Parent Berry curvature and the ideal anomalous Hall crystal

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 leads 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. We further show that the resulting quasiparticle bands are "ideal" for realizing fractionalized topological states. Our theory provides a unified perspective for understanding several aspects of the recently observed integer and fractional quantum anomalous Hall effects in rhombohedral pentalayer graphene.