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Moire superlattices of transition metal dichalcogenide (TMD) bilayers havebeen shown to host correlated electronic states, which arises from theinterplay of emergent moire potential and long-range Coulomb interactions. Herewe theoretically investigate structural relaxation and single-particleelectronic properties in moire superlattices of transition metal dichalcogenidehomobilayer and study the ground state charge orders in the effective honeycomblattice of MX and XM region. From the large-scale density functional theorycalculation and continuum model with layer degrees of freedom, we find that theout of plane gating field creates a tunable charge transfer gap and introducesa mass term in the Dirac spectrum. At the flat band limit, we observe a seriesof 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 phasetransition between different electron crystals at fixed filling n = 1/2, 2/3.Our work demonstrates that transition metal dichalcogenide homobilayer providesa powerful platform for the investigation of tunable charge transfer insulatorand charge orders.

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