Many-Body Effects on the Zero-Point Renormalization of the Band Structure

Abstract

We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative ${G}_{0}{W}_{0}$ approximation as well as quasiparticle self-consistent $GW$. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when ${G}_{0}{W}_{0}$ corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.