Dark excitons and the elusive valley polarization in transition metal dichalcogenides

A rate equation model for the dark and bright excitons kinetics is proposed which explains the wide variation in the observed degree of circular polarization of the PL emission in different TMDs monolayers. Our work suggests that the dark exciton states play an important, and previously unsuspected role in determining the degree of polarization of the PL emission. A dark exciton ground state provides a robust reservoir for valley polarization, which tries to maintain a Boltzmann distribution of the bright exciton states in the same valley via the intra valley bright dark exciton scattering mechanism. The dependence of the degree of circular polarization on the detuning energy of the excitation in MoSe$_2$ suggests that the electron-hole exchange interaction dominates over two LA phonon emission mechanism for inter valley scattering in TMDs.