Exciton-Phonon Coupling and Band-Gap Renormalization in Monolayer WSe$_{2}$

Using a fully ab-initio methodology, we demonstrate how the lattice vibrations couple with neutral excitons in monolayer WSe2 and contribute to the non-radiative excitonic lifetime. We show that only by treating the electron-electron and electron-phonon interactions at the same time it is possible to obtain an unprecedented agreement of the zero and finite-temperature optical gaps and absorption spectra with the experimental results. The bare energies were calculated by solving the Kohn-Sham equations, whereas G$_{0}$W$_{0}$ many body perturbation theory was used to extract the excited state energies. A coupled electron-hole Bethe-Salpeter equation was solved incorporating the polaronic energies to show that it is the in-plane torsional acoustic phonon branch that contributes mostly to the A and B exciton build-up. We find that the three A, B and C excitonic peaks exhibit different behaviour with temperature, displaying different non-radiative linewidths. There is no considerable transition in the strength of the excitons with temperature but A-exciton exhibits darker nature in comparison to C-exciton. Further, all the excitonic peaks redshifts as temperature rises. Renormalization of the bare electronic energies by phonon interactions and the anharmonic lattice thermal expansion causes a decreasing band-gap with increasing temperature. The zero point energy renormalization (31 meV) is found to be entirely due to the polaronic interaction with negligible contribution from lattice anharmonicites. These findings may find a profound impact on electronic and optoelectronic device technologies based on these monolayers.