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

Abstract

Recent experiments on rhombohedral pentalayer graphene flakes with a substrate induced moiré potential have identified both Chern insulators and fractional Quantum Hall states in the absence of an applied magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moiré lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles we study an interacting model of electrons in this geometry, first within the self-consistent Hartree-Fock (SCHF) approximation. We find an isolated Chern band with Chern number $|C|=1$, that moreover is relatively flat and shows good quantum geometry. Exact diagonalization and density matrix renormalization group methods at fractional filling establish the presence of fractional quantum anomalous Hall (FQAH) states. The $|C|=1$ band in SCHF is remarkably robust to varying microscopic parameters, and is also found in the $N_L=4$ and $N_L=6$ layer systems. Remarkably, it appears stable even to switching off the moiré potential, pointing to spontaneous breaking of translation symmetry. We term this topological crystalline state the ``anomalous Hall crystal" (AHC), and argue that it constitutes a general mechanism for creating stable Chern bands in rhombohedral graphene. Our work elucidates the physics behind the recent rhombohedral pentalayer graphene observations, predicts the appearance of the same phase in other systems, and opens the door to studying the interplay between electronic topology and spontaneous translation symmetry breaking.

5+9 pages, 4+4 figures

References in corpus (56)

• The electronic properties of graphene
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional quantum Hall effect in the absence of Landau levels
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
• Superconductivity in rhombohedral trilayer graphene
• Band Structure of ABC-Stacked Graphene Trilayers
• Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Spin-Orbit Enhanced Superconductivity in Bernal Bilayer Graphene
• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Quantum cascade of new correlated phases in trigonally warped bilayer graphene
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• Programming Correlated Magnetic States via Gate Controlled Moiré Geometry
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Orbital Multiferroicity in Pentalayer Rhombohedral Graphene
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene
• Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
• Mapping twist-tuned multiband topology in bilayer WSe${}_2$
• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Moiré band model and band gaps of graphene on hexagonal boron nitride
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Pressure--enhanced fractional Chern insulators in moiré transition metal dichalcogenides along a magic line
• Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Interaction-driven topological phase diagram of twisted bilayer MoTe${}_2$
• Ideal Chern bands are Landau levels in curved space
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Unrestricted Hartree-Fock theory of Wigner crystals
• Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity
• Theory of tunable flux lattices in the homobilayer moiré of twisted and uniformly strained transition metal dichalcogenides
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Electrical control of spin and valley in spin-orbit coupled graphene multilayers
• Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices
• Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
• Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study
• Strong correlations in ABC-stacked trilayer graphene: Moiré is important
• Stability of fractional Chern insulators with a non-Landau level continuum limit
• Moiré phonons in graphene/hexagonal boron nitride moiré superlattice
• Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides

Cited by in corpus (61)

• A Microscopic Perspective on Moiré Materials
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Tunable moiré materials for probing Berry physics and topology
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Parent Berry curvature and the ideal anomalous Hall crystal
• Moiré Fractional Chern Insulators III: Hartree-Fock Phase Diagram, Magic Angle Regime for Chern Insulator States, the Role of the Moiré Potential and Goldstone Gaps in Rhombohedral Graphene Superlattices
• Band structure engineering using a moiré polar substrate
• Topological electronic crystals in twisted bilayer-trilayer graphene
• Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
• Theory of Generalized Landau Levels and Implication for non-Abelian States
• Higher vortexability: zero field realization of higher Landau levels
• Fractional quantum anomalous Hall effect in a singular flat band
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice
• A New Moiré Platform Based on M-Point Twisting
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Phonons in Electron Crystals with Berry Curvature
• $\lambda$-Jellium Model for the Anomalous Hall Crystal
• Spontaneous vortex-antivortex lattice and Majorana fermions in rhombohedral graphene
• High spatial resolution charge sensing of quantum Hall states
• Quarter Metal Superconductivity
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• Single-particle spectral function of fractional quantum anomalous Hall states
• Electric-field switchable chirality in rhombohedral graphene Chern insulators stabilized by tungsten diselenide
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Broken Symmetry in Ideal Chern Bands
• Berry Phase Dynamics of Sliding Electron Crystals
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Fractional Chern insulator states in an isolated flat band of zero Chern number
• Artificial moiré engineering for an ideal BHZ model
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Quantum anomalous Hall effects and emergent $\mathrm{SU}(2)$ Hall ferromagnets at fractional filling of helical trilayer graphene
• Multi-Band Exact Diagonalization and an Iteration Approach to Hunt For Fractional Chern Insulators in Rhombohedral Multilayer Graphene
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Real-space study of zero-field correlation in tetralayer rhombohedral graphene
• Purely electronic model for exciton-polaron formation in moiré heterostructures
• Ordering the topological order in the fractional quantum Hall effect
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• Designing (higher) Hall crystals
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Various electronic crystal phases in rhombohedral graphene multilayers
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Quantum melting a Wigner crystal into Hall liquids
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• General Many-Body Perturbation Framework for Moiré Systems
• Instability of Laughlin FQH liquids into gapless power-law correlated states with continuous exponents in ideal Chern bands: rigorous results from plasma mapping
• Topological Order Without Band Topology in Moiré Graphene