Critical assessment of $G_0W_0$ calculations for 2D materials: the example of monolayer MoS$_2$

TL;DR

This paper critically evaluates the accuracy of $G_0W_0$ calculations for 2D materials, specifically monolayer MoS$_2$, analyzing how computational choices influence the results and identifying optimal conditions for agreement with experiments.

Contribution

It systematically investigates the effects of calculation parameters on $G_0W_0$ results for monolayer MoS$_2$, providing guidelines for more accurate electronic structure predictions.

Findings

Best agreement with experiments using HSE06 starting point

Including spin-orbit coupling improves accuracy

Using a truncated Coulomb potential and analytical singularity treatment enhances results

Abstract

Two-dimensional (2D) materials combine many fascinating properties that make them more interesting than their three-dimensional counterparts for a variety of applications. For example, 2D materials exhibit stronger electron-phonon and electron-hole interactions, and their energy gaps and effective carrier masses can be easily tuned. Surprisingly, published band gaps of several 2D materials obtained with the $GW$ approach, the state-of-the-art in electronic-structure calculations, are quite scattered. The details of these calculations, such as the underlying geometry, the starting point, the inclusion of spin-orbit coupling, and the treatment of the Coulomb potential can critically determine how accurate the results are. Taking monolayer MoS$_2$ as a representative material, we employ the linearized augmented planewave + local orbital method to systematically investigate how all these aspects affect the quality of $G_0W_0$ calculations, and also provide a summary of literature data. We conclude that the best overall agreement with experiments and coupled-cluster calculations is found for $G_0W_0$ results with HSE06 as a starting point including spin-orbit coupling, a truncated Coulomb potential, and an analytical treatment of the singularity at $q=0$.