Electronic structure of chromium trihalides beyond density functional theory

Abstract

We explore the electronic band structure of freestanding monolayers of chromium trihalides CrX 3 , 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 (QSG W ) 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 QSG W 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 CrBr 3 and CrI 3 , we observe remarkable differences between the QSGW and QSG W valence band structures, while their eigenfunctions are very similar. We show that weak perturbations, like moderate strain, weak changes to the d-p hybridization, and adding small U , can flip the valence band structures between these two solutions in these materials.

Full versus quasi-particle self consistency in vertex corrected GW approaches

“…As it is shown in this study, combining the vertex corrected calculations with QP self-consistency as it is advocated in Refs. [13][14][15], can only be successful if vertex corrections are evaluated with a number of restrictive approximations or 'constraints' such as polarizability only correction, static W (ν = 0) in vertex diagrams, and Tamm-Dancoff approximation when solving BSE. From this point of view, quasi-particle self-consistency combined with vertex-corrected GW approach can be considered as an ad hoc theory where one imposes specific constraints on the vertex part in order to avoid too large (and destructive for the final result) effect.…”

“…However, similar to the approach used in Refs. [13][14][15], our implementation of QSGW+DMFT also uses 'constraints' for the vertex (DMFT) part: i) only one iteration which includes DMFT (one-shot type of DMFT correction performed on top of QSGW); ii) effective interaction in DMFT part is not evaluated from proper DMFT self-consistency condition, [50], but is provided by constrained random-phase approximation (cRPA, [51]). Specifically, the second constraint (using the cRPA) can clearly be considered as an ad hoc part where the setup parameters of cRPA are adjusted in order to get reasonable effective interaction.…”

“…Vertex corrected (diagrammatically) GW calculations for realistic materials now only begin to appear [12][13][14][15][16][17][17][18][19][20][21][22] . Their increased complexity (even comparative to G0W0) as well as their relatively recent introduction to the field make the reproducibility of results an open and important issue.…”

A Theory for Colors of Strongly Correlated Electronic Systems

“…We begin with a study of NiO, and employ an advanced many-body perturbative Green's function GW theory QSG W [14,15,49,52], a self-consistent extension of QSGW [53][54][55], where the polarizability needed to construct W is computed including vertex corrections (ladder diagrams) by solving a Bethe-Salpeter equation (BSE) for the two-particle Hamiltonian [15]. There are some crucial differences in the implementation of QSG W presented here from other widely used implementations of BSE.…”

“…There are some crucial differences in the implementation of QSG W presented here from other widely used implementations of BSE. First the calculations are self-consistent in both self energy Σ and the charge density [52,56]; also the screened coulomb interaction W (ω, q) is calculated with ladders included in the polarizability. (W used as ladders in the construction of W is approximated with a static RPA W , as is customary [46][47][48]).…”