Sublattice structure and topology in spontaneously crystallized electronic states

Abstract

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. In this Letter, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective `time-reversal symmetry' and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

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• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
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• 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
• Berry Phase Dynamics of Sliding Electron Crystals
• 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-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• 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
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Spin-triplet paired Wigner crystal stabilized by quantum geometry
• Topological Order Without Band Topology in Moiré Graphene
• Doping-induced Quantum Anomalous Hall Crystals and Topological Domain Walls
• Elementary Excitations, Melting Temperature, and Correlation Energy in Wigner Crystals
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature