Electronic structures, charge transfer and charge orders in twisted transition metal dichalcogenide bilayers.

Moire superlattices of transition metal dichalcogenide (TMD) bilayers have been shown to host correlated electronic states, which arises from the interplay of emergent moire potential and long-range Coulomb interactions. Here we theoretically investigate structural relaxation and single-particle electronic properties in moire superlattices of transition metal dichalcogenide homobilayer and study the ground state charge orders in the effective honeycomb lattice of MX and XM region. From the large-scale density functional theory calculation and continuum model with layer degrees of freedom, we find that the out of plane gating field creates a tunable charge transfer gap and introduces a mass term in the Dirac spectrum. At the flat band limit, we observe a series of charge-ordered insulating states at various filling n = 1/4, 1/3, 1/2, 2/3, 1 with Monte Carlo simulations, and predict that gating field induces a phase transition between different electron crystals at fixed filling n = 1/2, 2/3. Our work demonstrates that transition metal dichalcogenide homobilayer provides a powerful platform for the investigation of tunable charge transfer insulator and charge orders.