Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model

Abstract

We propose a minimal "three-patch model" for the anomalous Hall crystal (AHC), a topological electronic state that spontaneously breaks both time-reversal symmetry and continuous translation symmetry. The proposal for this state is inspired by the recently observed integer and fractional quantum Hall states in rhombohedral multilayer graphene at zero magnetic field. There, interaction effects appear to amplify the effects of a weak moiré potential, leading to the formation of stable, isolated Chern bands. It has been further shown that Chern bands are stabilized in mean field calculations even without a moiré potential, enabling a realization of the AHC state. Our model is built upon the dissection of the Brillouin zone into patches centered around high symmetry points. Within this model, the wavefunctions at high symmetry points fully determine the topology and energetics of the state. We extract two quantum geometrical phases of the non-interacting wavefunctions that control the stability of the topologically nontrivial AHC state. The model predicts that the AHC state wins over the topological trivial Wigner crystal in a wide range of parameters, and agrees very well with the results of full self-consistent Hartree-Fock calculations of the rhombohedral multilayer graphene Hamiltonian.

arXiv comment15+10 pages, 9+5 figures

References in corpus (54)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological quantum chemistry
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice
• Chiral superconductivity from repulsive interactions in doped graphene
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Fractional Chern Insulator
• Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites
• Topological Flat Band Models and Fractional Chern Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Band Structure of ABC-Stacked Graphene Trilayers
• Nearly Flat Chern Bands in Moiré Superlattices
• Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene
• Ab-Initio Theory of Moiré Superlattice Bands in Layered Two-Dimensional Materials
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Electronic properties of graphene hexagonal boron nitride moiré superlattice
• Signatures of bilayer Wigner crystals in a transition metal dichalcogenide heterostructure
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Truncation of a 2-dimensional Fermi surface due to quasiparticle gap formation at the saddle points
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs/AlGaAs at B=0
• Spin-fermion model near the quantum critical point: one-loop renormalization group results
• Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices
• Band Representations and Topological Quantum Chemistry
• Magnetic texture-induced thermal Hall effects
• Superconductivity from weak repulsion in hexagonal lattice systems
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• Competing correlated states around the zero field Wigner crystallization transition of electrons in two-dimensions
• Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Density-functional investigation of rhombohedral stacks of graphene: topological surface states, nonlinear dielectric response, and bulk limit
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• Experimental determination of the energy per particle in partially filled Landau levels
• Microscopic verification of topological electron-vortex binding in the lowest-Landau-level crystal state
• Competing Crystal Phases in the Lowest Landau Level
• Quantum anomalous Hall crystal at fractional filling of moiré superlattices
• Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis
• Sublattice structure and topology in spontaneously crystallized electronic states
• Topological flat bands in rhombohedral tetralayer and multilayer graphene on hexagonal boron nitride moire superlattices
• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Magnetic skyrmion crystal at a topological insulator surface
• Topological magnetic textures in magnetic topological insulators
• Electron-solid and electron-liquid phases in graphene
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Renormalization Group Analysis of a Fermionic Hot Spot Model

Cited by in corpus (29)

• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Topological electronic crystals in twisted bilayer-trilayer graphene
• Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• Efficient prediction of superlattice and anomalous miniband topology from quantum geometry
• Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field
• Phonons in Electron Crystals with Berry Curvature
• $\lambda$-Jellium Model for the Anomalous Hall Crystal
• Layer-Dependent Quantum Anomalous Hall Effect in Rhombohedral Graphene
• Quantum anomalous Hall crystals in moiré bands with higher Chern number
• Quantum anomalous, spin, and valley Hall effects in pentalayer rhombohedral graphene moiré superlattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene
• Berry Phase Dynamics of Sliding Electron Crystals
• 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
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Generic integer and fractional quantum anomalous Hall crystals from interaction-driven band folding
• Berry Curvature of Low-Energy Excitons in Rhombohedral Graphene
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Various electronic crystal phases in rhombohedral graphene multilayers
• Higher Chern bands in helical homotrilayer transition metal dichalcogenides
• Continuous transition and gapless roton inside fractional quantum anomalous Hall states
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Topological Order Without Band Topology in Moiré Graphene
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Quantum melting a Wigner crystal into Hall liquids