All-electron self-consistentGWin the Matsubara-time domain: Implementation and benchmarks of semiconductors and insulators

Abstract

The $GW$ approximation is a well-known method to improve electronic structure predictions calculated within density functional theory. In this work, we have implemented a computationally efficient $GW$ approach that calculates central properties within the Matsubara-time domain using the modified version of elk, the full-potential linearized augmented plane wave (FP-LAPW) package. Continuous-pole expansion (CPE), a recently proposed analytic continuation method, has been incorporated and compared to the widely used Pad\'e approximation. Full crystal symmetry has been employed for computational speedup. We have applied our approach to 18 well-studied semiconductors/insulators that cover a wide range of band gaps computed at the levels of single-shot ${G}_{0}{W}_{0}$, partially self-consistent $G{W}_{0}$, and fully self-consistent $GW$ (full-$GW$), in conjunction with the diagonal approximation. Our calculations show that ${G}_{0}{W}_{0}$ leads to band gaps that agree well with experiment for the case of simple $s\ensuremath{-}p$ electron systems, whereas full-$GW$ is required for improving the band gaps in $3d$ electron systems. In addition, $G{W}_{0}$ almost always predicts larger band gap values compared to full-$GW$, likely due to the substantial underestimation of screening effects as well as the diagonal approximation. Both the CPE method and Pad\'e approximation lead to similar band gaps for most systems except strontium titantate, suggesting that further investigation into the latter approximation is necessary for strongly correlated systems. Moreover, the calculated cation $d$ band energies suggest that both full-$GW$ and $G{W}_{0}$ lead to results in good agreement with experiment. Our computed band gaps serve as important benchmarks for the accuracy of the Matsubara-time $GW$ approach.