Spin-flip processes and radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers

We perform a theoretical study of radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. This decay necessarily involves an electronic spin flip. The intrinsic decay mechanism due to interband spin-flip dipole moment perpendicular to the monolayer plane, gives a rate about 100--1000 times smaller than that of bright excitons. However, we find that this mechanism also introduces an energy splitting due to a local field effect, and the whole oscillator strength is contained in the higher-energy component, while the lowest-energy state remains dark and needs an extrinsic spin-flip mechanism for the decay. Rashba effect due to a perpendicular electric field or a dielectric substrate, gives a negligible radiative decay rate (about $10^7$ times slower than that of bright excitons). Spin flip due to Zeeman effect in a sufficiently strong in-plane magnetic field can give a decay rate comparable to that due to the intrinsic interband spin-flip dipole.