First-principles calculations of the II-VI semiconductor $\beta$-HgS: Metal or semiconductor

Relativistic all-electron full-potential first-principles calculations have been performed in order to study the symmetry of the energy levels around the valence band maximum in the zinc blende II-VI semiconductors $\beta$-HgS, HgSe, and HgTe. It is demonstrated that in general, an inverted band-structure does not necessarily lead to a zero fundamental energy gap for systems with zinc blende symmetry. Specifically, $\beta$-HgS is found to have at the same time an inverted band structure, and a small, slightly indirect, fundamental energy gap. Possibly, the energy levels around the valence band maximum order differently in each of these systems.