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 longitudinal-transverse 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.

• Received 8 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.226404