Strong Renormalization of the Electronic Band Gap due to Lattice Polarization in the GW Formalism

The self-consistent GW band gaps are known to be significantly overestimated. We show that this overestimation is, to a large extent, due to the neglect of the contribution of the lattice polarization to the screening of the electron-electron interaction. To solve this problem, we derive within the GW formalism a generalized plasmon-pole model that accounts for lattice polarization. The resulting GW self-energy is used to calculate the band structures of a set of binary semiconductors and insulators. The lattice contribution always decreases the band gap. The shrinkage increases with the size of the longitudinaltransverse optical splitting and it can represent more than 15% of the band gap in highly polar compounds, reducing the band-gap percentage error by a factor of 3.