bilayer graphene including trigonal warping effects, we find that an anomalous Hall crystal state with spontaneous quantized anomalous Hall conductivity would emerge when the carrier density is below $\sim 1\times 10^{11}\,\text{cm}^{-2}$, and it becomes the unique ground state over trivial Wigner crystal when the density is further lower. Counter intuitively, such topological anomalous Hall crystal becomes more stable than the trivial Wigner crystal due to the lower correlation energy gained from dynamical charge fluctuations, which is beyond mean-field description. Our work suggests that slightly carrier-doped bilayer graphene is one of the most promising candidates to realize anomalous Hall crystal. Moreover, the method developed in this work can be readily applied to other interacting 2D systems including moir\'e superlattices.

Fluctuating magnetism and Pomeranchuk effect in multilayer graphene

Authors: Ludwig Holleis, Tian Xie, Siyuan Xu, Haoxin Zhou, Caitlin L. Patterson, Archisman Panigrahi, Takashi Taniguchi, Kenji Watanabe, Leonid S. Levitov, Chenhao Jin, Erez Berg, Andrea F. Young

Published: Thu, 16 Jan 2025 00:00:00 -0500

arXiv:2407.13763v2 Announce Type: replace Abstract: Magnetism typically arises from the effect of exchange interactions on highly localized fermionic wave functions in f- and d-atomic orbitals. In rhombohedral multilayer graphene (RMG), in contrast, magnetism-manifesting as spontaneous polarization into one or more spin and valley flavors[1-7]-originates from itinerant electrons near a Van Hove singularity. Here, we show experimentally that the electronic entropy in this system shows signatures typically associated with disordered local magnetic moments, unexpected for electrons in a fully itinerant metal. Specifically, we find a contribution $\Delta$ S $\approx$ 1k$_B$/charge carrier that onsets at the Curie temperature and survives over one order of magnitude in temperature. First order phase transitions show an isospin `Pomeranchuk effect' in which the fluctuating moment phase is entropically favored over the nearby symmetric Fermi liquid[8, 9]. Our results imply that despite the itinerant nature of the electron wave functions, the spin- and valley polarization of individual electrons are decoupled, a phenomenon typically associated with localized moments, as happens, for example, in solid 3He[10]. Transport measurements, surprisingly, show a finite temperature resistance minimum within the fluctuating moment regime, which we attribute to the interplay of fluctuating magnetic moments and electron phonon scattering. Our results highlight the universality of soft isospin modes to two-dimensional flat band systems.

Extended quantum anomalous Hall states in graphene/hBN moiré superlattices

Authors: Zhengguang Lu, Tonghang Han, Yuxuan Yao, Zach Hadjri, Jixiang Yang, Junseok Seo, Lihan Shi, Shenyong Ye, Kenji Watanabe, Takashi Taniguchi, Long Ju

Published: 2025-01-22

Nature, Published online: 22 January 2025; doi:10.1038/s41586-024-08470-1

New topological states have been observed in rhombohedral graphene/hBN moiré superlattices, including fractional and extended quantum anomalous Hall effects, at ultra-low temperatures, demonstrating the rich quantum phenomena emerging from correlated electrons in topological flat bands.

Electric-field switchable chirality in rhombohedral graphene Chern insulators stabilized by tungsten diselenide

Authors: Jing Ding, Hanxiao Xiang, Jiannan Hua, Wenqiang Zhou, Naitian Liu, Le Zhang, Na Xin, Bing Wu, Kenji Watanabe, Takashi Taniguchi, Zdenek Sofer, Wei Zhu, Shuigang Xu

Published: Mon, 27 Jan 2025 00:00:00 -0500

arXiv:2406.14289v2 Announce Type: replace Abstract: Chern insulators host topologically protected chiral edge currents with quantized conductance characterized by their Chern number. Switching the chirality of a Chern insulator, namely, the direction of the edge current, is highly challenging due to topologically forbidden backscattering but is of considerable importance for the design of topological devices. Nevertheless, this can be achieved by reversing the sign of the Chern number through a topological phase transition. Here, we report electrically switchable chirality in rhombohedral multilayer graphene-based Chern insulators. By introducing moire superlattices in rhombohedral heptalayer graphene, we observed a cascade of topological phase transitions at quarter electron filling of a moire band with the Chern number tunable from -1, 1 to 2. Furthermore, integrating monolayer tungsten diselenide at the moireless interface of rhombohedral decalayer graphene/h-BN superlattices stabilizes the Chern insulators, enabling quantized anomalous Hall resistance of h/2e^2. Remarkably, the Chern number can be switched from -1 to 2 using displacement fields. Our work establishes rhombohedral multilayer graphene moire superlattices as a versatile platform for topological engineering, with switchable chirality offering significant promise for integrating chiral edge currents into topological electronic circuits.

Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene

Authors: Qiao-Chu Zhang and Jing Wang

Published: 2025-01-31T10:00:00+00:00

Author(s): Qiao-Chu Zhang and Jing Wang

The effects of short-range fermion-fermion interactions on the low-energy properties of rhombohedral trilayer graphene are comprehensively investigated using the momentum-shell renormalization group method. We take into account all one-loop corrections and establish the energy-dependent coupled evol…

[Phys. Rev. B 111, 014111] Published Fri Jan 31, 2025

Tunable Fractional Chern Insulators in Rhombohedral Graphene Superlattices

Authors: Jian Xie, Zihao Huo, Xin Lu, Zuo Feng, Zaizhe Zhang, Wenxuan Wang, Qiu Yang, Kenji Watanabe, Takashi Taniguchi, Kaihui Liu, Zhida Song, X. C. Xie, Jianpeng Liu, Xiaobo Lu

Published: Mon, 03 Feb 2025 00:00:00 -0500

arXiv:2405.16944v2 Announce Type: replace Abstract: Fractional Chern insulators (FCIs) showing a transport effect with fractionally quantized Hall plateaus emerging under zero magnetic field, provide a radically new opportunity to engineer topological quantum electronics. By construction of topological flat band with moire engineering, intrinsic FCIs have been observed in twisted MoTe2 system and rhombohedral pentalayer graphene/hBN moire superlattices with anomalous Hall resistivity quantization number C <= 2/3 including the gapless composite Fermi-liquid state with C = 1/2. Here, we experimentally demonstrate a new system of rhombohedral hexalayer graphene (RHG)/hBN moire superlattices, which exhibit both integer and fractional quantum anomalous Hall effects with rich tunability including electric displacement field, perpendicular magnetic field and in-plane magnetic field. By tuning the electrical and magnetic fields at 0 < v < 1, we have observed a quantum phase transition showing a sign reversal of the Hall resistivity at finite magnetic fields. Surprisingly, the FCI state at v = 2/3 survives in the phase transitions, exhibiting a robust quantized Hall resistivity across both phases. Finally we have further demonstrated the indispensable role moire potential plays in the formation of the flat Chern band from a theoretical perspective. Our work has established RHG/hBN moire superlattices as a promising platform for exploring quasi-particles with fractional charge and non-Abelian anyons at zero magnetic field.

Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers

Authors: Zezhu Wei, Ang-Kun Wu, Miguel Gon\c{c}alves, Shi-Zeng Lin

Published: Mon, 03 Feb 2025 00:00:00 -0500

arXiv:2409.05043v2 Announce Type: replace Abstract: Fractional Chern insulators (FCI) with fractionally quantized Hall conductance at fractional fillings and an extended quantum anomalous Hall (EQAH) crystal with an integer quantized Hall conductance over an extended region of doping were recently observed in pentalayer graphene. One particularly puzzling observation is the transition between the EQAH and FCI regimes, driven either by temperature or electrical current. Here we propose a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases and should be most relevant at temperature scales below the energy gap. Our consideration is based on the simple assumption that the edge velocity in FCI is smaller than that in EQAHE and thus contributes to a higher entropy. We further argue that domains with opposite fractionally quantized Hall conductance are ubiquitous in the devices due to disorder, which gives rise to a network of edge modes. The velocity of the edge modes between domains is further reduced due to edge reconstruction. The edge velocity can also be reduced by current when the occupation of the edge mode approaches the gap edge. The edge entropy therefore drives the transition from EQAH to FCI either by temperature or current at a nonzero temperature.

Impact of Spin-Orbit Coupling on Superconductivity in Rhombohedral Graphene

Authors: Jixiang Yang, Xiaoyan Shi, Shenyong Ye, Chiho Yoon, Zhengguang Lu, Vivek Kakani, Tonghang Han, Junseok Seo, Lihan Shi, Kenji Watanabe, Takashi Taniguchi, Fan Zhang, Long Ju

Published: Tue, 04 Feb 2025 00:00:00 -0500

arXiv:2408.09906v2 Announce Type: replace Abstract: Spin-orbit coupling (SOC) has played an important role in many topological and correlated electron materials. In graphene-based systems, SOC induced by transition metal dichalcogenide (TMD) at proximity was shown to drive topological states and strengthen superconductivity. However, in rhombohedral multilayer graphene, a robust platform for electron correlation and topology, superconductivity and the role of SOC remain largely unexplored. Here we report transport measurements of TMD-proximitized rhombohedral trilayer graphene (RTG). We observed a new hole-doped superconducting state SC4 with Tc = 230 mK. On the electron-doped side, we identified a new isospin-symmetry breaking three-quarter-metal (TQM) phase and observed the nearby weak superconducting state SC3 is significantly enhanced. Surprisingly, the original superconducting state SC1 in bare RTG is strongly suppressed in the presence of TMD - opposite to the effect of SOC on all other graphene superconductivities. Our observations form the basis of exploring superconductivity and non-Abelian quasiparticles in rhombohedral graphene devices.

Incommensurate intervalley coherent states in ABC graphene: Collective modes and superconductivity

Authors: Yaar Vituri, Jiewen Xiao, Keshav Pareek, Tobias Holder, and Erez Berg

Published: 2025-02-03T10:00:00+00:00

Author(s): Yaar Vituri, Jiewen Xiao, Keshav Pareek, Tobias Holder, and Erez Berg

Here, the authors identify incommensurate intervalley fluctuations between concentric hole and electron pockets as the primary particle-hole instability in hole-doped $ABC$-graphene’s half-metallic state. At intermediate densities, these fluctuations lead to a low-temperature superconducting instability with a sign-changing $s$-wave order parameter as revealed through a generalized RPA analysis. Closer to charge neutrality, the system develops finite-momentum intervalley coherent order, followed by a transition to a valley polarized state.

[Phys. Rev. B 111, 075103] Published Mon Feb 03, 2025

Electron correlation strengthened in multilayer rhombohedral graphite

Authors: Péter Nemes-Incze

Published: 2025-02-10

Nature Nanotechnology, Published online: 10 February 2025; doi:10.1038/s41565-024-01839-3

Two decades after the exfoliation of graphene, the focus is shifting to ‘reassembling’ graphite to uncover new insights into interacting electrons.

Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field

Authors: Ke Huang, Sankar Das Sarma, and Xiao Li

Published: 2025-02-13T10:00:00+00:00

Author(s): Ke Huang, Sankar Das Sarma, and Xiao Li

We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the noninteracting continuum model and the many-body Coulomb interactio…

[Phys. Rev. B 111, 075130] Published Thu Feb 13, 2025

Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field

Authors: Ke Huang, Sankar Das Sarma, Xiao Li

Published: Mon, 17 Feb 2025 00:00:00 -0500

arXiv:2408.05139v2 Announce Type: replace Abstract: We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the noninteracting continuum model and the many-body Coulomb interaction. We then discuss the integer quantum anomalous Hall (IQAH) effect in RnG and the role of the Hartree-Fock approach in understanding its appearance. Next, we explore the FQAH effect in RnG for $n=3$--$6$ using a combination of constrained Hartree-Fock and exact diagonalization methods. We characterize the stability of the FQAH phase by the size of the FQAH gap and find that RnG generally has a stable FQAH phase, although the required displacement field varies significantly among different $n$ values. Our work establishes the theoretical universality of both IQAH and FQAH in RnG.

Quantum geometric photocurrents of quasiparticles in superconductors

Authors: Daniel Kaplan, Kevin P. Lucht, Pavel A. Volkov, J. H. Pixley

Published: Wed, 19 Feb 2025 00:00:00 -0500

arXiv:2502.12265v1 Announce Type: new Abstract: Nonlinear optical response is a sensitive probe of the geometry and symmetry of electronic Bloch states in solids. Here, we extend this notion to the Bogoliubiov-de-Gennes (BdG) quasiparticles in superconductors. We present a theory of photocurrents in superconductors and show that they sensitively depend on the quantum geometry of the BdG excitation spectrum. For all light polarizations, the photocurrent is proportional to the quantum geometric tensor: for linear polarized light it is related to the quantum metric and for circular polarization -- the Berry curvature dipole of the associated BdG bands. We further relate the photocurrent to the ground state symmetries, providing a symmetry dictionary for the allowed photocurrent responses. For light not at normal incidence to the sample, photocurrent probes time-reversal symmetry breaking in systems with chiral point groups (such as twisted bilayers). We demonstrate that photocurrents allow to probe topology and TRS breaking in twisted $d$-wave superconductors and test the nature of superconductivity in twisted WSe$_2$ and multilayer stacks of rhombohedral graphene. Our results pave the way to contactless measurement of the quantum geometric properties and symmetry of superconductivity in materials and heterostructures.

Asynchronous mass inversion enriched quantum anomalous Hall states in multilayer graphene

Authors: Xilin Feng, Zi-Ting Sun, K. T. Law

Published: Thu, 20 Feb 2025 00:00:00 -0500

arXiv:2502.13229v1 Announce Type: new Abstract: Recently, multilayer graphene systems have attracted significant attention due to the discovery of a variety of intriguing phases, particularly quantum anomalous Hall (QAH) states. In rhombohedral pentalayer graphene, both $C = -5$ and $C = -3$ QAH states have been observed. While the $C = -5$ QAH state is well understood, the origin of the $C = -3$ QAH state remains unclear. In this letter, we propose that the $C = -3$ QAH state in rhombohedral pentalayer graphene (RPG) arises from an asynchronous mass inversion mechanism, driven by the interplay between trigonal warping and staggered layer order under an applied displacement field. Trigonal warping splits the low-energy bands into a central touching point and three "leg" Dirac cones. In the presence of staggered layer order, this splitting enables mass inversions driven by the displacement field to occur asynchronously at the central touching point and the "leg" Dirac cones, potentially leading to the formation of the $C = -3$ QAH state. Furthermore, this mechanism can also be applied to Bernal multilayer graphene systems, predicting the existence of additional QAH states beyond $C = \pm N, \pm 2N$ for $N$-layer graphene.

Signatures of Chiral Superconductivity in Rhombohedral Graphene

Authors: Tonghang Han, Zhengguang Lu, Zach Hadjri, Lihan Shi, Zhenghan Wu, Wei Xu, Yuxuan Yao, Armel A. Cotten, Omid Sharifi Sedeh, Henok Weldeyesus, Jixiang Yang, Junseok Seo, Shenyong Ye, Muyang Zhou, Haoyang Liu, Gang Shi, Zhenqi Hua, Kenji Watanabe, Takashi Taniguchi, Peng Xiong, Dominik M. Zumb\"uhl, Liang Fu, Long Ju

Published: Fri, 21 Feb 2025 00:00:00 -0500

arXiv:2408.15233v2 Announce Type: replace Abstract: Chiral superconductors are unconventional superconducting states that break time reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetra- and penta-layer graphene in the absence of moir\'e superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with Tc up to 300 mK and charge density ne as low as 2.4*1011 cm-2 in three tetralayer and two pentalayer devices. Spontaneous time-reversal-symmetry-breaking (TRSB) due to electron's orbital motion is found, and several observations indicate the chiral nature of these superconducting states, including: 1. In the superconducting state, Rxx shows magnetic hysteresis in varying out-of-plane magnetic field B, which is absent from all other superconductors; 2. the superconducting states are immune to in-plane magnetic field and are developed within a spin- and valley-polarized quarter-metal phase; 3. the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. We also observed a critical B of up to 1.4 Tesla, higher than any graphene superconductivity reported so far and indicates a strong-coupling superconductivity close to the BCS-BEC crossover. Our observations establish a pure carbon material for the study of topological superconductivity, and pave the way to explore Majorana modes and topological quantum computing.

Layer-dependent quantum anomalous Hall effect in rhombohedral graphene

Authors: Zhaochen Liu and Jing Wang

Published: 2025-02-21T10:00:00+00:00

Author(s): Zhaochen Liu and Jing Wang

The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of the high Chern number QAH effect in pentalayer and tetralayer rhombohedral graphene highligh…

[Phys. Rev. B 111, L081111] Published Fri Feb 21, 2025

Fractional topological states in rhombohedral multilayer graphene modulated by kagome superlattice

Authors: Yanran Shi, Bo Xie, Fengfan Ren, Xinyu Cai, Zhongqing Guo, Qiao Li, Xin Lu, Zhongkai Liu, Jianpeng Liu

Published: Tue, 25 Feb 2025 00:00:00 -0500

arXiv:2502.17320v1 Announce Type: new Abstract: Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moir\'e heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned SiO$_2$ substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is benchmarked by transport measurements in the weak superlattice-potential and large filling factor regime. We find that the system may exhibit nearly ideal topological flat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at 1/3, 2/3, 2/5, 3/5 and 1/2 fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field.

Quarter Metal Superconductivity

Authors: Chiho Yoon, Tianyi Xu, Yafis Barlas, Fan Zhang

Published: Wed, 26 Feb 2025 00:00:00 -0500

arXiv:2502.17555v1 Announce Type: new Abstract: We investigate the recently discovered multiple superconducting states in rhombohedral graphene quarter metal. We demonstrate that one of these states features a single-spin, single-valley, single-band, single-Fermi-pocket parent state and is most likely a chiral topological pair-density wave, marked by a threefold symmetry that may not be spontaneously broken, unpaired Majorana zero modes at edges, vortices, and dislocations, and an anomalous intrinsic superconducting diode effect.

Continuously tunable anomalous Hall crystals in rhombohedral heptalayer graphene

Authors: Hanxiao Xiang, Jing Ding, Jiannan Hua, Naitian Liu, Wenqiang Zhou, Qianmei Chen, Kenji Watanabe, Takashi Taniguchi, Na Xin, Wei Zhu, Shuigang Xu

Published: Wed, 26 Feb 2025 00:00:00 -0500

arXiv:2502.18031v1 Announce Type: new Abstract: The interplay of electronic interactions and nontrivial topology can give rise to a wealth of exotic quantum states. A notable example is the formation of Wigner crystals driven by strong electron-electron interactions. When these electronic crystals emerge in a parent band carrying a large Berry curvature, they can exhibit topologically nontrivial properties as anomalous Hall crystals, spontaneously breaking both continuous translational symmetry and time-reversal symmetry. Here, we report the experimental observation of tunable anomalous Hall crystals in rhombohedral heptalayer graphene moir\'e superlattices. At filling factors near one electron per moir\'e unit cell (v=1), we identify a series of incommensurate Chern insulators with a Chern number of C=1. Furthermore, we observe spontaneous time-reversal symmetry breaking spanning the entire filling range from v=1 to v=2, manifesting as anomalous Hall effects with pronounced magnetic hysteresis. Notably, anomalous Hall crystals with a high Chern number C=3 are observed over generic fillings ranging from v=1.5 to v=2. These anomalous Hall crystals are incommensurate with the moir\'e superlattice and exhibit dispersive fan diagrams consistent with the Streda formula, with their positions continuously tunable through displacement fields. Remarkably, these partially filled Chern insulators display Chern numbers distinct from their parent bands. Our findings demonstrate the rich variety of electronic crystalline states in rhombohedral graphene moir\'e superlattices, offering valuable insights into the strongly correlated topological phases.

Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene

Authors: Qiao-Chu Zhang, Jing Wang

Published: Thu, 27 Feb 2025 00:00:00 -0500

arXiv:2406.01877v2 Announce Type: replace Abstract: The effects of short-range fermion-fermion interactions on the low-energy properties of rhombohedral trilayer graphene are comprehensively investigated using the momentum-shell renormalization group method. We take into account all one-loop corrections and establish the energy-dependent coupled evolutions of independent fermionic couplings that carry the physical information stemming from the interplay of various fermion-fermion interactions. With detailed numerical analysis, we observe that the ferocious competition among all fermion-fermion interactions can drive fermionic couplings to four distinct fixed points, dubbed $\textrm{FP}_{1}$, $\textrm{FP}_{2}$, $\textrm{FP}_{3}$, and $\textrm{FP}_{4}$, in the interaction-parameter space. These fixed points primarily dictate the fate of the system in the low-energy regime and are always associated with some instabilities characterized by specific symmetry breakings, leading to certain phase transitions. To determine the favorable states arising from the potential phase transitions, we introduce a number of fermion-bilinear source terms to characterize the underlying candidate states. By comparing their related susceptibilities, we find that the dominant states correspond to spin-singlet superconductivity, spin-triplet pair-density-waves, and spin-triplet superconductivity for fixed points $\textrm{FP}_{1,3}$, $\textrm{FP}_{2}$, and $\textrm{FP}_{4}$, respectively. These provide valuable insights into the low-energy properties of rhombohedral trilayer graphene and analogous materials.

Band Renormalization, Quarter Metals, and Chiral Superconductivity in Rhombohedral Tetralayer Graphene

Authors: Guillermo Parra-Martinez, Alejandro Jimeno-Pozo, Vo Tien Phong, Hector Sainz-Cruz, Daniel Kaplan, Peleg Emanuel, Yuval Oreg, Pierre A. Pantaleon, Jose Angel Silva-Guillen, Francisco Guinea

Published: Fri, 28 Feb 2025 00:00:00 -0500

arXiv:2502.19474v1 Announce Type: new Abstract: Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been observed in rhombohedral tetralayer graphene. To explain this finding, we study the role of electron-electron interactions in determining flavor symmetry breaking, using the Hartree Fock (HF) approximation, and also superconductivity driven by repulsive interactions. Though mean field HF correctly predicts the isospin flavors and reproduces the experimental phase diagram, it overestimates the band renormalization near the Fermi energy and suppresses superconducting instabilities. To address this, we introduce a physically motivated scheme that includes internal screening in the HF calculation. Superconductivity arises in the spin-valley polarized phase for a range of electric fields and electron doping. Our findings reproduce the experimental observations and reveal a $p$-wave, finite-momentum, time-reversal symmetry broken superconducting state, encouraging further investigation into exotic phases in graphene multilayers.

Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

Authors: Dacen Waters, Anna Okounkova, Ruiheng Su, Boran Zhou, Jiang Yao, Kenji Watanabe, Takashi Taniguchi, Xiaodong Xu, Ya-Hui Zhang, Joshua Folk, and Matthew Yankowitz

Published: 2025-02-27T10:00:00+00:00

Author(s): Dacen Waters, Anna Okounkova, Ruiheng Su, Boran Zhou, Jiang Yao, Kenji Watanabe, Takashi Taniguchi, Xiaodong Xu, Ya-Hui Zhang, Joshua Folk, and Matthew Yankowitz

Electric-field control of topological states in a pentalayer graphene moiré system reveals tunable quantum phases, correlated insulating states, and evidence of fractional charge quasiparticles.

[Phys. Rev. X 15, 011045] Published Thu Feb 27, 2025

Tailoring of charge carriers with deposition temperature in pulsed laser deposited BiFeO3 thin films

Authors: Viswajit R S, Jinesh K. B, Ashok K

Published: Tue, 04 Mar 2025 00:00:00 -0500

arXiv:2503.00544v1 Announce Type: new Abstract: This research investigates the structural, topological, electrical and optical properties of pulsed laser deposited polycrystalline BiFeO3 thin films on silicon and glass substrate at varying deposition temperatures ranging from 400 degC to 700 degC. X-ray diffraction confirm rhombohedral phase and X-ray photoelectron spectroscopy reveals stoichiometric BiFeO3 films. The optical bandgap of thin films obtained from absorption spectra increases with the substrate temperature. Photoluminescence emission spectrum reveals the defects and Atomic Force Microscopy analysis bring out the surface topography and crystallinity improvement with temperature. The charge transport studies reveal a transition in conductivity from n-type at lower deposition temperature to p-type at higher deposition temperature, attributed to oxygen and bismuth vacancies respectively. The intricate understanding of conductivity tuning and the leaky nature of BiFeO3 thin film opens avenues for applications in nonvolatile memories, particularly neuromorphic devices.

Electrical switching of Chern insulators in moire rhombohedral heptalayer graphene

Authors: Zhiyu Wang, Qianling Liu, Xiangyan Han, Zhuoxian Li, Wenjun Zhao, Zhuangzhuang Qu, Chunrui Han, Kenji Watanabe, Takashi Taniguchi, Zheng Vitto Han, Sicheng Zhou, Bingbing Tong, Guangtong Liu, Li Lu, Jianpeng Liu, Fengcheng Wu, Jianming Lu

Published: Tue, 04 Mar 2025 00:00:00 -0500

arXiv:2503.00837v1 Announce Type: new Abstract: In orbital Chern insulators, the chemical potential acts as a tuning knob to reverse chirality in dissipationless edge currents, enabling electric-field control of magnetic order-key for future quantum electronics. Despite the rise of orbital Chern insulators, electrically switchable quantum anomalous Hall effect (QAHE) remains rare, necessitating further investigation. Here, we demonstrate electric-field-induced reversal of orbital Chern insulators in a moire superlattice composed of rhombohedral heptalayer graphene (r-7LG) aligned with hexagonal boron nitride. At one electron per moire unit cell, two emerging Chern insulating phases - one pointing away from and the other toward graphene's charge neutrality point in the phase diagram of carrier density (n) versus magnetic field (B) - exhibit energetic competition modulated by both n and B. This switchable QAHE chirality in r-7LG demonstrates a layer-number dependent response: similar phenomena in moire r-6LG require much higher magnetic fields and are absent in thinner rhombohedral graphene. Our findings establish moire-engineered rhombohedral graphene as a promising platform for exploring topological quantum materials with electrically controllable chiral edge modes and magnetic order.

Ephemeral Superconductivity Atop the False Vacuum

Authors: Gal Shavit, Stevan Nadj-Perge, Gil Refael

Published: Wed, 05 Mar 2025 00:00:00 -0500

arXiv:2409.02992v2 Announce Type: replace Abstract: A many body system in the vicinity of a first-order phase transition may get trapped in a local minimum of the free energy landscape. These so-called false-vacuum states may survive for exceedingly long times if the barrier for their decay is high enough. The rich phase diagram obtained in graphene multilayer devices presents a unique opportunity to explore transient superconductivity on top of a correlated false vacuum. Specifically, we consider superconductors which are terminated by an apparent first-order phase transition to a correlated phase with different symmetry. We propose that quenching across this transition leads to a non-equilibrium ephemeral superconductor, readily detectable using straightforward transport measurements. Besides enabling a simple detection scheme, the transient superconductor also generically enhances the false vacuum lifetime, potentially by orders of magnitude. In several scenarios, the complimentary effect takes place as well: superconductivity is temporarily emboldened in the false vacuum, albeit ultimately decaying. We demonstrate the applicability of these claims for two different instances of superconductivity terminated by a first order transition in rhombohedral graphene. The obtained decay timescales position this class of materials as a promising playground to unambiguously realize and measure non-equilibrium superconductivity.

Superconductivity and quantized anomalous Hall effect in rhombohedral graphene

Authors: Youngjoon Choi, Ysun Choi, Marco Valentini, Caitlin L. Patterson, Ludwig F. W. Holleis, Owen I. Sheekey, Hari Stoyanov, Xiang Cheng, Takashi Taniguchi, Kenji Watanabe, Andrea F. Young

Published: 2025-03-05

Nature, Published online: 05 March 2025; doi:10.1038/s41586-025-08621-y

Rhombohedral tetralayer graphene aligned to a hexagonal boron nitride substrate hosts gate-tunable superconductivity and quantized anomalous Hall states, and thermodynamic compressibility measurements further show a fractional Chern insulator at zero magnetic field, paving the way for new hybrid interfaces between superconductors and topological edge states.

How pairing mechanism dictates topology in valley-polarized superconductors with Berry curvature

Authors: Julian May-Mann, Tobias Helbig, Trithep Devakul

Published: Mon, 10 Mar 2025 00:00:00 -0400

arXiv:2503.05697v1 Announce Type: new Abstract: We investigate how the pairing mechanism influences topological superconductivity in valley-polarized systems with Berry curvature. We demonstrate that short-range attractive interactions, such as those mediated by phonons, favor superconducting states where the Bogoliubov-de Gennes (BdG) Chern number has the same sign as the Berry curvature. In contrast, overscreened repulsive interactions, as in the Kohn-Luttinger mechanism, favor superconducting states where the BdG Chern number has the opposite sign as the Berry curvature. We establish these trends in a fully controlled limit and apply them to a recently reported chiral superconductor in rhombohedral multilayer graphene. Our theory provides a concrete experimental criterion for distinguishing between different pairing mechanisms in valley-polarized topological superconductors.

Electric-Field Switchable Chirality in Rhombohedral Graphene Chern Insulators Stabilized by Tungsten Diselenide

Authors: Jing Ding, Hanxiao Xiang, Jiannan Hua, Wenqiang Zhou, Naitian Liu, Le Zhang, Na Xin, Bing Wu, Kenji Watanabe, Takashi Taniguchi, Zdeněk Sofer, Wei Zhu, and Shuigang Xu

Published: 2025-03-10T10:00:00+00:00

Author(s): Jing Ding, Hanxiao Xiang, Jiannan Hua, Wenqiang Zhou, Naitian Liu, Le Zhang, Na Xin, Bing Wu, Kenji Watanabe, Takashi Taniguchi, Zdeněk Sofer, Wei Zhu, and Shuigang Xu

Multilayer graphene can host quantum anomalous Hall states with edge currents controllable via an electric field, offering new possibilities for low-power electronics and quantum computing.

[Phys. Rev. X 15, 011052] Published Mon Mar 10, 2025

Orbital Longitudinal Magneto-electric Coupling in Multilayer Graphene

Authors: Jin-Xin Hu, Justin C. W. Song

Published: Wed, 12 Mar 2025 00:00:00 -0400

arXiv:2503.07822v1 Announce Type: new Abstract: Magneto-electric coupling enables the manipulation of magnetization by electric fields and vice versa. While typically found in heavy element materials with large spin-orbit coupling, recent experiments on rhombohedral-stacked pentalayer graphene (RPG) have demonstrated a {\it longitudinal magneto-electric coupling} (LMC) without spin-orbit coupling. Here we present a microscopic theory of LMC in multilayer graphene and identify how it is controlled by a ``layer-space'' quantum geometry and interaction-driven valley polarization. Strikingly, we find that the interplay between valley-polarized order and LMC produces a butterfly shaped magnetic hysteresis controlled by out-of-plane electric field: a signature of LMC and a multiferroic valley order. Furthermore, we identify a nonlinear LMC in multilayer graphene under time-reversal symmetry, while the absence of centrosymmetry enables the generation of a second-order nonlinear electric dipole moment in response to an out-of-plane magnetic field. Our theoretical framework provides a quantitative understanding of LMC, as well as the emergent magneto-electric properties of multilayer graphene.

Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene

Authors: Zhaochen Liu, Jing Wang

Published: Wed, 12 Mar 2025 00:00:00 -0400

arXiv:2401.13413v2 Announce Type: replace Abstract: The quantum anomalous Hall (QAH) effect, first proposed in the Haldane model, is a paradigmatic example of the application of band topology in condensed matter physics. The recent experimental discoveries of high Chern number QAH effect in pentalayer and tetralayer rhombohedral graphene highlight the intriguing interplay between strong interactions and spin-orbit coupling (SOC). Here we propose a minimal interacting model for spin-orbit-coupled rhombohedral graphene and use the Hartree-Fock analysis to explore the phase diagram at charge neutrality. We find that with Ising SOC on one outmost graphene layer, the in-plane layer-antiferromagnetic order is the insulating ground state without displacement field. Upon increasing the gate displacement field, we find that the QAH state with Chern number being equal to the layer number emerges between layer-antiferromagnetic state and layer-polarized state, which is consistent with experimental observations. Remarkably, we study the phase diagram for different thicknesses and find pentalayer is optimal for the QAH effect. Finally, we propose that the QAH state is enlarged by engineering opposite Ising SOC on the opposite outmost layers of rhombohedral graphene. These results will facilitate the realization of QAH states in rhombohedral graphene with different thicknesses. Our work serves as a foundation for further exploration of correlated physics of insulating state in rhombohedral graphene.

Fermion-fermion interaction driven phase transitions in rhombohedral trilayer graphene

Authors: Qiao-Chu Zhang, Jing Wang

Published: Wed, 12 Mar 2025 00:00:00 -0400

arXiv:2406.01877v3 Announce Type: replace Abstract: The effects of short-range fermion-fermion interactions on the low-energy properties of rhombohedral trilayer graphene are comprehensively investigated using the momentum-shell renormalization group method. We take into account all one-loop corrections and establish the energy-dependent coupled evolutions of independent fermionic couplings that carry the physical information stemming from the interplay of various fermion-fermion interactions. With detailed numerical analysis, we observe that the ferocious competition among all fermion-fermion interactions can drive fermionic couplings to four distinct fixed points, dubbed $\textrm{FP}_{1}$, $\textrm{FP}_{2}$, $\textrm{FP}_{3}$, and $\textrm{FP}_{4}$, in the interaction-parameter space. These fixed points primarily dictate the fate of the system in the low-energy regime and are always associated with some instabilities characterized by specific symmetry breakings, leading to certain phase transitions. To determine the favorable states arising from the potential phase transitions, we introduce a number of fermion-bilinear source terms to characterize the underlying candidate states. By comparing their related susceptibilities, we find that the dominant states correspond to spin-singlet superconductivity, spin-triplet pair-density-waves, and spin-triplet superconductivity for fixed points $\textrm{FP}_{1,3}$, $\textrm{FP}_{2}$, and $\textrm{FP}_{4}$, respectively. These provide valuable insights into the low-energy properties of rhombohedral trilayer graphene and analogous materials.

Scanning tunneling microscopy study of twisted Bernal-stacked tetralayer graphene

Authors: Wen-Xiao Wang, Tongtong Chen, Long-Jing Yin, Jiabin Qiao, Zhen Ma, and Juntao Song

Published: 2025-03-11T10:00:00+00:00

Author(s): Wen-Xiao Wang, Tongtong Chen, Long-Jing Yin, Jiabin Qiao, Zhen Ma, and Juntao Song

Twisted multilayer graphene provides an unprecedented platform for studying strongly correlated and topological physics, such as twisted monobilayer graphene (TMBG) featured with electric-field tunable superconductivity. Adding an extra layer to TMBG, twisted tetralayer graphene emerges with more fa…

[Phys. Rev. B 111, 115410] Published Tue Mar 11, 2025

Elastic Response and Instabilities of Anomalous Hall Crystals

Authors: F\'elix Desrochers, Mark R. Hirsbrunner, Joe Huxford, Adarsh S. Patri, T. Senthil, Yong Baek Kim

Published: Thu, 13 Mar 2025 00:00:00 -0400

arXiv:2503.08784v1 Announce Type: new Abstract: Anomalous Hall crystals (AHCs) are exotic phases of matter that simultaneously break continuous translation symmetry and exhibit the quantum anomalous Hall effect. AHCs have recently been proposed as an explanation for the observation of an integer quantum anomalous Hall phase in a multilayer graphene system. Despite intense theoretical and experimental interest, little is known about the mechanical properties of AHCs. We study the elastic properties of AHCs, first by utilizing a continuum model with uniform Berry curvature. In contrast to Wigner crystals, we find that the stiffness of the AHC weakens and eventually vanishes as electronic interactions are increased. Furthermore, we demonstrate that the triangular lattice AHC arising in an experimentally relevant parameter regime of a realistic model of rhombohedral pentalayer graphene is unstable, emphasizing the importance of understanding the mechanical properties of AHCs for interpreting experiments.

"Berry Trashcan" Model of Interacting Electrons in Rhombohedral Graphene

Authors: B. Andrei Bernevig, Yves H. Kwan

Published: Fri, 14 Mar 2025 00:00:00 -0400

arXiv:2503.09692v1 Announce Type: new Abstract: We present a model for interacting electrons in a continuum band structure that resembles a ``trashcan'', with a flat bottom of radius $k_b$ beyond which the dispersion increases rapidly with velocity $v$. The form factors of the Bloch wavefunctions can be well-approximated by the Girvin-MacDonald-Platzman algebra, which encodes the uniform Berry curvature. We demonstrate how this model captures the salient features of the low-energy Hamiltonian for electron-doped pristine $n$-layer rhombohedral graphene (R$n$G) for appropriate values of the displacement field, and provide corresponding expressions for $k_b$. In the regime where the Fermi wavevector is close to $k_b$, we analytically solve the Hartree-Fock equations for a gapped Wigner crystal in several limits of the model. We introduce a new method, the sliver-patch approximation, which extends the previous few-patch approaches and is crucial in both differentiating even vs odd Chern numbers of the ground state and gapping the Hartree-Fock solution. A key parameter is the Berry flux $\varphi_{\text{BZ}}$ enclosed by the (flat) bottom of the band. We analytically show that there is a ferromagnetic coupling between the signs of $\varphi_{\text{BZ}}$ and the Chern number $C$ of the putative Wigner crystal. We also study the competition between the $C=0$ and $1$ solutions as a function of the interaction potential for parameters relevant to R$n$G. By exhaustive comparison to numerical Hartree-Fock calculations, we demonstrate how the analytic results capture qualitative trends of the phase diagram, as well as quantitative details such as the enhancement of the effective velocity. Our analysis paves the way for an analytic and numerical examination of the stability and competition beyond mean-field theory of the Wigner crystals in this model.

Intertwined Nematicity, Multiferroicity, and Nonlinear Hall Effect in Rhombohedral Pentalayer Graphene

Authors: Erin Morissette, Peiyu Qin, K. Watanabe, T. Taniguchi, J. I. A. Li

Published: Fri, 14 Mar 2025 00:00:00 -0400

arXiv:2503.09954v1 Announce Type: new Abstract: Electronic nematicity-the spontaneous reduction of rotational symmetry-has been widely studied in strongly correlated quantum materials, yet its interplay with other symmetry-breaking phases remains an outstanding experimental challenge to unravel, particularly in van der Waals heterostructures. Here, using angle-resolved transport measurements, we reveal a unique intertwinement of nematicity, orbital multiferroicity, and the nonlinear Hall effect in rhombohedral pentalayer graphene. This coupling enables electric-field-driven switching of the nematic principal axis and the nonlinear Hall polar vector, coinciding with the butterfly-shaped hysteresis of the multiferroic order. We identify two sharply defined nematic phase transitions: the first coincides with the onset of orbital ferromagnetism, while the second, at lower temperatures, aligns with the emergence of ferroelectricity. Our findings point to a nematic-driven instability that intertwines rotational, time-reversal, and inversion symmetry breaking. This is consistent with spontaneous momentum polarization, proposed to occur under the influence of the Coulomb-driven flocking effect. Together, our observations establish nematicity as a fundamental organizing principle in the landscape of intertwined electronic orders in strongly correlated two-dimensional systems.

Single-gate tracking behavior in flat-band multilayer graphene devices

Authors: Kry\v{s}tof Kol\'a\v{r}, Dacen Waters, Joshua Folk, Matthew Yankowitz, Cyprian Lewandowski

Published: Mon, 17 Mar 2025 00:00:00 -0400

arXiv:2503.10749v1 Announce Type: new Abstract: A central feature of many van der Waals (vdW) materials is the ability to precisely control their charge doping, $n$, and electric displacement field, $D$, using top and bottom gates. For devices composed of only a few layers, it is commonly assumed that $D$ causes the layer-by-layer potential to drop linearly across the structure. Here, we show that this assumption fails for a broad class of crystalline and moir\'e vdW structures based on Bernal- or rhombohedral-stacked multilayer graphene. We find that the electronic properties at the Fermi level are largely dictated by special layer-polarized states arising at Bernal-stacked crystal faces, which typically coexist in the same band with layer-delocalized states. We uncover a novel mechanism by which the layer-delocalized states completely screen the layer-polarized states from the bias applied to the remote gate. This screening mechanism leads to an unusual scenario where voltages on either gate dope the band as expected, yet the band dispersion and associated electronic properties remain primarily (and sometimes exclusively) governed by the gate closer to the layer-polarized states. Our results reveal a novel electronic mechanism underlying the atypical single-gate-controlled transport characteristics observed across many flat-band graphitic structures, and provide key theoretical insights essential for accurately modeling these systems.

A controllable theory of superconductivity due to strong repulsion in a polarized band

Authors: Zhiyu Dong, Patrick A. Lee

Published: Mon, 17 Mar 2025 00:00:00 -0400

arXiv:2503.11079v1 Announce Type: new Abstract: Can strong repulsive interaction be shown to give rise to pairing in a controllable way? We find that for a single flavor polarized band, there is a small expansion parameter in the low density limit, once the Bloch wavefunction overlap is taken into account. A perturbative expansion is possible, even if the interaction is much stronger than the Fermi energy $\epsilon_F$. We illustrate our method with a two-band model that is often used to describe multi-layer rhombohedral graphene and comment on the relationship with experiments. This work opens a reliable pathway to search for topological superconductors with high-$T_c$ (relative to $\epsilon_F$) in materials with strongly interactions. We summarize the requirements and suggest some illustrative design structures.

Fractional topological states in rhombohedral multilayer graphene modulated by kagome superlattice

Authors: Yanran Shi, Bo Xie, Fengfan Ren, Xinyu Cai, Zhongqing Guo, Qiao Li, Xin Lu, Nicolas Regnault, Zhongkai Liu, Jianpeng Liu

Published: Mon, 17 Mar 2025 00:00:00 -0400

arXiv:2502.17320v2 Announce Type: replace Abstract: Fractional quantum anomalous Hall effects realized in twisted bilayer MoTe$_2$ and multilayer-graphene-based moir\'e heterostructures have captured a tremendous growth of interest. In this work, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned SiO$_2$ substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is well benchmarked by transport measurements in the weak superlattice-potential regime. We find that the system may exhibit nearly ideal topological flat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at 1/3, 2/3, 2/5, 3/5 and 1/2 fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field.

Texture- and Stress-Dependent Electromechanical Response in Ferroelectric PZT: Insights from a Micromechanical Model

Authors: Saujatya Mandal, Debashish Das

Published: Tue, 18 Mar 2025 00:00:00 -0400

arXiv:2503.12057v1 Announce Type: new Abstract: The performance of PbZr0.52Ti0.48O3 (PZT)-based microelectromechanical systems (MEMS) and other piezoelectric devices can be significantly enhanced by optimizing crystallographic texture, which directly influences polarization switching and electromechanical response. However, the combined effect of texture and residual stress on the nonlinear behavior of PZT remains poorly understood, particularly in morphotropic phase boundary (MPB) compositions, where both tetragonal and rhombohedral domain switching mechanisms coexist. While several computational models have been developed to predict the response of ferroelectric materials, most studies either focus exclusively on tetragonal ceramics, require computationally expensive self-consistent schemes, or fail to explicitly capture key experimental observables, such as butterfly loops and D3-E3 hysteresis loops. Furthermore, the lack of accessible numerical implementations limits the ability of experimentalists to engage with and refine these models. To address these challenges, this work presents an efficient micro-electromechanical model based on Hwang et al. (1998), implemented in an open-source MATLAB framework to predict the effects of preferred crystallographic orientation and residual stress on polarization switching in MPB PZT. Despite its simplicity, the model successfully captures key experimentally observed trends, making it an invaluable tool for understanding domain-switching processes in ferroelectrics. By making the code freely available, this study provides a practical and scalable computational approach that allows researchers, especially experimentalists, to simulate, analyze, and refine polarization switching behavior, bridging the gap between theoretical modeling and real-world ferroelectric device optimization.

Probing superconductivity with tunneling spectroscopy in rhombohedral graphene

Authors: Denis Sedov, Mathias S. Scheurer

Published: Tue, 18 Mar 2025 00:00:00 -0400

arXiv:2503.12650v1 Announce Type: new Abstract: Motivated by experiments on rhombohedral tetralayer graphene showing signs of superconductivity emerging from a valley-polarized normal state, we here analyze theoretically how scanning tunneling spectroscopy can be used to probe the superconducting order parameter of the system. To describe different pairing scenarios on equal footing, we develop a microscopic tunneling approach that can capture arbitrary, including finite-momentum, superconducting order parameters and low-symmetry normal-state Hamiltonians. Our analysis shows that the broken time-reversal symmetry in a single valley leads to unique features in the weak-tunneling regime that are different for commensurate and incommensurate Cooper pair momenta. We further uncover an unconventional spatial dependence of the Andreev conductance, allowing to distinguish between three topologically distinct classes of single-$\mathbf{q}$ pairing states in the system, and compute the signatures of a competing translational-symmetry breaking three-$\mathbf{q}$ ''moir\'e superconductor''.

Visualizing isospin magnetic texture and intervalley exchange interaction in rhombohedral tetralayer graphene

Authors: Nadav Auerbach, Surajit Dutta, Matan Uzan, Yaar Vituri, Yaozhang Zhou, Alexander Y. Meltzer, Sameer Grover, Tobias Holder, Peleg Emanuel, Martin E. Huber, Yuri Myasoedov, Kenji Watanabe, Takashi Taniguchi, Yuval Oreg, Erez Berg, Eli Zeldov

Published: Wed, 19 Mar 2025 00:00:00 -0400

arXiv:2503.14146v1 Announce Type: new Abstract: Multilayer rhombohedral graphene offers a rich platform for strong electron interactions without a moire superlattice. The in situ tunable band structure and nontrivial topology lead to a variety of novel correlated electronic states with isospin order dictated by the interplay of spin-orbit coupling and Hunds exchange interactions. However, versatile methods for mapping local isospin textures and determining the exchange energies are currently lacking. Utilizing a nanoscale superconducting quantum interference device in a vector magnetic field, we image the magnetization textures in tetralayer rhombohedral graphene. We reveal sharp magnetic phase transitions marking spontaneous time reversal symmetry breaking. In the quarter metal phase, the spin and orbital moments align closely, providing a bound on the spin-orbit coupling energy. The half metal phase is shown to have a very small magnetic anisotropy, providing the first experimental lower bound on the intervalley Hunds exchange interaction energy, which is found to be close to its theoretical upper bound. By contrasting to magnetotransport measurements, we show that high-field electronic states are governed by unique topological magnetic band reconstruction. The ability to resolve the local isospin texture and the different interaction energies, paves the way to a better understanding of the phase transition hierarchy and the numerous correlated electronic states arising from spontaneous and induced isospin symmetry breaking in graphene heterostructures.

Finite-momentum pairing and superlattice superconductivity in valley-imbalanced rhombohedral graphene

Authors: Maine Christos, Pietro M. Bonetti, Mathias S. Scheurer

Published: Thu, 20 Mar 2025 00:00:00 -0400

arXiv:2503.15471v1 Announce Type: new Abstract: Inspired by the recent experimental discovery of superconductivity emerging from a time-reversal symmetry-breaking normal state in tetralayer rhombohedral graphene, we here investigate superconducting instabilities in this system. We classify the possible pairing instabilities, including states with commensurate and incommensurate center of mass momenta. As rotational symmetry is broken in the latter type of pairing states, their momentum-space structure is most naturally characterized by a "valley-independent Chern number", measuring the relative chirality between the normal and superconducting state. We further demonstrate that superconductivity can condense at multiple incommensurate momenta simultaneously, leading to the spontaneous formation of a translational-symmetry-breaking superlattice superconductor. Studying multiple different pairing mechanisms and varying the degree of spin and valley polarization in the normal state, we compare the energetics of these superconductors. Our results demonstrate that valley-imbalanced rhombohedral tetralayer graphene can give rise to rich superconducting phenomenologies.

Fluctuating magnetism and Pomeranchuk effect in multilayer graphene

Authors: Ludwig Holleis, Tian Xie, Siyuan Xu, Haoxin Zhou, Caitlin L. Patterson, Archisman Panigrahi, Takashi Taniguchi, Kenji Watanabe, Leonid S. Levitov, Chenhao Jin, Erez Berg, Andrea F. Young

Published: 2025-03-19

Nature, Published online: 19 March 2025; doi:10.1038/s41586-025-08725-5

Itinerant magnetism in rhombohedral multilayer graphene shows a large excess entropy from magnetic fluctuations above its critical temperature—typically only associated with local moments—which implies the decoupling of charge and isospin degrees of freedom, and results in the isospin Pomeranchuk effect.

Impact of spin–orbit coupling on superconductivity in rhombohedral graphene

Authors: Jixiang Yang, Xiaoyan Shi, Shenyong Ye, Chiho Yoon, Zhengguang Lu, Vivek Kakani, Tonghang Han, Junseok Seo, Lihan Shi, Kenji Watanabe, Takashi Taniguchi, Fan Zhang, Long Ju

Published: 2025-03-19

Nature Materials, Published online: 19 March 2025; doi:10.1038/s41563-025-02156-3

The authors present transport measurements of rhombohedral trilayer graphene proximitized by transition metal dichalcogenides. They find that the presence of transition metal dichalcogenides enables the emergence of new superconducting and metallic phases and affects the superconducting states present in bare rhombohedral trilayer graphene.

Spontaneous vortex-antivortex lattice and Majorana fermions in rhombohedral graphene

Authors: Filippo Gaggioli, Daniele Guerci, Liang Fu

Published: Fri, 21 Mar 2025 00:00:00 -0400

arXiv:2503.16384v1 Announce Type: new Abstract: The discovery of superconducting states in multilayer rhombohedral graphene with spin and valley polarization has raised an interesting question: how does superconductivity cope with time-reversal symmetry breaking? %In the normal state, spin and valley polarization break time-reversal symmetry, while trigonal warping enforces $C_{3z}$. Below the critical temperature, the superconducting phase displays signatures of chiral behavior and is stabilized by out-of-plane fields as large as $\sim 0.5\,\text{T}$. In this work, using Ginzburg-Landau theory and microscopic calculation, we predict the existence of a new superconducting state at low electron density, which exhibits a spontaneously formed lattice of vortices and antivortices hosting Majorana zero-modes in their cores. We further identify this vortex-antivortex lattice (VAL) state in the experimental phase diagram and describe its experimental manifestations.

Phonons in Electron Crystals with Berry Curvature

Authors: Junkai Dong, Ophelia Evelyn Sommer, Tomohiro Soejima, Daniel E. Parker, Ashvin Vishwanath

Published: Fri, 21 Mar 2025 00:00:00 -0400

arXiv:2503.16390v1 Announce Type: new Abstract: Recent advances in 2D materials featuring nonzero Berry curvature have inspired extensions of the Wigner crystallization paradigm. This paper derives a low-energy effective theory for such quantum crystals, including the anomalous Hall crystal (AHC) with nonzero Chern number. First we show that the low frequency dispersion of phonons in AHC, despite the presence of Berry curvature, resembles that of the zero field (rather than finite magnetic field) Wigner crystal due to the commutation of translation generators. We explain how key parameters of the phonon theory such as elastic constants and effective mass can be extracted from microscopic models, and apply them to two families of models: the recently introduced $\lambda$-jellium model and a model of rhombohedral multilayer graphene (RMG). In the $\lambda$-jellium model, we explore the energy landscape as crystal geometry shifts, revealing that AHC can become "soft" under certain conditions. This causes transitions in lattice geometry, although the quantized Hall response remains unchanged. Surprisingly, the Berry curvature seems to enhance the effective mass, leading to a reduction in phonon speed. For the AHC in RMG, we obtain estimates of phonon speed and shear stiffness. We also identify a previously overlooked "kineo-elastic" term in the phonon effective action that is present in the symmetry setting of RMG, and leads to dramatic differences in phonon speeds in opposite directions. We numerically confirm these predictions of the effective actions by time-dependent Hartree-Fock calculations. Our work points to the wealth of new phenomena that can arise when electron crystallization occurs in the presence of band geometry and topology.

Intrinsic superconducting diode effect and nonreciprocal superconductivity in rhombohedral graphene multilayers

Authors: Yinqi Chen, Constantin Schrade

Published: Fri, 21 Mar 2025 00:00:00 -0400

arXiv:2503.16391v1 Announce Type: new Abstract: Rhombohedral tetralayer graphene has recently emerged as an exciting platform for a possible chiral superconducting state. Here, we theoretically demonstrate and study the emergence of nonreciprocal superconductivity and an intrinsic superconducting diode effect in this system. Our results are based on a fully self-consistent framework for determining the superconducting order parameter from a Kohn-Luttinger mechanism to superconductivity and show that large diode efficiencies, $\sim$ 60%, are achievable and highly tunable by an external displacement field. Moreover, we also find that the diodicity shows a characteristic angular dependence with multiple enhanced lobes, which depend on the Fermi surface structure of the underlying normal state. Hence, our results suggest that the intrinsic superconducting diode effect could provide insights into the type of Fermi surface topology from which superconductivity arises.

Valley-dependent giant orbital moments and transport feature in rhombohedral graphene multilayers

Authors: X. Mu, J. Zhou

Published: Mon, 24 Mar 2025 00:00:00 -0400

arXiv:2503.16761v1 Announce Type: new Abstract: Recent years have witnessed a great interest in orbital related electronics (also termed as orbitronics). In the current work, we present a first-principles density functional theory calculation on the orbital magnetic moments, intrinsic orbital Hall effect, and ordinary magnetoconductivity effects in rhombohedral graphene multilayers. Our calculations suggest a giant orbital moment that arises from inter-atomic cycloid motion, reaching over 30 muB under an intermediate gate voltage. This leads to a valley polarization under an external magnetic field, as observed in recent experiments [Nature 623, 41-47 (2023)]. In addition, the orbital-related transport feature exhibit significant responses that are potentially observed in experiments. We also suggest that under a periodic field driven (such as high frequency light field), the ungated graphene multilayers could host strong quantum anomalous and orbital Hall effects, engineered by the layer number. As the graphene multilayers are intrinsically nonmagnetic with negligible spin-orbit coupling, the orbital moments would not be entangled by spin-related signals. Thus, they serve as an ideal platform to conduct orbitronic measurements and utilization for next generation information read/write nanodevices.

Gate and Carriers tunable Valley Imbalance in Topological Proximitized Rhombohedral Trilayer Graphene

Authors: Sovan Ghosh, Bheema Lingam Chittari

Published: Mon, 24 Mar 2025 00:00:00 -0400

arXiv:2503.17098v1 Announce Type: new Abstract: We investigated the electronic structure, Fermi surface topology and the emergence of valley imbalance in rhombohedral trilayer graphene (RTG) induced by the topological proximity and the electric fields. We show that, a strong proximity strength isolates the unperturbed low energy bands at the charge neutrality and the isolated topological bands show metallic nature under the influence of applied electric fields. Our calculations indicate that valley-resolved metallic states with a finite Chern number $|C| =$3 can appear near charge neutrality for appropriate electric fields and second-nearest-neighbor strengths. The Fermi surface topology of these metallic bands greatly influenced by the applied electric fields and carrier doping. The valley imbalance lead to the dominant carriers of either $e^-$ or $h^+$ Fermi surface pockets and the choice of carriers is subjected to the direction of electric fields. The gate-tunable and carrier-induced valley imbalance in topologically proximated rhombohedral trilayer graphene may have potential applications toward the realization of superconductivity.

Phase-Coherent Dynamics in Intervalley Coherent States

Authors: Mainak Das, Chunli Huang

Published: Mon, 31 Mar 2025 00:00:00 -0400

arXiv:2503.22003v1 Announce Type: new Abstract: Electron transport driven by the phase coherence and interference of quantum many-body wavefunctions is a fascinating phenomenon with potential technological significance. Superconductivity, for example, enables dissipationless transport through macroscopic phase twisting. Similarly, in charge-density waves, once the phase degree of freedom-representing the collective position of electrons relative to the lattice-is depinned, it generates characteristic broadband noise and intriguing AC-DC interference patterns. In this work, we point out a phase-coherent transport phenomena in the intervalley coherent (IVC) state, also known as the bond-ordered or Kekule distorted state, frequently reported in rhombohedral multilayer graphene. Under a static magnetic field, the IVC state responds with an oscillating orbital magnetization, inducing an AC Hall effect similar to the AC Josephson effect in superconductors. In this analogy, the magnetic field acts as the DC voltage, while the oscillating magnetization acts as the AC Josephson current. We present detailed microscopic calculations for all the parameters of the phase-number free-energy in rhombohedral trilayer graphene, predicting an oscillation frequency of approximately 12 GHz at 0.1 Tesla. We comment on this phase-coherent transport in twisted homobilayer transition metal dichalcogenides, where the IVC state has been theoretically proposed.

Valley-dependent giant orbital moments and transport features in rhombohedral graphene multilayers

Authors: Xingchi Mu and Jian Zhou

Published: 2025-04-01T10:00:00+00:00

Author(s): Xingchi Mu and Jian Zhou

Light-element systems with marginal spin-orbital coupling effect serve as an excellent platform for investigating orbital degrees of freedom and exotic physical behaviors. Here, the authors determine via first-principles calculations the orbital magnetic moments, the orbital Hall effect, and the ordinary magnetoconductivity in gated rhombohedral multilayer graphene sheets. Furthermore, the topological properties can be effectively changed for the broken time-reversal symmetry, induced by Floquet light engineering. The study reveals the remarkable tunability of rhombohedral multilayer graphene in orbitronics, valleytronics, and multiferroic applications.

[Phys. Rev. B 111, 165102] Published Tue Apr 01, 2025

Quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity

Authors: Guodong Jiang, Tero Heikkil\"a, P\"aivi T\"orm\"a

Published: Mon, 07 Apr 2025 00:00:00 -0400

arXiv:2504.03617v1 Announce Type: new Abstract: We investigate the quantum geometry of rhombohedral graphite/graphene (RG) surface electronic states and its effects on superconductivity. We find that the RG surface bands have a non-vanishing quantum metric at the center of the drumhead region, and the local inequality between quantum metric and Berry curvature is an equality. Therefore, their quantum geometry is analogous to the lowest Landau level (LLL). The superconducting order parameters on the two surface orbitals of RG can be polarized by the surface potential, which boosts the superconducting transition in trilayer RG triggered by the displacement field. Analyzing the superfluid properties of multilayer RG, we make a connection with the topological heavy fermion model suggested to describe magic-angle twisted bilayer graphene (MATBG). It shows that RG fits in an unusual heavy-fermion picture with the flattest part of the surface bands carrying a nonzero supercurrent. These results may constrain the models constructed for the correlated phases of RG.

Superconductivity, Anomalous Hall Effect, and Stripe Order in Rhombohedral Hexalayer Graphene

Authors: Erin Morissette, Peiyu Qin, HT Wu, K. Watanabe, T. Taniguchi, J. I. A. Li

Published: Tue, 08 Apr 2025 00:00:00 -0400

arXiv:2504.05129v1 Announce Type: new Abstract: We report the discovery of a unique superconducting phase in rhombohedral hexalayer graphene characterized by its simultaneous emergence with both the anomalous Hall effect and stripe charge order. The onset of stripe charge order is revealed through angle-resolved transport measurements, which show thermally activated insulating behavior along one axis and highly conductive transport along the orthogonal direction. Superconductivity develops exclusively along the high-conductivity axis, giving rise to a one-dimensional-like superconducting channel. This superconducting state exhibits first-order transitions under an out-of-plane magnetic field, consistent with a chiral order parameter that breaks time-reversal symmetry. Most remarkably, thermally driven superconducting transitions display pronounced hysteresis-an uncommon phenomenon that reflects the complex interplay among stripe formation, broken time-reversal symmetry, and superconductivity. Together, these results uncover a previously unidentified quantum phase: a chiral superconductor embedded within an anomalous Hall crystal.

A controllable theory of superconductivity due to strong repulsion in a polarized band

Authors: Zhiyu Dong, Patrick A. Lee

Published: Tue, 08 Apr 2025 00:00:00 -0400

arXiv:2503.11079v2 Announce Type: replace Abstract: Can strong repulsive interactions be shown to give rise to pairing in a controllable way? We find that for a single flavor polarized band, there is a small expansion parameter in the low density limit, once the Bloch wavefunction form factor is taken into account. A perturbative expansion is possible, even if the interaction is much stronger than the Fermi energy $\epsilon_F$. We illustrate our method with a two-band model that is often used to describe multi-layer rhombohedral graphene and comment on the relationship with experiments.

Moir\'e enhanced flat band in rhombohedral graphene

Authors: Hongyun Zhang, Jinxi Lu, Kai Liu, Yijie Wang, Fei Wang, Size Wu, Wanying Chen, Xuanxi Cai, Kenji Watanabe, Takashi Taniguchi, Jose Avila, Pavel Dudin, Matthew D. Watson, Alex Louat, Takafumi Sato, Pu Yu, Wenhui Duan, Zhida Song, Guorui Chen, Shuyun Zhou

Published: Wed, 09 Apr 2025 00:00:00 -0400

arXiv:2504.06251v1 Announce Type: new Abstract: The fractional quantum anomalous Hall effect (FQAHE) is a fascinating emergent quantum state characterized by fractionally charged excitations in the absence of magnetic field,which could arise from the intricate interplay between electron correlation, nontrivial topology and spontaneous time-reversal symmetry breaking. Recently, FQAHE has been realized in aligned rhombohedral pentalayer graphene on BN superlattice (aligned R5G/BN), where the topological flat band is modulated by the moir\'e potential. However, intriguingly, the FQAHE is observed only when electrons are pushed away from the moir\'e interface. The apparently opposite implications from these experimental observations, along with different theoretical models, have sparked intense debates regarding the role of the moir\'e potential. Unambiguous experimental observation of the topological flat band as well as moir\'e bands with energy and momentum resolved information is therefore critical to elucidate the underlying mechanism. Here by performing nanospot angle-resolved photoemission spectroscopy (NanoARPES) measurements, we directly reveal the topological flat band electronic structures of R5G, from which key hopping parameters essential for determining the fundamental electronic structure of rhombohedral graphene are extracted. Moreover, a comparison of electronic structures between aligned and non-aligned samples reveals that the moir\'e potential plays a pivotal role in enhancing the topological flat band in the aligned sample. Our study provides experimental guiding lines to narrow down the phase space of rhombohedral graphene, laying an important foundation for understanding exotic quantum phenomena in this emerging platform.

Electrical switching of Chern insulators in moire rhombohedral heptalayer graphene

Authors: Zhiyu Wang, Qianling Liu, Xiangyan Han, Zhuoxian Li, Wenjun Zhao, Zhuangzhuang Qu, Chunrui Han, Kenji Watanabe, Takashi Taniguchi, Zheng Vitto Han, Sicheng Zhou, Bingbing Tong, Guangtong Liu, Li Lu, Jianpeng Liu, Fengcheng Wu, Jianming Lu

Published: Wed, 09 Apr 2025 00:00:00 -0400

arXiv:2503.00837v2 Announce Type: replace Abstract: In orbital Chern insulators, the chemical potential acts as a tuning knob to reverse chirality in dissipationless edge currents, enabling electric-field control of magnetic order-key for future quantum electronics. Despite the rise of orbital Chern insulators, electrically switchable quantum anomalous Hall effect (QAHE) remains rare, necessitating further investigation. Here, we demonstrate electric-field-induced reversal of orbital Chern insulators in a moire superlattice composed of rhombohedral heptalayer graphene (r-7LG) aligned with hexagonal boron nitride. At one electron per moire unit cell, two emerging Chern insulating phases - one pointing away from and the other toward graphene's charge neutrality point in the phase diagram of carrier density (n) versus magnetic field (B) - exhibit energetic competition modulated by both n and B. This switchable QAHE chirality in r-7LG demonstrates a layer-number dependent response: similar phenomena in moire r-6LG require much higher magnetic fields and are absent in thinner rhombohedral graphene. Our findings establish moire-engineered rhombohedral graphene as a promising platform for exploring topological quantum materials with electrically controllable chiral edge modes and magnetic order.

Momentum-Space AC Josephson Effect and Intervalley Coherence in Multilayer Graphene

Authors: Mainak Das, Chunli Huang

Published: Wed, 09 Apr 2025 00:00:00 -0400

arXiv:2503.22003v2 Announce Type: replace Abstract: Electron transport driven by the phase coherence and interference of quantum many-body wavefunctions is a fascinating phenomenon with potential technological significance. Superconductivity, for example, enables dissipationless transport through macroscopic phase twisting. Similarly, in charge-density waves, once the phase degree of freedom-representing the collective position of electrons relative to the lattice-is depinned, it generates characteristic broadband noise and intriguing AC-DC interference patterns. In this work, we point out a phase-coherent dynamics in the intervalley coherent (IVC) state, also known as the bond-ordered or Kekul\'e distorted state, frequently reported in rhombohedral multilayer graphene. Under a static magnetic field, the IVC state responds with an oscillating intervalley current, which in turn causes oscillating orbital magnetization, thereby inducing a detectable AC Hall effect. This mechanism mirrors the AC Josephson effect observed in superconductors but now happening in momentum space. In this analogy, the static magnetic field acts as the DC voltage, while the oscillating intervalley current assumes the role of the AC Josephson current. We present detailed microscopic calculations for all the parameters of the phase-number free-energy in rhombohedral trilayer graphene, predicting an orbital magnetization oscillation frequency of approximately 12 GHz at 0.1 Tesla. We comment on this phase-coherent dynamics in other 2D materials like twisted homobilayer transition metal dichalcogenides.

Microscopic theory of multiferroic behavior in rhombohedral multilayer graphene

Authors: Mainak Das and Chunli Huang

Published: 2025-04-08T10:00:00+00:00

Author(s): Mainak Das and Chunli Huang

We introduce a many-body state termed superpolarized electron-hole liquid to explain the multiferroic properties observed in a recent experiment on rhombohedral pentalayer graphene by Han et al. [Nature (London) 623, 41 (2023)]. Superpolarization refers to a state where electrons and holes are fully…

[Phys. Rev. B 111, L161106] Published Tue Apr 08, 2025

Rhombohedral graphite junctions as a platform for continuous tuning between topologically trivial and non-trivial electronic phases

Authors: Luke Soneji, Simon Crampin, Marcin Mucha-Kruczynski

Published: Thu, 10 Apr 2025 00:00:00 -0400

arXiv:2504.06759v1 Announce Type: new Abstract: Manipulating the topological properties of quantum states can provide a way to protect them against disorder. However, typically, changing the topology of electronic states in a crystalline material is challenging because their nature is underpinned by chemical composition and lattice symmetry that are difficult to modify. We propose junctions between rhombohedral graphite crystals as a platform that enables smooth transition between topologically trivial and non-trivial regimes distinguished by the absence or presence of topological junction states. By invoking an analogy with the Su-Schrieffer-Heeger model, the appearance of topological states is related to the symmetry of the atomic stacking at the interface between the crystals. The possibility to explore both the topological and non-topological phases is provided by sliding the crystals with respect to each other.

Optical imaging of spontaneous electric polarizations in tetralayer graphene

Authors: Zhou Zhou, Xiyao Peng, Jianfeng Bi, Fei Xue, Jie Jiang, Huizhen Wu, Zhiwen Shi, Haoliang Qian, Toshikaze Kariyado, Sihan Zhao

Published: Thu, 10 Apr 2025 00:00:00 -0400

arXiv:2504.06874v1 Announce Type: new Abstract: The recent discovery of sliding ferroelectricity has sparked intense interests in studying interfacial polarizations in two-dimensional (2D) van der Waals materials. However, akin to the conventional ferroelectrics, the studies have predominantly reported semiconducting and/or insulating moir\'e systems and binary compounds. Spontaneous electric polarizations in elemental metallic phases remain scarcity. Here, we report the first optical imaging of intrinsic out-of-plane electric polarizations and domain wall (DW) sliding dynamics in tetralayer graphene, a 2D conductive layer composed entirely of carbon. Using scanning near-field optical microscopy (SNOM), we directly visualize adjacent ABAC and ABCB stacking orders with intrinsic and opposite electric polarizations. Our gate-dependent SNOM measurements reveal distinct optical response that systematically changes upon carrier doping and unconventional interplay between DW sliding and electric polarizations, which are supported by density functional theory (DFT) calculations. Independent corroboration through Kelvin probe force microscopy (KPFM) and Raman spectroscopy confirms the polar nature and their polarization directions. Furthermore, reversible mechanical switching of polar states via atomic force microscopy (AFM) tip manipulation is also demonstrated. Our work establishes SNOM as a critical tool for probing sliding ferroelectricity in conductive 2D layers, opening avenues for exploring multiferroic behaviors and nonvolatile memory applications in atomically thin metals at room temperature.

Stacking-induced ferroelectricity in tetralayer graphene

Authors: Amit Singh, Shuigang Xu, Patrick Johansen Sarsfield, Pablo Diaz Nunez, Ziwei Wang, Sergey Slizovskiy, Nicholas Kay, Jun Yin, Yashar Mayamei, Takashi Taniguchi, Kenji Watanabe, Qian Yang, Kostya S. Novoselov, Vladimir I. Falko, Artem Mishchenko

Published: Fri, 11 Apr 2025 00:00:00 -0400

arXiv:2504.07935v1 Announce Type: new Abstract: Recent studies have reported emergent ferroelectric behavior in twisted or moir\'e-engineered graphene-based van der Waals heterostructures, yet the microscopic origin of this effect remains under debate. Pristine mono- or few-layer graphene lacks a permanent dipole due to its centrosymmetric lattice, making the emergence of ferroelectricity unlikely. However, mixed-stacked graphene, such as the ABCB tetralayer configuration, breaks both inversion and mirror symmetry and has been theoretically predicted to support electrically switchable dipoles. ABCB graphene represents the simplest natural graphene polytype exhibiting intrinsic out-of-plane polarization, arising from asymmetric charge carrier distribution across its layers. Here, we report robust ferroelectric behavior in dual-gated, non-aligned ABCB tetralayer graphene encapsulated in hexagonal boron nitride. The device exhibits pronounced hysteresis in resistance under both top and bottom gate modulation, with the effect persisting up to room temperature. This hysteresis originates from reversible layer-polarized charge reordering, driven by gate-induced transitions between ABCB and BCBA stacking configurations -- without requiring moir\'e superlattices. Our findings establish stacking-order-induced symmetry breaking as a fundamental route to electronic ferroelectricity in graphene and open pathways for non-volatile memory applications based on naturally occurring mixed-stacked multilayer graphene.

Band Renormalization, Quarter Metals, and Chiral Superconductivity in Rhombohedral Tetralayer Graphene

Authors: Guillermo Parra-Martinez, Alejandro Jimeno-Pozo, Vo Tien Phong, Hector Sainz-Cruz, Daniel Kaplan, Peleg Emanuel, Yuval Oreg, Pierre A. Pantaleon, Jose Angel Silva-Guillen, Francisco Guinea

Published: Tue, 15 Apr 2025 00:00:00 -0400

arXiv:2502.19474v2 Announce Type: replace Abstract: Recently, exotic superconductivity emerging from a spin-and-valley-polarized metallic phase has been discovered in rhombohedral tetralayer graphene. To explain this observation, we study the role of electron-electron interactions in driving flavor symmetry breaking, using the Hartree-Fock (HF) approximation, and in stabilizing superconductivity mediated by repulsive interactions. Though mean-field HF correctly predicts the isospin flavors and reproduces the experimental phase diagram, it overestimates the band renormalization near the Fermi energy and suppresses superconducting instabilities. To address this, we introduce a physically motivated scheme that includes internal screening in the HF calculation. Using this formalism, we find superconductivity arising from the spin-valley polarized phase for a range of electric fields and electron dopings. Our findings reproduce the experimental observations and reveal a p-wave, finite-momentum, time-reversal-symmetry-broken superconducting state, encouraging further investigation into exotic phases in graphene multilayers.

Superconductivity and quantized anomalous Hall in rhombohedral graphene

Authors: Youngjoon Choi, Ysun Choi, Marco Valentini, Caitlin L. Patterson, Ludwig F. W. Holleis, Owen I. Sheekey, Hari Stoyanov, Xiang Cheng, Takashi Taniguchi, Kenji Watanabe, Andrea F. Young

Published: Wed, 16 Apr 2025 00:00:00 -0400

arXiv:2408.12584v2 Announce Type: replace Abstract: Inducing superconducting correlations in chiral edge states is predicted to generate topologically protected zero energy modes with exotic quantum statistics. Experimental efforts to date have focused on engineering interfaces between superconducting materials typically amorphous metals and semiconducting quantum Hall or quantum anomalous Hall (QAH) systems. However, the interfacial disorder inherent in this approach can prevent the formation of isolated topological modes. An appealing alternative is to use low-density flat band materials where the ground state can be tuned between intrinsic superconducting and quantum anomalous Hall states using only the electric field effect. However, quantized transport and superconductivity have not been simultaneously achieved. Here, we show that rhombohedral tetralayer graphene aligned to a hexagonal boron nitride substrate hosts a quantized anomalous Hall state at superlattice filling $\nu=-1$ as well as a superconducting state at $\nu-3.5$ at zero magnetic field. Remarkably, gate voltage can also be used to actuate nonvolatile switching of the chirality in the quantum anomalous Hall state, allowing, in principle, arbitrarily reconfigurable networks of topological edge modes in locally gated devices. Thermodynamic compressibility measurements further reveal a topologically ordered fractional Chern insulator at $\nu=2/3$-also stable at zero magnetic field-enabling proximity coupling between superconductivity and fractionally charged edge modes. Finally, we show that, as in rhombohedral bi- and trilayers, integrating a transition metal dichalcogenide layer to the heterostructure nucleates a new superconducting pocket, while leaving the topology of the $\nu=-1$ quantum anomalous Hall state intact. Our results pave the way for a new generation of hybrid interfaces between superconductors and topological edge states in the low-disorder limit.

Superconductivity, Anomalous Hall Effect, and Stripe Order in Rhombohedral Hexalayer Graphene

Authors: Erin Morissette, Peiyu Qin, Hai-Tian Wu, Naiyuan J. Zhang, K. Watanabe, T. Taniguchi, J. I. A. Li

Published: Thu, 17 Apr 2025 00:00:00 -0400

arXiv:2504.05129v2 Announce Type: replace Abstract: Unconventional superconducting phases are distinguished by broken symmetries in their order parameters. Here, we report the discovery of an exotic superconducting phase in rhombohedral hexalayer graphene at high displacement fields, marked by its coexistence with both a stripe charge order and the anomalous Hall effect. In angle-resolved transport measurements, the onset of stripe order is manifested as thermally activated insulating behavior along one axis, with highly conductive transport along the orthogonal direction. Upon cooling, superconductivity emerges exclusively along the high-conductivity axis, forming one-dimensional-like superconducting channels. This anisotropic superconducting phase exhibits multiple first-order hysteretic transitions. Pronounced thermal hysteresis-between warming and cooling across the superconducting transition-suggests a melting transition of the underlying stripe phase. Additionally, magnetic-field-induced switching-similar to phenomena reported in tetra- and pentalayer graphene-supports the chiral nature of the superconducting state. Together, these findings identify a previously unrecognized quantum phase: a chiral superconductor embedded within a stripy Hall crystal.

Topologically enabled superconductivity: possible implications for rhombohedral graphene

Authors: Francesca Paoletti, Daniele Guerci, Giorgio Sangiovanni, Urban F. P. Seifert, Elio J. K\"onig

Published: Fri, 18 Apr 2025 00:00:00 -0400

arXiv:2504.13166v1 Announce Type: new Abstract: We present a topological mechanism for superconductivity emerging from Chern-2 insulators. While, naively, time-reversal symmetry breaking is expected to prevent superconductivity, it turns out that the opposite is the case: An explicit model calculation for a generalized attractive-U Haldane-Hubbard model demonstrates that superconductivity is only stabilized near the quantum anomalous Hall state, but not near a trivial, time-reversal symmetric band insulator. As standard Bardeen-Cooper-Schrieffer-like mean-field theory fails to capture any superconducting state, we explain this using an effective fractionalized field theory involving fermionic chargeons, bosonic colorons and an emergent U(1) gauge field. When the chargeons form a gapped topological band structure, the proliferation of single monopoles of this gauge field is forbidden. However, long-ranged monopole-antimonopole correlations emerge, and we argue that those correspond to superconducting order. Using random phase approximation on top of extensive slave-rotor mean-field calculations we characterize coherence length and stiffness of the superconductor. Thereby, we deduce the phase diagram in parameter space and furthermore discuss the effect of doping, temperature and an external magnetic field. We complement the fractionalized theory with calculations using an effective spin model and Gutzwiller projected wavefunctions. While mostly based on a simple toy model, we argue that our findings contribute to a better understanding of superconductivity emerging out of spin- and valley polarized rhombohedral graphene multilayers in a parameter regime with nearby quantum anomalous Hall insulators.

Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry

Authors: Ammar Jahin, Shi-Zeng Lin

Published: Wed, 23 Apr 2025 00:00:00 -0400

arXiv:2411.09664v2 Announce Type: replace Abstract: We study the effect of the electron wavefunction on Kohn-Luttinger superconductivity. The role of the wavefunction is encoded in a complex form factor describing the topology and geometry of the bands. We show that the electron wavefunction significantly impacts the superconducting transition temperature and superconducting order parameter. We illustrate this using the lowest Landau level form factor and find exponential enhancement of Tc for the resulting topological superconductor. We find that the ideal band geometry, which favors a fractional Chern insulator in the flat band limit, has an optimal Tc. Finally, we apply this understanding to a model relevant to rhombohedral graphene multilayers and unravel the importance of the band geometry for achieving robust superconductivity.

Tunable fractional Chern insulators in rhombohedral graphene superlattices

Authors: Jian Xie, Zihao Huo, Xin Lu, Zuo Feng, Zaizhe Zhang, Wenxuan Wang, Qiu Yang, Kenji Watanabe, Takashi Taniguchi, Kaihui Liu, Zhida Song, X. C. Xie, Jianpeng Liu, Xiaobo Lu

Published: 2025-04-22

Nature Materials, Published online: 22 April 2025; doi:10.1038/s41563-025-02225-7

The authors report their observation of the fractional quantum anomalous Hall effect in rhombohedral hexalayer graphene/hBN moiré superlattice devices.

Nanoscale infrared and microwave imaging of stacking faults in multilayer graphene

Authors: Ludwig Holleis, Liam Cohen, Noah Samuelson, Caitlin L. Patterson, Ysun Choi, Marco Valentini, Owen Sheekey, Youngjoon Choi, Jiaxi Zhou, Hari Stoyanov, Takashi Taniguchi, Kenji Watanabe, Qichi Hu, Jin Hee Kim, Cassandra Phillips, Peter De Wolf, Andrea F. Young

Published: Fri, 25 Apr 2025 00:00:00 -0400

arXiv:2504.17783v1 Announce Type: new Abstract: Graphite occurs in a range of metastable stacking orders characterized by both the number and direction of shifts between adjacent layers by the length of a single carbon-carbon bond. At the extremes are Bernal (or ``ABAB...'') stacking, where the direction of the interlayer shift alternates with each layer, and rhombohedral (or ``ABCABC...'') stacking order where the shifts are always in the same direction. However, for an N-layer system, there are in principle $N-1$ unique metastable stacking orders of this type. Recently, it has become clear that stacking order has a strong effect on the low energy electronic band structure with single-layer shifts completely altering the electronic properties. Most experimental work has focused on the extremal stacking orders in large part due to the difficulty of isolating and identifying intermediate orders. Motivated by this challenge, here we describe two atomic force microscopy (AFM) based techniques to unambiguously distinguish stacking orders and defects in graphite flakes. Photo-thermal infrared atomic force microscope (AFM-IR) is able to distinguish stacking orders across multiple IR wavelengths and readily provides absolute contrast via IR spectral analysis. Scanning microwave impedance microscopy (sMIM) can distinguish the relative contrast between Bernal, intermediate and rhombohedral domains. We show that both techniques are well suited to characterizing graphite van der Waals devices, providing high contrast determination of stacking order, subsurface imaging of graphene flakes buried under a hexagonal boron nitride (hBN) dielectric layer, and identifying nanoscale domain walls. Our results pave the way for the reliable fabrication of graphene multilayer devices of definite interlayer registry.

Micro-tip manipulated origami for robust twisted few-layer graphene

Authors: Ruo-Jue Zou, Long Deng, Si-Min Xue, Feng-Fei Cai, Ling-Hui Tong, Yang Zhang, Yuan Tian, Li Zhang, Lijie Zhang, Zhihui Qin, Long-Jing Yin

Published: Tue, 29 Apr 2025 00:00:00 -0400

arXiv:2504.18869v1 Announce Type: new Abstract: Twisted few-layer graphene (tFLG) has emerged as an ideal model system for investigating novel strongly correlated and topological phenomena. However, the experimental construction of tFLG with high structural stability is still challenging. Here, we introduce a highly accessible method for fabricating robust tFLG by polymer micro-tip manipulated origami. Through using a self-prepared polymer micro-tip, which is composed of multiple dimethylpolysiloxane, poly(vinyl chloride), and graphite sheets, to fold graphene layers, we fabricated tFLG with different twist angles (0{\deg}-30{\deg}) and various layers, including twisted bilayers (1+1), twisted double-bilayers (2+2), twisted double-trilayers (3+3), and thicker layers. Even ABC-stacked tFLG were created, such as twisted ABC/ABC and ABC/ABA graphene coexisting in an ABC-ABA domain wall region. We found that the origami-fabricated tFLG exhibits high stability against thermal and mechanical perturbations including heating and transferring, which could be attributed to its special folding and tearing structures. Moreover, based on the rich types of samples, we revealed twist-angle and stacking-order dependent Raman characteristics of tFLG, which is valuable for understanding the stacking-modulated phonon spectroscopy. Our experiments provide a simple and efficient approach to construct structurally robust tFLG, paving the way for the study of highly stable twisted van der Waals heterostructures.

Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene

Authors: Heqiu Li, B. Andrei Bernevig, Nicolas Regnault

Published: Wed, 30 Apr 2025 00:00:00 -0400

arXiv:2504.20140v1 Announce Type: new Abstract: We perform a multi-band exact diagonalization (ED) study of rhombohedral pentalayer graphene twisted on hexagonal boron nitride with a focus on fractional Chern insulators (FCI) in systems with weak moir\'e gaps, complementing the results of [Yu et al., arXiv:2407.13770]. We consider both the charge-neutrality (CN) and average (AVE) interaction schemes. Saliently and surprisingly, we now find using the particle entanglement spectrum that the FCI at filling factor 1/3 in the CN scheme predicted by single-(Hartree-Fock) band ED is unstable towards a transition to charge density wave once a small fraction of electrons is allowed to occupy the higher bands. Meanwhile, the FCI at filling 2/3 in the AVE scheme remains more robust under similar band mixing until being suppressed when increasing band mixing. To tackle truncation errors that arise from including multiple bands in larger system sizes, we propose an ED iteration method that iteratively optimizes the single-particle basis so that the particles in the ground state should reside mainly in the lowest band. Nevertheless, we find that the FCI gap remains absent after convergence when the mixing with higher bands is considered. These findings highlight the delicate sensitivity of FCIs to multi-band effects and the shortcoming of all of the current models to explain the experimental emergence of such phases.

From local spin nematicity to altermagnets: Footprints of band topology

Authors: Sanjib Kumar Das and Bitan Roy

Published: 2025-05-01T10:00:00+00:00

Author(s): Sanjib Kumar Das and Bitan Roy

Altermagnets are crystallographic rotational symmetry breaking spin-ordered states, possessing a net zero magnetization despite manifesting Kramer's nondegenerate bands. Here, we show that momentum-independent local spin-nematic orders in monolayer, Bernal bilayer, and rhombohedral trilayer graphene…

[Phys. Rev. B 111, L201102] Published Thu May 01, 2025

From local spin nematicity to altermagnets: Footprints of band topology

Authors: Sanjib Kumar Das, Bitan Roy

Published: Mon, 05 May 2025 00:00:00 -0400

arXiv:2403.14620v3 Announce Type: replace Abstract: Altermagnets are crystallographic rotational symmetry breaking spin-ordered states, possessing a net zero magnetization despite manifesting Kramer's non-degenerate bands. Here, we show that momentum-independent local spin nematic orders in monolayer, Bernal bilayer, and rhombohedral trilayer graphene give rise to $p$-wave, $d$-wave, and $f$-wave altermagnets, respectively, thereby inheriting the topology of linear, quadratic and cubic free fermion band dispersions that are also described in terms of angular momentum $\ell=1,\; 2$, and $3$ harmonics in the reciprocal space. The same conclusions also hold inside a spin-triplet nematic superconductor, featuring Majorana altermagnets. Altogether, these findings highlight the importance of electronic band structure in identifying such exotic magnetic orders in quantum materials. We depict the effects of in-plane magnetic fields on altermagnets, and propose spin-disordered alter-valley magnets in these systems.

Tunable Chern Insulators in Moir\'e-Distant and Moir\'e-Proximal Rhombohedral Pentalayer Graphene

Authors: Chushan Li, Zheng Sun, Kai Liu, Lei Qiao, Yifan Wei, Chuanqi Zheng, Chenyu Zhang, Kenji Watanabe, Takashi Taniguchi, Hao Yang, Dandan Guan, Liang Liu, Shiyong Wang, Yaoyi Li, Hao Zheng, Canhua Liu, Bingbing Tong, Li Lu, Jinfeng Jia, Zhiwen Shi, Jianpeng Liu, Guorui Chen, Tingxin Li, Xiaoxue Liu

Published: Tue, 06 May 2025 00:00:00 -0400

arXiv:2505.01767v1 Announce Type: new Abstract: Rhombohedral-stacked multilayer graphene aligned with hexagonal boron nitride has emerged as an excellent platform for investigating exotic quantum states arising from the interplay between electron correlations and topology. Here, we report the electrical transport properties of a rhombohedral pentalayer graphene/hexagonal boron nitride moir\'e device with a twist angle of 1.02{\deg} and a moir\'e period of approximately 10.1 nm. In this device, we observe anomalous Hall effects and integer Chern insulators in both moir\'e-proximal and moir\'e-distant regimes. Specifically, in the moir\'e-distant regime, an integer Chern insulator with Chern number C = 1 emerges at moir\'e filling {\nu} = 1 under a moderate magnetic field. In the moir\'e-proximal regime, we identify a rich set of topological and correlated phases near {\nu} = 1, including integer Chern insulator states with C = \pm 1 and trivial insulators, and they are highly sensitive to both the applied displacement field and magnetic field. Moreover, at {\nu} = 2 in the moir\'e-proximal regime, Chern insulators with C = \pm 1 has also been observed. Our results underscore the sensitivity of topological quantum states to the moir\'e potential strength and highlight the importance of twist-angle engineering in exploring novel quantum states in rhombohedral-stacked multilayer graphene moir\'e systems.

Transdimensional anomalous Hall effect in rhombohedral thin graphite

Authors: Qingxin Li, Hua Fan, Min Li, Yinghai Xu, Junwei Song, Kenji Watanabe, Takashi Taniguchi, Hua Jiang, X. C. Xie, James Hone, Cory Dean, Yue Zhao, Jianpeng Liu, Lei Wang

Published: Thu, 08 May 2025 00:00:00 -0400

arXiv:2505.03891v1 Announce Type: new Abstract: Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the intricate interplay between magnetic order and orbital motions of electrons[1-4]. In two dimensional (2D) systems, AHE is always coupled with out-of-plane orbital magnetization associated in-plane chiral orbital motions. In three dimensional (3D) systems, carriers can tunnel or scatter along the third dimension within the vertical mean free path lz. When sample thickness far exceeds lz, scattering disrupts coherent out-of-plane motion, making 3D AHE effectively a thickness-averaged 2D counterpart[4]- still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here, we explore an uncharted regime where the sample thickness is much larger than the atomic layer thickness yet smaller than or comparable to lz. In such "transdimensional" regime, carriers can sustain coherent orbital motions both within and out of the 2D plane, leading to a fundamentally new type of AHE that couples both out-of-plane and in-plane orbital magnetizations. We report the first observation of such phenomenon- transdimensional AHE (TDAHE)- in electrostatically gated rhombohedral ennealayer graphene. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron-electron interactions. Such TDAHE manifests as concurrent out-of-plane and in-plane Hall resistance hysteresis, controlled by external magnetic fields along either direction. Our findings unveils a new class of AHE, opening an unexplored paradigm for correlated and topological physics in transdimensional systems.

Superconductivity and spin canting in spin–orbit-coupled trilayer graphene

Authors: Caitlin L. Patterson, Owen I. Sheekey, Trevor B. Arp, Ludwig F. W. Holleis, Jin Ming Koh, Youngjoon Choi, Tian Xie, Siyuan Xu, Yi Guo, Hari Stoyanov, Evgeny Redekop, Canxun Zhang, Grigory Babikyan, David Gong, Haoxin Zhou, Xiang Cheng, Takashi Taniguchi, Kenji Watanabe, Martin E. Huber, Chenhao Jin, Étienne Lantagne-Hurtubise, Jason Alicea, Andrea F. Young

Published: 2025-05-07

Nature, Published online: 07 May 2025; doi:10.1038/s41586-025-08863-w

Introducing spin–orbit coupling by substrate proximity effect leads to an enhancement of superconducting phases in rhombohedral trilayer graphene.

Fermi lune and transdimensional orbital magnetism in rhombohedral multilayer graphene

Authors: Min Li, Qingxin Li, Xin Lu, Hua Fan, Kenji Watanabe, Takashi Taniguchi, Yue Zhao, Xin-Cheng Xie, Lei Wang, Jianpeng Liu

Published: Fri, 09 May 2025 00:00:00 -0400

arXiv:2505.05414v1 Announce Type: new Abstract: The symmetry and geometry of the Fermi surface play an essential role in governing the transport properties of a metallic system. A Fermi surface with reduced symmetry is intimately tied to unusual transport properties such as anomalous Hall effect and nonlinear Hall effect. Here, combining theoretical calculations and transport measurements, we report the discovery of a new class of bulk Fermi surface structure with unprecedented low symmetry, the ``Fermi lune", with peculiar crescent shaped Fermi energy contours, in rhombohedral multilayer graphene. This emergent Fermi-lune structure driven by electron-electron interactions spontaneously breaks time-reversal, mirror, and rotational symmetries, leading to two distinctive phenomena: giant intrinsic non-reciprocity in longitudinal transport and a new type of magnetism termed ``transdimensional orbital magnetism". Coupling the Fermi lune to a superlattice potential further produces a novel Chern insulator exhibiting quantized anomalous Hall effect controlled by in-plane magnetic field. Our work unveils a new symmetry breaking state of matter in the transdimensional regime, which opens an avenue for exploring correlated and topological quantum phenomena in symmetry breaking phases.

Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers $\mathcal{C} > 1$ in Twisted Rhombohedral Trilayer-Bilayer Graphene

Authors: Vo Tien Phong, Cyprian Lewandowski

Published: Wed, 14 May 2025 00:00:00 -0400

arXiv:2505.07981v1 Announce Type: new Abstract: Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moir\'{e} materials when a topologically nontrivial band with Chern number $\mathcal{C}=1$ is partially doped. Remarkably, superlattice Bloch bands can carry higher Chern numbers that defy the Landau-level paradigm and may even host exotic fractionalized states with non-Abelian quasiparticles. Inspired by this exciting possibility, we propose twisted \textit{rhombohedral} trilayer-bilayer graphene at $\theta \sim 1.2^\circ$ as a field-tunable quantum anomalous Chern insulator that features spectrally-isolated, kinetically-quenched, and topologically-nontrivial bands with $\mathcal{C} = 2,3$ favorable for fractional phases once fractionally doped, as characterized by their quantum geometry. Based on extensive self-consistent mean-field calculations, we show that these phases are stabilized by Coulomb interactions and are robust against variations in dielectric environment, tight-binding hopping parameters, and lattice relaxation.

High Chern Number Quantum Anomalous Hall States in Haldane-Graphene Multilayers

Authors: Yuejiu Zhao, Long Zhang, Fu-Chun Zhang

Published: Thu, 15 May 2025 00:00:00 -0400

arXiv:2505.09227v1 Announce Type: new Abstract: Quantum anomalous Hall (QAH) systems with high Chern number ($|C|>1$) are rare. This Letter introduces a Haldane-graphene multilayer heterostructure hosting QAH states with arbitrary Chern number. In a rhombohedral-stacked graphene $N$-layer, the Dirac points at $K_{\pm}$ become $N^\text{th}$-order zeros of the low-energy effective Hamiltonian. When an extra layer of Haldane model is stacked on top of the multilayer, the high-order Dirac points are gapped out and the heterostructure enters QAH phases with $|C|=N+1$. Therefore, gapping out high-order Dirac points paves a new way to high Chern number QAH states.

Electrochemical performance and diffusion kinetics of a NASICON type Na$_{3.3}$Mn$_{1.2}$Ti$_{0.75}$Mo$_{0.05}$(PO$_4$)$_3$/C cathode for low-cost sodium-ion batteries

Authors: Madhav Sharma, Rajendra S. Dhaka

Published: Mon, 19 May 2025 00:00:00 -0400

arXiv:2505.10572v1 Announce Type: cross Abstract: We report the electrochemical performance and diffusion kinetics of a newly designed NASICON type Na$_{3.3}$Mn$_{1.2}$Ti$_{0.75}$Mo$_{0.05}$(PO$_4$)$_3$/C composite material as a cathode for cost-effective sodium-ion batteries. A novel strategy of small Mo doping successfully stabilizes the sample having high Mn content in single phase rhombohedral symmerty. The high-resolution microscopy analysis reveals nanocrystallites of around $\sim$18 nm, uniformly embedded within the semi-graphitic carbon matrix, which enhances the surface electronic conductivity and effectively shortens the sodium-ion diffusion path. More importantly, we demonstrate a stable electrochemical behavior, with enhanced discharge capacity of 124 mAh/g at 0.1 C, having good reversibility and retaining 77\% of its capacity after 300 cycles, and 70\% even after 400 cycles at 2 C. The sodium-ion diffusion coefficients, estimated using both galvanostatic intermittent titration technique (GITT) and cyclic voltammetry are found to lie within the range of $10^{-9}$ to $10^{-11}$~cm$^2$/s. Additionally, the bond-valence site energy mapping predicted a sodium-ion migration energy barrier of 0.76 eV. A detailed distribution of relaxation times (DRT) analysis is used to deconvolute the electrochemical impedance spectra into distinct processes based on their characteristic relaxation times. Notably, the solid-state diffusion of sodium ions within the bulk electrode, with a relaxation time of $\sim$50 s, shows a consistent trend with the diffusion coefficients obtained from GITT and Warburg-based evaluations across the state of charge.

Intrinsic layer polarization and multi-flatband transport in non-centrosymmetric mixed-stacked multilayer graphene

Authors: Kai Liu, Yating Sha, Bo Yin, Shuhan Liu, Yulu Ren, Zhongxun Guo, Jingjing Gao, Ming Tian, Neng Wan, Kenji Watanabe, Takashi Taniguchi, Bingbing Tong, Guangtong Liu, Li Lu, Yuanbo Zhang, Weidong Luo, Zhiwen Shi, Quansheng Wu, Guorui Chen

Published: Tue, 20 May 2025 00:00:00 -0400

arXiv:2505.12478v1 Announce Type: new Abstract: Graphene multilayers exhibit electronic spectra that depend sensitively on both the number of layers and their stacking order. Beyond trilayer graphene, mixed stacking sequences (alternating Bernal and rhombohedral layers) give rise to multiple coexisting low-energy bands. Here we investigate ABCBC-stacked pentalayer graphene, a less-studied non-centrosymmetric mixed sequence. This stacking can be regarded as an ABC (rhombohedral) trilayer on top of an AB (Bernal) bilayer, so its low-energy band structure contains both a cubic band and a parabolic band that hybridize. In transport measurements, we observe an intrinsic band gap at charge neutrality whose magnitude changes asymmetrically under an applied perpendicular displacement field. This behavior reflects the spontaneous layer polarization inherent to the broken inversion symmetry and mirror symmetry. By tuning the displacement field and carrier density, we drive multiple Lifshitz transitions in the Fermi surface topology and realize Landau levels with different degeneracies arising from the multi-flatband system. Remarkably, a v = -6 quantum Hall state emerges at an exceptionally low magnetic field (~20 mT), indicating the interplay between spontaneous symmetry breaking and Berry curvatures. Our results establish mixed-stacked multilayer graphene as a tunable platform with various broken symmetries and multiple flatbands, suitable for exploring emergent correlated electronic states.

Intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene

Authors: Yang-Zhi Chou, Jihang Zhu, Sankar Das Sarma

Published: Tue, 20 May 2025 00:00:00 -0400

arXiv:2409.06701v2 Announce Type: replace Abstract: We study the intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene, which has been discovered experimentally in Han $et$ $al$ arXiv:2408.15233. We construct a minimal model for the intravalley spin-polarized superconductivity, assuming a simplified anisotropic interaction that depends only on the angle between the incoming and outgoing momenta. Despite the absence of \textit{Fermi surface nesting}, we show that superconductivity can emerge near the Van Hove singularity with the maximal $T_c$ near a bifurcation point of the peaks in the density of states. We identify the $p+ip$, $h+ih$, and the nodal $f$-wave pairings as the possible states, which are all pair density wave orders due to the intravalley nature. Furthermore, these pair density wave orders require a finite attractive threshold for superconductivity, resulting in {a narrow stripe shape of superconducting region}, consistent with experimental findings. We point out that the Kohn-Luttinger mechanism is a plausible explanation with a dominant $p+ip$ pairing. The possibility of realizing intravalley spin-polarized superconductivity in other rhombohedral graphene systems is also discussed.