Splitting between bright and dark excitons in transition metal dichalcogenide monolayers

The optical properties of 2D semiconductors made of transition metal dichalcogenide monolayers, such as MoX₂ and WX₂ (X=S, Se), are dominated by excitons. The light emission yield for optoelectronics applications depends on whether the electron-hole transitions are optically allowed (bright) or forbidden (dark). No direct evidence of the energetic ordering of these exciton states is currently available. The authors here solve the Bethe-Salpeter equation with G0{0ex}W wave functions in order to determine the sign and amplitude of the splitting between bright and dark exciton states in the entire MoX₂ and WX₂ monolayer family. They also evaluate the influence of pin-orbit coupling on the optical spectra and clearly demonstrate the strong impact of the intravalley Coulomb exchange term on the dark-bright exciton splitting, an important ingredient for engineering optoelectronics and spintronics applications.