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.

References in corpus (36)

• Maximally-localized generalized Wannier functions for composite energy bands
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Maximally localized Wannier functions: Theory and applications
• Maximally-localized Wannier functions for entangled energy bands
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Intrinsic quantized anomalous Hall effect in a moiré heterostructure
• Optical detection of Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Topological insulators in twisted transition metal dichalcogenide homobilayers
• Topological Mott Insulators
• Quantum anomalous Hall effect from intertwined moiré bands
• Colloquium: Quantum anomalous Hall effect
• Pseudospin Magnetism in Graphene
• Signatures of bilayer Wigner crystals in a transition metal dichalcogenide heterostructure
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Exact Landau Level Description of Geometry and Interaction in a Flatband
• Wigner crystallization and metal-insulator transition of two-dimensional holes in GaAs/AlGaAs at B=0
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides
• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• Stability, dynamical properties and melting of a classical bi-layer Wigner Crystal
• Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene
• Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
• Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study
• Lindemann melting criterion in two dimensions
• Observation of Spontaneous Ferromagnetism in a Two-Dimensional Electron System
• Pseudospin Order in Monolayer, Bilayer, and Double-Layer Graphene
• Ideal Chern bands are Landau levels in curved space
• Topological Insulating States in Laterally Patterned Ordinary Semiconductors
• Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers
• Wigner crystallization in transition metal dichalcogenides: A new approach to correlation energy
• Massive Dirac fermions in moiré superlattices: a route towards topological flat minibands
• Gate-tunable topological phases in superlattice modulated bilayer graphene
• Chiral model of twisted bilayer graphene realized in a monolayer
• Tuning the topological insulator states of artificial graphene
• Realizing Topological Mott Insulators from the RKKY Interaction

Cited by in corpus (24)

• Stability of Anomalous Hall Crystals in multilayer rhombohedral graphene
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Parent Berry curvature and the ideal anomalous Hall crystal
• 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