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The interlayer couplings in commensurate and incommensurate bilayerstructures of transition metal dichalcogenides are investigated withperturbative treatment. The interlayer coupling in \pm K valleys can bedecomposed into a series of hopping terms with distinct phase factors. InH-type and R-type commensurate bilayers, the interference between the threemain terms leads to a sensitive dependence of the interlayer coupling strengthon the translation. The magnitudes of the main hopping terms are found to somedozen of meV by fitting to the ab initio results. The interlayer couplings in\Gamma valley of valence band and Q valley of conduction band are also studied.The obtained strong coupling strengths of several hundred meV can playimportant roles in mediating the ultrafast interlayer charge transfer inheterobilayers of transition metal dichalcogenides.

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