Parent Berry curvature and the ideal anomalous Hall crystal

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.

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Cited by in corpus (29)

• Topological electronic crystals in twisted bilayer-trilayer graphene
• Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene
• Quantum Geometric Kohn-Luttinger Superconductivity
• Extended quantum anomalous Hall effect in moiré structures: phase transitions and transport
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