Exact diagonalization studies of semiconductor moiré materials

Semiconductor moiré materials based on transition metal dichalcogenides (TMDs) provide a platform to study the interplay between strong electronic correlations and band topology, promising to reveal new quantum phases of matter. Depending on the TMD monolayer constituents, topologically trivial or non-trivial flat bands, that are well described by low-energy continuum models, are expected in these systems. We use exact diagonalization to study moiré TMD continuum models projected to the topmost flat band. For C = 0 bands, we investigate the correlated insulating states at half- and fractional-fillings, determining their magnetic properties and how phase transitions from antiferromagnetic to ferromagnetic ground states can take place. For C = 1 bands, we study the feasibility of fractional Chern insulating ground states and their instability towards a charge density wave phase. We suggest guiding principles for the phase transitions and discuss possible realizations in experiments.