Theory of anomalous Hall crystals

The anomalous Hall crystal is a two-dimensional electron crystal state that spontaneously breaks continuous translational symmetry at low electron density, similar to the Wigner crystal, but different in that it is topologically nontrivial and thus exhibits the quantum anomalous Hall effect. First proposed in the context of rhombohedral pentalayer graphene, the anomalous Hall crystal more generally appears in two-dimensional electron systems with strong quantum geometry effects as an intermediate state between the Fermi liquid and Wigner crystal states. In this talk I will first present the energetic competition between the Wigner crystal and anomalous Hall crystal in a general electron system with nontrivial quantum geometry [1], and then derive a set of semiclassical equations that describe the sliding dynamics of both types of crystals in the absence of impurities. I will show that nontrivial quantum geometry and the associated violation of Galilean invariance play a crucial role in the static and dynamic properties of anomalous Hall crystals.

[1] Y. Zeng, D. Guerci, V. Crépel, A. J. Millis, and J. Cano, Phys. Rev. Lett. 132, 236601 (2024).