GW calculations including spin-orbit coupling: Application to Hg chalcogenides

We present self-energy calculations for Hg chalcogenides (Hg$X$, $X=\text{S}$, 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 ${\ensuremath{\Gamma}}_{6}$ 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.