Electron–phonon coupling in semiconductors within the GW approximation

The magnitude of the renormalization of the band gaps due to zero-point motions of the lattice is calculated for 18 semiconductors, including diamond and silicon. This particular collection of semiconductors constitute a wide range of band gaps and atomic masses. The renormalized electronic structures are obtained using stochastic methods to sample the displacement related to the vibrations in the lattice. Specifically, a recently developed one-shot method is utilized where only a single calculation is needed to get similar results as the one obtained by standard Monte-Carlo sampling. In addition, a fast real-space GW method is employed and the effects of G0W0 corrections on the renormalization are also investigated. We find that the band-gap renormalizations inversely depend on the mass of the constituting ions, and that for the majority of investigated compounds the G0W0 corrections to the renormalization are very small and thus not significant.