Orbital Chemistry That Leads to High Valley Degeneracy in PbTe

PbTe is one of the highest-performing known thermoelectric materials. Much of its promising thermoelectric performance can be attributed to high valley degeneracy due to having a valence band minimum (VBM) and conduction band maximum (CBM) at the L-point in the first Brillouin zone, which has 4-fold degeneracy, instead of at Gamma, which has 1-fold degeneracy. The existence of the VBM at L has been explained by the contribution of Pb-s states that make up the valence band edge. However, the dominance of Te-p states and the presence of Pb-p states near the VBM suggest that the Pb-s orbitals may not be as crucial as previously thought. The tightbinding (TB) or linear combination of atomic orbitals (LCAO) method of calculating electronic structures is ideally suited to gain qualitative insights to explain how simple chemistry and bonding principles lead to complex electronic structures of materials. In this study, we use a physically self-consistent TB model to understand the extent to which various atomic orbital interactions contribute to having a VBM at L instead of G. Based on the dominant interactions at play, a simple molecular orbital (MO) picture is developed that when extended into the periodic crystal explains the shape of the valence band dispersion between L and G. We find that there is sufficient interaction between Pb-p and Te-p states to provide the MO with the proper s-type symmetry to place the VBM at L rather than the usual p-type symmetry of the VB in rocksalt structures, where the VBM is at G. Furthermore, we show that the VBM would be at L even if the Pb-s states were removed and that the Pb-p states are at least as critical of a factor in dictating the position of the VBM in PbTe and in the other lead chalcogenides.