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Phonon-assisted exciton and trion conversion efficiency in transition metal Dichalcogenides

Photoluminescence spectra, shows that monolayer Transition-metal dichalcogenides (MLTMDCs), possess charged exciton binding energies, conspicuously similar to the energy of optical phonons. This enigmatic coincidence has offered opportunities to investigate many-body interactions between trion, exciton and phonon and led to efficient excitonic anti-Stokes processes with the potential for laser refrigeration and energy harvesting. In this study, we show that in WSe2 materials, the trion binding energy matches two phonon modes, the outofplane HP and the in-plane LO mode. In this respect, using the Fermi golden rule together with the effective mass approximation, we investigate the rate of the population transfers between exciton and trion, mediated by a single phonon. We demonstrate that, while the absolute importance of the two phonon modes on the upconversion process strongly depend on the experimental conditions such as the temperature and the dielectric environment (substrate), both modes lead to an up-conversion process on time scales in the range of few picoseconds to sub-nanosecond, consistent with recents experimental findings. The conjugate process is also investigated in our study, as a function of temperature and electron density . We prove that exciton to trion down-conversion process is very unlikely at low electron density and high temperature while it increases dramatically to reach few picoseconds time scale at low temperature and for electron density . Finally, our results show that conversion process occurs more rapidly in exemplary monolayer molybdenum-based dichalcogenides (MoSe2 and MoTe2) than tungsten dichalcogenides .