Valley polarization of singlet and triplet trions in WS$_2$ monolayer in magnetic fields

The spectral signatures associated with different negatively charged exciton complexes (trions) in a WS$_2$ monolayer encapsulated in hBN, are analyzed from low temperature and polarization resolved reflectance contrast (RC) and photoluminescence (PL) experiments, with an applied magnetic field. Based on results obtained from the RC experiment, we show that the valley Zeeman effect affects the optical response of both the singlet and the triplet trion species through the evolution of their energy and of their relative intensity, when applying an external magnetic field. Our analysis allows us to estimate a free electron concentration of $\sim 1.3 \cdot 10^{11}$ cm$^{-2}$. The observed evolutions based on PL experiments on the same sample are different and can hardly be understood within the same simple frame highlighting the complexity of relaxation processes involved in the PL response.