\(\overrightarrow K \cdot \overrightarrow \pi\) Interpolation and the Calculation of Vacancy States in PbTe
The purpose of this paper is to describe the implementation of the Koster-Slater1 theory of impurity states as applied to vacancies in PbTe. The nature of the vacancy levels and their physical consequences has already been discussed in the literature.2 Parada3 has also published a more detailed account of his vacancy calculations. Also the \(\overrightarrow K \cdot \overrightarrow \pi\) method using APW Bloch functions has appeared in press before. However, many of the key steps have never been fully described. The basic contributions to the \(\overrightarrow K \cdot \overrightarrow \pi\)method using APW wave functions were made by Ferreira4 in his evaluation of the deformation potentials for PbTe. The techniques developed by Ferreira for finding matrix elements of the strain Hamiltonian were later used by him to calculate the momentum matrix elements required in the \(\overrightarrow K \cdot \overrightarrow \pi\) scheme for PbTe5 and later for Bi.6 This paper is chiefly concerned with explaining Ferreira’s approach to \(\overrightarrow K \cdot \overrightarrow \pi\), In addition, however, we review the application of the \(\overrightarrow K \cdot \overrightarrow \pi\) results to the evaluation of vacancy states.
KeywordsIrreducible Representation Secular Equation Bloch Function Wannier Function Vacancy State
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