Simple vertex correction improves GW band energies of bulk and two-dimensional crystals

TL;DR

This paper introduces a simple vertex correction to the GW method that improves quasiparticle energy calculations for bulk and 2D crystals by better accounting for short-range correlations, shifting band gaps closer to experimental values.

Contribution

The authors propose a computationally efficient vertex correction compatible with LDA that enhances GW band energy predictions for solids and 2D materials.

Findings

Vertex correction shifts band gap centers by ~0.5 eV, aligning with experiments.

Short-range correlations are mainly improved by the vertex correction.

The method enhances basis set convergence and requires no extra computational cost.

Abstract

The GW self-energy method has long been recognized as the gold standard for quasiparticle (QP) calculations of solids in spite of the fact that the neglect of vertex corrections and the use of a DFT starting point lacks rigorous justification. In this work we remedy this situation by including a simple vertex correction that is consistent with an LDA starting point. We analyse the effect of the self-energy by splitting it into a short-range and long-range term which are shown to govern respectively the center and size of the band gap. The vertex mainly improves the short-range correlations and therefore has a small effect on the band gap, while it shifts the band gap center up in energy by around 0.5 eV in good agreement with experiments. Our analysis also explains how the relative importance of short- and long-range interactions in structures of different dimensionality is reflected in their QP energies. Inclusion of the vertex comes at practically no extra computational cost and even improves the basis set convergence compared to GW. The method thus provides an efficient and rigorous improvement over the GW approximation and sets a new standard for quasiparticle calculations of solids.