Quantum Phase Diagram of a Moir\'e-Hubbard Model

TL;DR

This paper explores a generalized moiré-Hubbard model revealing diverse quantum phases, including Wigner crystals and Chern insulators, tunable by filling factor, interaction strength, and twist angle, offering a platform for novel quantum states.

Contribution

It introduces a comprehensive theoretical study of a moiré-Hubbard model showing how various lattice geometries and topological phases emerge from electron interactions and filling factors.

Findings

Wigner crystals form at fractional fillings with various lattice geometries.

Interaction-induced Chern insulators can appear even in topologically trivial bands.

The model enables tuning between different quantum phases by adjusting carrier density.

Abstract

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.