The question of macroscopic occupation and the spontaneous emergence of coherence for exciton ensembles has gained renewed attention due to the rise of van der Waals heterostructures made of atomically thin semiconductors. The hosted interlayer excitons exhibit nanosecond lifetimes, long enough to allow for excitonic thermalization in time. Several experimental studies reported signatures of macroscopic occupation effects at elevated exciton densities. With respect to theory, excitons are composite particles formed by fermionic constituents, and a general theoretical argument for a bosonic thermalization of an exciton gas beyond the linear regime is still missing. Here, we derive an equation for the phonon mediated thermalization at densities above the classical limit, and identify which conditions favor the thermalization of fermionic or bosonic character, respectively. In cases where acoustic, quasielastic phonon scattering dominates the dynamics, our theory suggests that transition metal dichalcogenide excitons might be bosonic enough to show bosonic thermalization behavior and decreasing dephasing for increasing exciton densities. This can be interpreted as a signature of an emerging coherence in the exciton ground state, and thus provides an explanation for the unexpected recent experimentally observed feature of a decreasing linewidth for increasing densities [Phys. Rev. Res. 2, 042044(R) (2020)]. Also, this interpretation would be in line with a recently observed long coherence length in the same material [Phys. Rev. Lett. 131, 036902 (2023)].

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• Composite bosons
• Electron-phonon coupling
• Electronic structure
• Excitons
• Fermions
• Quantum many-body systems
• Quantum wells
• Transition metal dichalcogenides
• Two-dimensional electron gas