Magnetoluminescence study of WS$_{2}$ monolayers*

We have studied the photoluminescence (PL) spectra\footnote{W. Zhao, et al., ACS nano, \textbf{7}, 791 (2013).} from WS$_{2}$ monolayers in the 5-150 K temperature range in magnetic fields up to 7 tesla applied along the normal to the sample plane. The luminescence was excited by a 488nm linearly polarized laser beam. The PL spectra have two features identified as the neutral ($X)$ and negatively charged ($X^{-})$ exciton. At zero magnetic field the $X^{-}$ feature has a large (as high as 30\%), laser power-dependent circular polarization, in contrast to the small polarization of $X$that does not depend on laser power. The application of an external magnetic field has a profound effect on the circular polarization of the charged exciton. Its polarization increases by 10\% at 7 tesla for any laser-power while its energy exhibits a small magnetic splitting (2meV at 7 tesla). On the other hand, the emitted circular polarization of the free exciton is not affected by the external magnetic field.