Self-screening corrections beyond the random-phase approximation: Applications to band gaps of semiconductors

The self-screening error in the random-phase approximation and the GW approximation (GWA) is a well-known issue and has received attention in recent years with several methods for a correction being proposed. Here, we apply two of these, a self-screening and a so-called self-polarization correction scheme, to model calculations to examine their applicability. We also apply a local form of the self-screening correction to ab initio calculations of real materials. We find indications for the self-polarization scheme to be the more appropriate choice of correction for localized states, while we additionally observe that it suffers from causality violations in the strongly correlated regime. The self-screening correction, on the other hand, significantly improves the description in more delocalized states. It is found to provide a notable reduction in the remaining GWA error when calculating the band gaps of several semiconductors, indicating a physical explanation for a part of the remaining discrepancy in one-shot GW compared with experiment, while leaving the localized semicore d states mostly unaffected.