Long tailed trions in monolayer MoS$_2$: Temperature dependent asymmetry and red-shift of trion photoluminescence spectra

Monolayer molybdenum disulfide (MoS$_2$) has emerged as an excellent 2D model system because of its two inequivalent, direct-gap valleys that lead to exotic bound and excited states. Here we focus on one such bound state, the negatively charged trion. Unlike excitons, trions can radiatively decay with non-zero momentum by kicking out an electron, resulting in an asymmetric trion photoluminescence (PL) peak with a long low-energy tail. As a consequence, the peak position does not correspond to the zero momentum trion energy. By including the trion's long tail in our analysis we are able to accurately separate the exciton from the trion contributions to the PL spectra. According to theory, the asymmetric energy tail has both a size-dependent and a temperature-dependent contribution. Analysis of the temperature-dependent data reveals the effective trion size, consistent with literature, and the temperature dependence of the band gap and spin-orbit splitting of the valence band. Finally, we observe signatures of Pauli-blocking of the trion decay.