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.

15+10 pages, 9+5 figures

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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