Designing Hall crystals with variable Chern numbers.

Topological electronic crystals are electron crystals in which spontaneously broken translation symmetry coexists with or gives rise to a nontrivial topological response. Here, we introduce a novel platform and analytical theory for realizing interaction-induced Hall crystals, a class of topological electronic crystals, with various Chern numbers C. The platform consists of a two-dimensional semiconductor subjected to an out-of-plane magnetic field and one-dimensional modulation, which can be realized by moiré or dielectric engineering. Interactions drive the system to spontaneously break the residual translational symmetry, resulting in anisotropic Hall crystals with various C, including ∣C∣ > 1, tunable by field. Remarkably, these persist across continuous ranges of filling and field, and the global phase diagram can be understood in a unified manner.