Quantum phase diagram of a Moiré-Hubbard model

We theoretically study a generalized Hubbard model on Moir\'e superlattices of twisted bilayers, and find very rich filling-factor-dependent quantum phase diagrams tuned by interaction strength and twist angle. Strong long-range Coulomb interaction in the Moir\'e-Hubbard model induces Wigner crystals at a series of fractional filling factors. The effective lattice of the Wigner crystal is controlled by the filling factor, and can be triangle, rectangle, honeycomb, kagome, etc., providing a single platform to realize many different spin models on various lattices by simply tuning carrier density. In addition to Wigner crystals that are topologically trivial, interaction-induced Chern insulators emerge in the phase diagram. This finding paves a way for engineering interaction-induced quantum anomalous Hall effect in Moir\'e-Hubbard systems where the corresponding single-particle Moir\'e band is topologically trivial.