Polarization analysis of excitons in monolayer and bilayer transition-metal dichalcogenides

The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the optical spectra of these materials. We explain the differences between optical transitions in monolayer MoSe$_2$ and monolayer WSe$_2$, finding that indirect excitons in the latter correspond to several low-energy optical transitions that so far were attributed to excitons bound to impurities. A possible mechanism that can explain the vanishing polarization in MoSe$_2$ is discussed. Finally, we consider the effect of an out-of-plane electric field, showing that it can reduce the initial polarization of bright excitons due to a Rashba-type coupling with dark excitons.