Electronic structure of two-dimensional transition metal dichalcogenide bilayers fromab initiotheory

By means of first-principles $GW$ calculations, we have studied the electronic structure properties of $M{X}_{2}$ ($M=\text{Mo}$, W; $X=\text{S}$, Se, Te) bilayers, including hybrid structures of $M{X}_{2}$ building blocks. The effect of spin-orbit coupling on the electronic structure and the effect of van der Waals interaction on the geometry were taken into account. All the homogeneous bilayers are identified as indirect band-gap materials, with an increase of the band gap when Mo is changed to W, and a decrease of the band gap when the atomic number of $X$ is increased. The same behavior is also observed for hybrid bilayers with common chalcogen atoms, while bilayers with common metal atoms have a direct band gap. Finally, it is shown that due to their particular band alignment, some heterobilayers enable electron-hole separation, which is of interest for solar cell applications.