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The question of macroscopic occupation and spontaneous emergence of coherencefor exciton ensembles has gained renewed attention due to the rise of van derWaals heterostructures made of atomically thin semiconductors. The hostedinterlayer excitons exhibit nanosecond lifetimes, long enough to allow forexcitonic thermalization in time. Several experimental studies reportedsignatures of macroscopic occupation effects at elevated exciton densities.With respect to theory, excitons are composite particles formed by fermionicconstituents, and a general theoretical argument for a bosonic thermalizationof an exciton gas beyond the linear regime is still missing. Here, we derive anequation for the phonon mediated thermalization at densities above theclassical limit, and identify which conditions favor the thermalization offermionic or bosonic character, respectively. In cases where acoustic,quasielastic phonon scattering dominates the dynamics, our theory suggests thattransition metal dichalcogenide (TMDC) excitons might be bosonic enough to showbosonic thermalization behaviour and decreasing dephasing for increasingexciton densities. This can be interpreted as a signature of an emergingcoherence in the exciton ground state, and agrees well with the experimentallyobserved features, such as a decreasing linewidth for increasing densities.

Exciton-phonon-scattering: A competition between bosonic and fermionic nature of bound electron-hole pairs