GWcalculations including spin-orbit coupling: Application to Hg chalcogenides

Abstract

We present self-energy calculations for Hg chalcogenides (HgX, X = S, Se, and Te) with inverted band structures using an explicit spin-dependent formulation of the GW approximation. Spin-orbit coupling is fully taken into account in calculating the single-particle Green function G and the screened interaction W . We have found, apart from an upward shift of the occupied conductionlike 6 state by about 0.7 eV, an enhancement of spin-orbit splitting by about 0.1 eV, in good agreement with experiment. This renormalization originates mainly from spin-orbit induced changes in G rather than W , which is affected only little by spin-orbit coupling.

Quasiparticle band structures ofβ-HgS, HgSe, and HgTe

“…But for HgTe the full and hybrid QSGW also predict different level orderings. We agree with Sakuma et al 19 that the effect of including the SO coupling in the calculation of G is important. We add it as a formal perturbation.…”

“…12, 14, 15, and, apart from the marginal difference in the relative position in the Γ 6 level in HgS between Ref. 19 and the present work, we suggest that it might be worthwhile to re-evaluate the analyses of the experimental data, in particular those for HgS and HgSe. We are, however, aware that in particular the interpretation of the magnetoabsorption experiments, such as those by Dobrowolska et al 7 seems to rest on a rather firm foundation, the selection rules derived by Guldner et al 40,41 But these rules rely on a rather simple k·p s-p interaction band model, and it cannot be excluded that application of more realistic band structures including interactions with many other states could have important effects.…”

“…The LDA calculation by Delin and Klüner 38 gave ∆ 0 values which are very similar to those given in the upper part of the table. The SO splittings obtained by Sakuma et al 19 from their G 0 W 0 are somewhat larger in magnitude due to their inclusion of the SO coupling in the GW calculation.…”

“…a somewhat cruder appoximation as used in Ref. 19. However, we shall argue that effects of going beyond G 0 W 0 , i.e.…”

Optical properties of tungsten trioxide from first-principles calculations

“…Such a reduction comes from the lowering of the conduction band minimum (CBM): the CBM states have mostly W 5d characters and are thus more affected than the O 2p states at the valence band maximum (VBM). We assumed that the magnitude of SO effects on the band gap is similar at the LDA and G 0 W 0 level of theory (similar SO splittings, within 0.1 eV, were reported in LDA and GW calculations of several systems with heavy elements [55,56]). Next we consider the effect of electron phonon (e-ph) interaction on the band gap of WO 3 ; such an effect was discussed in several papers for numerous semiconductors and insulators [57][58][59][60][61][62].…”