Quasiparticle band structures of $\beta$-HgS, HgSe, and HgTe

The electronic structures of mercury chalcogenides in the zinc-blende structure have been calculated within the LDA, $GW$ ($G$${}_0$$W$${}_0$, “one-shot”) and quasi-particle self-consistent $GW$ ($\text{QS}GW$) approximations, including spin-orbit (SO) coupling. The slight tendency to overestimation of band gaps by $\text{QS}GW$ is avoided by using a hybridscheme (20$\%$ LDA and 80$\%$ $\text{QS}GW$). 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 $\text{QS}GW$, HgS is found to be a semiconductor, with a ${\Gamma }_6$ $s$-like conduction-band minimum state above the valence top ${\Gamma }_7$ and ${\Gamma }_8$ (“negative” SO splitting). HgSe and HgTe have negative gaps (inverted band structures), but for HgTe the ${\Gamma }_7$ state is below ${\Gamma }_6$ due to the large Te SO splitting, in contrast to HgSe where ${\Gamma }_6$ is below ${\Gamma }_7$. 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.

Figure 1

The band structure of HgTe as calculated within the LDA (dashed, red curves) and $\text{QS}GW$ (blue, full-line curves) approximations. The zero of energy is at the valence-band maximum.

Figure 2

Band structure of HgTe near the $\Gamma$ point as calculated by (a) the LDA approximation, (b) the full $\text{QS}GW$ approach, (c) the hybrid $\text{QS}GW$ approach. The unit along the $x$ axis is $2\pi /a$, with $a=6.47$ Å.

Figure 3

Band structure of HgSe near the $\Gamma$ point as calculated (a) within the LDA, (b) within the $\text{QS}GW$ approximation, and (c) with the hybrid $\text{QS}GW$ approach. The unit along the $x$ axis is $2\pi /a$, with $a=6.08$ Å. Note that the energy scale in (a) differs from those in (b) and (c).

Figure 4

Band structure of HgS near the $\Gamma$ point as calculated (a) within the LDA, (b) within the $\text{QS}GW$ approximation, and (c) with the hybrid $\text{QS}GW$ approach. $E=0$ corresponds to the valence-band maximum, which in case (a) is found displaced off the $\Gamma$ point, in the direction toward the $K$ point. The unit along the $x$ axis is $2\pi /a$, with $a=5.84$ Å.

Figure 5

The lowest conduction band and the effective (“curvature”) mass of HgS near the $\Gamma$ point as calculated by the hybrid $\text{QS}GW$ approach ($a_0$ is the Bohr radius).