The optical properties of transition metal dichalcogenide monolayers such as the two-dimensional semiconductors ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$ are dominated by excitons, Coulomb bound electron-hole pairs. The light emission yield depends on whether the electron-hole transitions are optically allowed (bright) or forbidden (dark). By solving the Bethe-Salpeter equation on top of $GW$ wave functions in density functional theory calculations, we determine the sign and amplitude of the splitting between bright and dark exciton states. We evaluate the influence of the spin-orbit coupling on the optical spectra and clearly demonstrate the strong impact of the intra-valley Coulomb exchange term on the dark-bright exciton fine structure splitting.

• Received 27 January 2016
• Revised 1 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.121107