Ab Initio Approach for Exciton-Phonon Interactions

We derive a formalism to compute exciton-phonon (ex-ph) interactions in crystals within the ab initio GW-Bethe Salpeter equation (BSE) approach. Using first order perturbation theory and the Tamm-Dancoff approximation, we express the ex-ph coupling constant as a superposition of electron- and hole-phonon coupling processes. We discuss numerical calculations of such ex-ph coupling and the related scattering rates, which are challenging as they combine electron-phonon and finite-momentum BSE calculations; we carry them out by using the YAMBO code to obtain exciton dispersions and the PERTURBO code to compute electron-phonon coupling and the ex-ph scattering rates. We apply this framework to investigate ex-ph interactions in bulk hexagonal boron nitride (h-BN), for which we compute the exciton relaxation time due to ex-ph interactions and map it onto the exciton dispersions. We also employ an exciton Boltzmann transport equation to simulate the out-of-equilibrium dynamics of excitons and their equilibration with phonons in h-BN. Our work is a first step toward understanding electron-phonon interactions in composite electronic quasiparticles. It sheds light on correlated electron-phonon processes and provides new computational tools to investigate excited state dynamics.