Implementation of an all-electron GW Approximation using the Projector Augmented Wave method: I. Formulation and application to the electronic structure of semiconductors

TL;DR

This paper presents an all-electron GW approximation implementation using the PAW method, applied to semiconductor band structures, highlighting convergence issues and limitations in predicting accurate band gaps.

Contribution

The paper introduces an all-electron GW method with PAW, compares plasmon-pole models, and analyzes convergence and accuracy in semiconductor quasiparticle energies.

Findings

All-electron GW improves semiconductor band structures.

Accuracy of quasiparticle energies is insensitive to plasmon-pole model details.

Decoupling of valence and core electrons affects band gap predictions.

Abstract

We have implemented the so called GW approximation (GWA) based on an all-electron full-potential Projector Augmented Wave (PAW) method. For the screening of the Coulomb interaction W we tested three different plasmon-pole dielectric function models, and showed that the accuracy of the quasiparticle energies is not sensitive to the the details of these models. We have then applied this new method to compute the quasiparticle band structure of some small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, SiMg$_2$, C and (insulator) LiCl. A special attention was devoted to the convergence of the self-energy with respect to both the {\bf k}-points in the Brillouin zone and to the number of reciprocal space $\bf G$-vectors. The most important result is that although the all-electron GWA improves considerably the quasiparticle band structure of semiconductors, it does not always provide the correct energy band gaps as originally claimed by GWA pseudopotential type of calculations. We argue that the decoupling between the valence and core electrons is a problem, and is some what hidden in a pseudopotential type of approach.