Quasiparticle band structures ofβ-HgS, HgSe, and HgTe

The electronic structures of mercury chalcogenides in the zinc-blende structure have been calculated within the LDA, $GW$ (G{}₀W{}₀$, ``one-shot'') and quasi-particle self-consistent $GW$ ($QSGW$) approximations, including spin-orbit (SO) coupling. The slight tendency to overestimation of band gaps by $QSGW$ is avoided by using a hybridscheme (20$%$ LDA and 80$%$ $QSGW$). The details of the $GW$ bands near the top of the valence bands differ significantly from the predictions obtained by calculations within the LDA. The results obtained by ${G}₀{W}₀$ depend strongly on the starting wave functions and are thus quite different from those obtained from QS$GW$. Within $QSGW$, HgS is found to be a semiconductor, with a ${{Γ}}₆$ $s$-like conduction-band minimum state above the valence top ${{Γ}}₇$ and ${{Γ}}₈$ (``negative'' SO splitting). HgSe and HgTe have negative gaps (inverted band structures), but for HgTe the ${{Γ}}₇$ state is below ${{Γ}}₆$ due to the large Te SO splitting, in contrast to HgSe where ${{Γ}}₆$ is below ${{Γ}}₇$. There appears to be significant differences, in particular for HgSe and HgS, between the ordering of the band-edge states as obtained from experiments and theory.