Orbital Chemistry That Leads to High Valley Degeneracy in PbTe,Chemistry of Materials

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Orbital Chemistry That Leads to High Valley Degeneracy in PbTe
Chemistry of Materials ( IF 7.2 ) Pub Date : 2020-11-13 , DOI: 10.1021/acs.chemmater.0c03740
Madison K. Brod ₁ , Michael Y. Toriyama ₁ , G. Jeffrey Snyder ₁

Affiliation

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.

中文翻译：

导致PbTe高谷简并的轨道化学

PbTe是已知性能最高的热电材料之一。它的大部分有希望的热电性能可以归因于高谷值简并性，这是因为在第一个布里渊区的L点具有价带最小（VBM）和导带最大（CBM），简并为4倍，而不是Γ简并为1倍。L处存在VBM用构成价带边缘的Pb-s状态的贡献来解释。然而，Te-p态的主导地位和VBM附近Pb-p态的存在表明，Pb-s轨道可能不像以前认为的那样重要。计算电子结构的紧密结合（TB）或原子轨道的线性组合（LCAO）方法非常适合获得定性见解，以解释简单的化学和键合原理如何导致材料的复杂电子结构。在这项研究中，我们使用物理自洽TB模型，以了解其对各个原子轨道间的相互作用，有助于形成具有在VBM程度大号而不是Γ。根据作用中的主要相互作用，开发了一个简单的分子轨道（MO）图片，当扩展到周期晶体中时，可以解释L和Γ之间的价带分散的形状。我们发现Pb-p和Te-p状态之间有足够的相互作用，可以为MO提供适当的s型对称性，以将VBM置于L处，而不是岩石盐结构中VB的通常p型对称性。 VBM在Γ处。此外，我们表明，即使去除了Pb-s状态，VBM也会处于L，并且Pb-p状态至少对决定VBM在PbTe和其他硫族化物中的位置至关重要。

更新日期：2020-11-25

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