Bethe-Salpeter equation approach with electron-phonon coupling for exciton binding energies

We introduce a simple scheme in order to account for the coupling with longitudinal phonons within the first-principles Bethe-Salpeter approach based on many-body perturbation theory. This allows one to evaluate the reduction of exciton binding energies observed in polar semiconductors. The electron-phonon coupling is modeled from the macroscopic dielectric response in the infrared which, in turn, is calculated through density functional perturbation theory. In this way, the additional computational cost determined by our method is negligible. We first illustrate our approach in the case of bulk ZnS. Then, we discuss the limit of the Bethe-Salpeter equation in the case of strongly delocalized excitons and we show how the excitonic series of bulk Cu₂O is well reproduced.