Hyperspectral imaging at cryogenic temperatures is used to investigate exciton and trion propagation in MoSe$_2$ monolayers encapsulated with hexagonal boron nitride (hBN). Under a tightly focused, continuous-wave laser excitation, the spatial distribution of neutral excitons and charged trions strongly differ at high excitation densities. Remarkably, in this regime the trion distribution develops a halo shape, similar to that previously observed in WS2 monolayers at room temperature and under pulsed excitation. In contrast, the exciton distribution only presents a moderate broadening without the appereance of a halo. Spatially and spectrally resolved luminescence spectra reveal the buildup of a significant temperature gradient at high excitation power, that is attributed to the energy relaxation of photoinduced hot carriers. We show, via a numerical resolution of the transport equations for excitons and trions, that the halo can be interpreted as thermal drift of trions due to a Seebeck term in the particle current. The model shows that the difference between trion and exciton profiles is simply understood in terms of the very different lifetimes of these two quasiparticles.
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