Twisted MX2/MoS2 heterobilayers: effect of van der Waals interaction on the electronic structure

A comprehensive first-principles study of the electronic properties of twisted 2D transition metal dichalcogenide (TMDC) heterobilayers MX2/MoS2 (M = Mo, Cr, W; X = S, Se) with different rotation angles has been performed. The van der Waals (vdW) interaction is found to have an important effect on the electronic structure of two-dimensional (2D) TMDC heterobilayers. Compared to non-twisted heterobilayers, the interlayer distance of twisted heterobilayers increases appreciably, thereby changing the vdW interaction of the heterobilayers as well as the electronic structure of the MX2/MoS2 systems. As a result, for CrSe2/MoS2 and MoSe2/MoS2 systems, the indirect bandgap (G-K) exhibits a notable enlargement (about 0.1 eV), leading to the indirect-to-direct gap transition. At twisting angles between 13.2 degrees and 46.8 degrees, the interlayer distance is nearly constant for the mismatched lattices over the entire sample, resulting in nearly the same electronic structure. Even after considering the spin-orbit coupling (SOC) effect, the indirect-to-direct transition is still predicted to occur in the WS2/MoS2 heterobilayer due to the large spin-orbit splitting.