Berry Phase Dynamics of Sliding Electron Crystals

Abstract

Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a non-vanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system's nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean non-invariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

References in corpus (25)

• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Semiclassical theories of the anomalous Hall effect
• Quantum cascade of new correlated phases in trigonally warped bilayer graphene
• Chiral plasmons without magnetic field
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene I: Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field
• Electric polarization in a Chern insulator
• Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures
• Dynamical response of a weakly pinned two-dimensional Wigner crystal
• Dynamical response of a pinned two-dimensional Wigner crystal
• Dynamical properties of the pinned Wigner crystal
• Theory of fractional Chern insulator states in pentalayer graphene moiré superlattice
• 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
• Sublattice structure and topology in spontaneously crystallized electronic states
• 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
• Intertwined fractional quantum anomalous Hall states and charge density waves
• Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
• Interaction-driven (quasi-) insulating ground states of gapped electron-doped bilayer graphene
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
• Evidence of zero-field Wigner solids in ultra-thin films of cadmium arsenide
• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect

Cited by in corpus (6)

• Phonons in Electron Crystals with Berry Curvature
• Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The ${\lambda }_N$-Jellium model
• Superfluid stiffness bounds in time-reversal symmetric superconductors
• Various electronic crystal phases in rhombohedral graphene multilayers
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Spin-triplet paired Wigner crystal stabilized by quantum geometry