Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures

Abstract

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 perpendicular displacement field, and correspond, experimentally, to full or partial filling of a valley polarized Chern-$1$ band. Such a band is absent in the non-interacting band structure. Here we show that electron-electron interactions play a crucial role, and present microscopic theoretical calculations demonstrating the emergence of a nearly flat, isolated, Chern-$1$ band and FQAH phases in this system. We also study the four and six-layer analogs and identify parameters where a nearly flat isolated Chern-$1$ band emerges which may be suitable to host FQAH physics.

5+9 pages, 7+9 figures; the first two authors contributed equally to this work

References in corpus (24)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• 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
• 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
• Origin of band gaps in graphene on hexagonal boron nitride
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• Fractional Chern Insulator in Twisted Bilayer MoTe${}_2$
• Fractional quantum anomalous Hall states in twisted bilayer MoTe${}_2$ and WSe${}_2$
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Cascade of isospin phase transitions in Bernal bilayer graphene at zero magnetic field
• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
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• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
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Cited by in corpus (55)

• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• 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
• 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
• Single-particle spectral function of fractional quantum anomalous Hall states
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• 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
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Berry Phase Dynamics of Sliding Electron Crystals
• 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
• Valley-dependent giant orbital moments and transport feature in rhombohedral graphene multilayers
• Correlated phases 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
• Anisotropic moiré band flattening in twisted bilayers of M-valley MXenes
• Ordering the topological order in the fractional quantum Hall effect
• Designing (higher) Hall crystals
• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States
• Purely electronic model for exciton-polaron formation in moiré heterostructures
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Full, three-quarter, half and quarter Wigner crystals in Bernal bilayer graphene
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe${}_2$
• Various electronic crystal phases in rhombohedral graphene multilayers
• Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe${}_2$
• Unconventional superconductivity mediated by exciton density wave fluctuations
• Charge ordering and spontaneous topological Hall effect in bilayer skyrmion crystals
• Quantum melting a Wigner crystal into Hall liquids
• General Many-Body Perturbation Framework for Moiré Systems
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Charge density waves and stripes in quarter metals of graphene heterostructures
• Topological Order Without Band Topology in Moiré Graphene
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals