Orbital Chemistry That Leads to High Valley Degeneracy in PbTe

Abstract

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 Γ, 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 tight-binding (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 Γ. 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 Γ. 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 Γ. 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.

Alternative Lone‐Pair ns2‐Cation‐Based Semiconductors beyond Lead Halide Perovskites for Optoelectronic Applications

“…In recent years, with continuous exploration of interatomic interactions, a few other rational explanation have emerged to account for the fundamental nature of a part of materials containing ns 2 cations. [ 304 ] In particular, Wuttig's group have raised a bonding mechanism dubbed as “metavalent” bonding (MVB) as an alternative approach. [ 305 ] From their point of view, the degrees of electron sharing (ES) and electron transfer (ET) between adjacent atoms are key factors affecting the chemical bonding mechanisms.…”

“…Thus, by mapping a series of materials, including PbX (X = S, Se, Te), Sb 2 Te 3 , Bi 2 X 3 (X = Se, Te), and inorganic halide perovskites, into a 2D space with the ES and ET as two coordinates, they found MVB had well‐defined borders to covalent, and iono‐covalent regions, indicating its distinction. [ 229–307 ] Such a map demonstrated that the MVB mechanism approximately possessed one shared electron and moderate electron transfer between adjacent atoms. This predictive model can also give rise to the favorable characteristics in above materials, including large Born effective charge, high optical dielectric constants, strong optical interband transition, etc.…”

How to Identify Lone Pairs, Van der Waals Gaps, and Metavalent Bonding Using Charge and Pair Density Methods: From Elemental Chalcogens to Lead Chalcogenides and Phase‐Change Materials

“…This had PbTe classified as a 'metavalent' compound according to a recent classification. [19] However, it is also commonly stated that the physico-chemical behavior of PbTe is linked to lone pairs, [30] although p-orbital overlap was shown recently to be responsible for the valence band dispersion [59] therefore questioning the relevance of lone pairs. Figure 9 shows a valence charge density (only s and p electrons) that is very much localized onto the atoms' cores, in agreement with the charge transfer of 0.7 electrons.…”

“…This had PbTe classified as a "metavalent" compound according to a recent classification. [19] However, it is also commonly stated that the physicochemical behavior of PbTe is linked to lone pairs, [30] although p-orbital overlap was shown recently to be responsible for the valence band dispersion, [59] therefore questioning the relevance of lone pairs.…”

“…This explains the absence of stereoactive lone pairs in SnTe, whereas these appear in SnS and SnSe. In addition , the relevance of lone pairs for thermoelectricity and optical properties in Pb-X systems has been questioned recently [28,59,61] as p-p bonding appears to drive the essential tures for these applications. We can also note that the dispersive nature of the top valence and bottom conduction bands is due to the dominant role of p-sigma bonding.…”