Self-consistent solution of Hedin's equations: semiconductors/insulators

TL;DR

This paper presents a self-consistent method for calculating band gaps in semiconductors and insulators using Hedin's equations, incorporating vertex corrections to improve accuracy over traditional GW approaches.

Contribution

It introduces and compares two vertex correction schemes within self-consistent Hedin's equations, demonstrating improved band gap predictions over standard GW methods.

Findings

Both schemes significantly improve band gap accuracy.

Vertex corrections outperform self-consistent GW and QS-GW methods.

Electron-phonon interactions are crucial for accurate band gap predictions.

Abstract

The band gaps of a few selected semiconductors/insulators are obtained from the self-consistent solution of the Hedin's equations. Two different schemes to include the vertex corrections are studied: (i) the vertex function of the first-order (in the screened interaction $W$) is applied in both the polarizability $P$ and the self-energy $\Sigma$, and (ii) the vertex function obtained from the Bethe-Salpeter equation is used in $P$ whereas the vertex of the first-order is used in $\Sigma$. Both schemes show considerable improvement in the accuracy of the calculated band gaps as compared to the self-consistent $GW$ approach (sc$GW$) and to the self-consistent quasi-particle $GW$ approach (QS$GW$). To further distinguish between the performances of two vertex-corrected schemes one has to properly take into account the effect of the electron-phonon interaction on the calculated band gaps which appears to be of the same magnitude as the difference between schemes i) and ii).