Interaction-Driven Filling-Induced Metal-Insulator Transitions in 2D Moiré Lattices

Using a realistic band structure for twisted WSe$_2 $ materials, we develop a theory for the interaction-driven correlated insulators to conducting metals transitions through the tuning of the filling factor around commensurate fractional fillings of the moir\'e unit cell in the 2D honeycomb lattice, focusing on the dominant half-filled Mott insulating state, which exists for both long- and short-range interactions. We find metallic states slightly away from half-filling, as have recently been observed experimentally. We discuss the stabilities and the magnetic properties of the resulting insulating and metallic phases, and comment on their experimental signatures. We also discuss the nature of the correlated insulator states at the rational fractional fillings.