Analysis of diagonal <i>G</i> and subspace <i>W</i> approximations within fully self-consistent <i>GW</i> calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques are computationally demanding and act as a bottleneck to include vertex function. In contrast, routinely used single-shot G₀W₀ approximation has an undesirable dependency on the choice of xc-functional. In this work, we consider AlAs, AlP, GaP, and ZnS as our prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. To reduce the computational cost, we present a framework within our sc-GW scheme to consider diagonal G and subspace W approximations. We analyse our results obtained from the above techniques by comparing against our fully sc-GW calculations and other similar approaches including experiments. The sub 2% difference in the values of the bandgap obtained from fully sc-GW and subspace W methods shows an encouraging direction to incorporate vertex function that could potentially improve overestimated sc-GW bandgaps.