Spontaneous circular polarization of photoluminescence from WS$_{2}$ single layers*

We have carried out a magnetoluminescence study of WS$_{2}$ single layer crystals excited with linearly polarized light. The photoluminescence (PL) contains two features. The first is associated with the neutral exciton ($X^{0})$; the second feature is due to the recombination of negatively charged excitons ($X^{-})$ in the presence of a two-dimensional electron gas (2DEG). The $X^{-}-2DEG$ feature has a non-zero circular polarization up to 19{\%} at zero magnetic field even though the PL excitation light is linearly polarized. The circular polarization is effected by an external magnetic field applied perpendicular to the crystal plane at $2\% /Tesla$. The zero field circular polarization of the $X^{-}-2DEG$ photoluminescence feature is interpreted as due to the existence of a spontaneously valley polarized 2DEG. This is a new state possible in WS$_{2}$ due to valley and spin locking and a strong electron-electron interaction.