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 (Γ-K) exhibits a notable enlargement (about 0.1 eV), leading to the indirect-to-direct gap transition. At twisting angles between 13.2° and 46.8°, 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.