Electronic structure of chromium trihalides beyond density functional theory

We explore the electronic band structure of freestanding monolayers of chromium trihalides CrX3, X = Cl, Br, I, within an advanced ab initio theoretical approach based on the use of Green’s function functionals. We compare the local density approximation with the quasiparticle self-consistent GW (QSGW) approximation and its self-consistent extension (QSGW) by solving the particle-hole ladder Bethe-Salpeter equations to improve the effective interaction W. We show that, at all levels of theory, the valence band consistently changes shape in the sequence Cl→Br →I, and the valence band maximum shifts from the M point to the point. By analyzing the dynamic and momentum-dependent self-energy, we show that QSGW adds to the localization of the systems in comparison with QSGW, thereby leading to a narrower band and reduced amount of halogens in the valence band manifold. Further analysis shows that X = Cl is most strongly correlated, and X = I is least correlated (most bandlike) as the hybridization between Cr d and X p enhances in the direction Cl→Br →I. For CrBr3 and CrI3, we observe remarkable differences between the QSGW and QSGW valence band structures, while their eigenfunctions are very similar. We show that weak perturbations, like moderate strain, weak changes to the d-p hybridizati