Ab initio calculation of effects of exciton-phonon couplings to the optical linewidth and exciton lifetime

In standard GW plus Bethe-Salpeter Equation (GW-BSE) calculations, it is common to introduce an artificial broadening parameter to match theoretical absorption spectra with experimental data. However, this empirical procedure lacks a rigorous physical foundation. A main source of the broadening of optical absorption features, especially its temperature dependence, arises primarily from exciton-phonon coupling, which leads to finite lifetimes of excitonic states. In this work, we use large, distorted supercells generated by special displacement method to incorporate the electron-phonon interaction into band gap renormalization and optical spectrum. Compared with the primitive unit cell, the absorption spectrum of the distorted supercell exhibits a splitting of the original excitonic peak into multiple subpeaks. By analyzing these peaks, we extract the full width at half maximum of the absorption spectrum, from which the exciton lifetime due to phonon-exciton coupling may be determined. Furthermore, we apply the time-dependent adiabatic GW (TD-aGW) method to simulate the evolution of system's density-matrix under an external field.