Engineering interaction-induced topological crystals in 2d heterostructures

We introduce a novel platform for realizing interaction-induced Hall crystals with diverse Chern numbers C. This platform consists of a two-dimensional semiconductor or graphene subjected to an out-of-plane magnetic field and a one-dimensional modulation, which can be realized by moir\'e or dielectric engineering. We show that interactions drive the system to spontaneously break the residual translational symmetry, resulting in Hall crystals with various C (including |C|>1). Remarkably, these phases persist across continuous ranges of filling and magnetic field, and the global phase diagram can be understood in a unified manner.

We also discuss magnetism in topological crystals, particularly anomalous Hall crystals, motivated by rhombohedral pentalayer graphene. While (trivial) Wigner crystals typically form a triangular lattice, topological crystals typically form a honeycomb. Within Hartree-Fock theory, we identify regimes in which the magnetic order is an antiferromagnet, which is naturally unfrustrated on the honeycomb in contrast with the triangular lattice. We also describe the melting into a paramagnetic or spin-polarized Fermi liquid, the latter of which is never realized in the trivial Wigner crystal phase diagram.