  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.
