First-principles calculations of phonon-mediated exciton relaxation in two-dimensional semiconductors*

Exciton-phonon coupling (ExPC) is crucial for energy relaxation in semiconductors, yet the first-principles calculation of such coupling remains challenging, especially for low-dimensional systems. Here, we present a newly developed algorithm for calculating and analyzing ExPC and apply the algorithm in the exciton relaxation problem of monolayer transition metal dichalcogenides. We find that the interplay between the exciton wave functions and electron-phonon coupling (EPC) results in distinct selection rules from the ones of EPC. We further generalize these selection rules to Wannier exciton-phonon couplings in two-dimensional semiconductors. To verify our theory and algorithm, we calculate inter-valley exciton relaxation time, which agrees well with a recent experiment.