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  • Open Access

Berry Phase Dynamics of Sliding Electron Crystals

Yongxin Zeng1,* and Andrew J. Millis1,2

  • *Contact author: yz4788@columbia.edu
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Phys. Rev. X 15, 031059 – Published 28 August, 2025

DOI: https://doi.org/10.1103/g1l3-5x6f

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 nonvanishing 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 noninvariance 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.

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Popular Summary

In a low-density electron gas, the repulsion between electrons can dominate over their individual motion, causing them to form an ordered “electron crystal” known as a Wigner crystal. In some materials with special electronic structures, such as rhombohedral graphene, theory predicts a new kind of electron crystal called an anomalous Hall crystal. This state is topologically nontrivial and can display the quantum anomalous Hall effect, where edge currents with quantized conductance flow in the absence of an external magnetic field. Because these crystals can slide collectively, we ask a new question: When an anomalous Hall crystal slides, does it move sideways?

We address this by deriving the semiclassical equations of motion for sliding anomalous Hall crystals. Our analysis reveals that they do indeed develop a transverse velocity when driven by an electric field. The key reason is that the relationship between motion and momentum is altered by nontrivial quantum geometry of the electron states. This breaks Galilean invariance, meaning that shifting to a moving reference frame no longer gives an equivalent crystal state. Using both analytical models and numerical simulations for rhombohedral pentalayer graphene, we find that this effect changes the sliding behavior and makes the Hall conductance generally unquantized.

Our results establish a theoretical foundation for understanding the motion of anomalous Hall crystals. Going forward, including the effects of disorder pinning and scattering will allow for concrete predictions that can be tested in experiments. More broadly, our work highlights how quantum geometry can influence the dynamics of states that break spatial symmetries.

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Phys. Rev. X 15, 031059– Published 28 August, 2025
  • Received 15 December 2024
  • Revised 6 June 2025
  • Accepted 5 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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