Parent Berry curvature and the ideal anomalous Hall crystal

TL;DR

This paper investigates how strong interactions in a system with uniform Berry curvature can lead to a topologically nontrivial crystal state with spontaneous translation symmetry breaking, relevant to quantum anomalous Hall effects.

Contribution

It introduces a model linking Berry curvature to the formation of anomalous Hall crystals and explores the effects of electrostatic potentials on topological states.

Findings

High Berry curvature induces anomalous Hall crystal formation.

Electrostatic potentials can create states with opposite Chern numbers.

Provides a framework for understanding quantum anomalous Hall effects in multilayer graphene.

Abstract

We study a model of electrons moving in a parent band of uniform Berry curvature. At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. Our results are established via a mapping to a problem of Wigner crystallization in a regular 2D electron gas. Interestingly, we find that a periodic electrostatic potential induces a competing state with opposite Chern number. Our theory offers a unified perspective for understanding several aspects of the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral multilayer graphene and provides a recipe for engineering new topological states.