Electronic band-edge properties of rock salt PbY and SnY (Y= S, Se, and Te)

We find that: (1) SnY are zero-gap semiconductors Eg = 0 if the spin-orbit (SO) interaction is excluded. The reason for this is that the conduction band (CB) and the valence band (VB) cross along the Q ≡ LW line. (2) Including the SO interaction splits this crossing and creates a direct gap along the Q-line, thus away from the L symmetry point. Hence, the fundamental band gap Eg in SnY is induced by the SO interaction and the energy gap is rather small Eg ≈ 0.2-0.3 eV. At the L-point, the CB state has symmetric L4+ and the VB state is antisymmetric L4- thereby the L-point pressure coefficient ∂Eg(L)/∂p is a positive quantity. (3) PbY have a direct band gap at the L-point both when SO coupling is excluded and included. In contrast to SnY, the SO interaction decreases the gap energy in PbY. (4) Including the SO interaction, the LDA yields incorrect symmetries of the band-edge states at the L-point; the CB state has L4+ and the VB state has L4- symmetry. However, a small increase of the cell volume corrects this LDA failure, producing an antisymmetric CB state and a symmetric VB state, and thereby also yields the characteristic negative pressure coefficient ∂Eg(L)/∂p in agreement with experimental findings. (5) Although PbY and SnY have different band-edge physics at their respective equilibrium lattice constants, the change of the band-edges with respect to cell volume is qualitatively the same for all six chalcogenides. (6) Finally, in the discussion of the symmetry of the band edges, it is important to clearly state the chosen unit cell origin; a shift by (a/2,0,0) changes the labeling L4+ ⇔ L4- of the irreducible representations.