Electronic structure of ${\mathrm{MoSe}}_2$, ${\mathrm{MoS}}_2$, and ${\mathrm{WSe}}_2$. II. The nature of the optical band gaps

From band-structure calculations it is shown that ${\mathrm{MoSe}}_2$, ${\mathrm{MoS}}_2$, and ${\mathrm{WSe}}_2$ are indirect-gap semiconductors. The top of the valence band is at the Γ point and the bottom of the conduction band is along the line T of the hexagonal Brillouin zone, halfway between the points Γ and K. The A and B excitons correspond to the smallest direct gap at the K point. This assignment of the exciton peaks is shown to be consistent with the polarization dependence of their intensities, their effective masses, and the observed dependence of their splitting on the spin-orbit splittings of the constituent elements. The wave function at the top of the valence band is shown to be a metal-nonmetal antibonding state, which explains the observed high stability of these materials in photoelectrochemical cells against photocorrosion.