Phonon-assisted exciton/trion conversion efficiency in transition metal dichalcogenides

Photoluminescence spectra show that monolayer transition-metal dichalcogenides (ML-TMDs) 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 X_, exciton X, 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 out-of-plane A(1)' and the in-plane E' modes. In this respect, using the Fermi golden rule together with the effective mass approximation, we investigate the rate of the population transfers between X and X_, mediated by a single phonon. We demonstrate that, while the absolute importance of the two phonon modes on the up-conversion process strongly depends 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 subnanoseconds, consistent with recent experimental findings. The conjugate process is also investigated in our study, as a function of temperature T and electron density N-e. We prove that the exciton to trion down-conversion process is very unlikely at low electron density N-e < 10(10) cm(-2) and high temperature T > 50 K while it increases dramatically to reach few picoseconds time scale at low temperature and for electron density N-e > 10(10) cm(-2). Finally, our results show that the conversion processes occur more rapidly in exemplary monolayer molybdenum-based dichalcogenides (MoSe2 and MoTe2) than tungsten dichalcogenides.