Electronic structure of van der Waals ferromagnet CrI3 from self-consistent vertex corrected GW approaches

Abstract

The electronic structure of layered van der Waals ferromagnet ${\mathrm{CrI}}_{3}$ is studied with self-consistent diagrammatic approaches beyond GW approximation. Considerable improvement in the calculated band gap as compared to the non-self-consistent ${G}_{0}{W}_{0}$ results has been found. Certain spectral features in the valence bands discovered recently by angle-resolved photoemission spectroscopy are reproduced better when we use full frequency-dependent self-energy. Density-functional theory and quasiparticle self-consistent GW method which are based on frequency-independent self-energy are unable to resolve these features. Nonlocality effects in the diagrams beyond GW approximation are large for both polarizability and self-energy. This finding can potentially have an impact on the development of methods like GW$+$dynamical mean field theory.