The electronic structure of $\beta$-HgS via $GW$ calculations

The electronic structure of the zincblende $\beta$-HgS is not well understood. Previous first-principles calculations using fully-relativistic density functional theory and many-body perturbation theory in the fully-relativistic $GW$ approach have predicted an inverted, topologically non-trivial ordering of these states, with the $s$-like $\Gamma_6$ state occupied. However, other calculations using the $GW$ approach in which spin-orbit coupling is added perturbatively ("$GW$+SOC") predict the $p$-$d$ hybridized $\Gamma_7$ and $\Gamma_8$ states to be occupied and the $\Gamma_6$ state to be unoccupied, suggesting that $\beta$-HgS is a topologically trivial small band gap semiconductor. In the present work, a plane-wave pseudopotential fully-relativistic $GW$ calculation finds a band ordering in agreement with the previous $GW$+SOC calculations. The calculated band gap is 0.10 eV and the electron effective mass is 0.07 $m_e$, in good agreement with experiment.