Imparity in valley population for single layer transition metal dichalcogenides under elliptical polarization

The illumination of a single-layer transition metal dichalcogenide with an elliptically-polarized light beam is shown to give rise to a differential rate of inter-band carrier excitation between the valence and conduction states around the valley edges, $K$ and $K^{'}$. This rate with a linear dependence on the beam ellipticity and inverse of the optical gap manifests as an asymmetric Fermi distribution between the valleys or a non-equilibrium population which under an external field and a Berry curvature induced anomalous velocity results in an externally tunable finite valley Hall current. Surface imperfections that influence the excitation rates are included through the self-consistent Born approximation. Additionally, we show that circular dichroism in the vicinity of the valley edges also exhibits an ellipticity dependence.