Extending the ab initio Bethe-Salpeter equation approach to include phonon screening

Exciton properties are critical to the optoelectronic response of materials, making their theoretical and computational description important to future technological devices. Many-body perturbation theory (MBPT), and specifically the ab initio GW-Bethe-Salpeter (BSE) equation approach [1], is a highly accurate method for predicting exciton properties that has been successfully applied in diverse systems. However, recent work has shown that electronic effects alone are not enough to provide an accurate description of exciton physics, and the effect of phonons can lead to significant renormalization of exciton peak positions [2] and electron-hole interactions [3]. An extension of the GW-BSE method to account for these phonon effects is therefore necessary. Here we present a first-principles approach based on MBPT, building on the framework introduced in prior work [3] to rigorously implement phonon screening effects into the ab initio BSE method. We apply our method to a variety of semiconductors, quantifying the role of phonon screening on exciton binding energies. We also discuss the effect of temperature on phonon screening of excitons, connecting our formulation to model electron-hole interactions that include exciton-phonon coupling, such as the Haken potential.