Interlayer coupling in commensurate and incommensurate bilayer structures of transition-metal dichalcogenides

The interlayer couplings in commensurate and incommensurate bilayer structures of transition-metal dichalcogenides are investigated with perturbative treatment. The interlayer coupling in +/- K valleys can be decomposed into a series of hopping terms with distinct phase factors. In H-type and R-type commensurate bilayers, the interference between the three main hopping terms leads to a sensitive dependence of the interlayer coupling strength on the translation that can explain the position dependent local band gap modulation in a heterobilayer moire superlattice. The interlayer couplings in the Gamma valley of valence band and Q valley of conduction band are also studied, where the strong coupling strengths of several hundred meV can play important roles in mediating the ultrafast interlayer charge transfer in heterobilayers of transition-metal dichalcogenides.