Computational Methods in Band Theory pp 400-408 | Cite as

# \(\overrightarrow K \cdot \overrightarrow \pi\) Interpolation and the Calculation of Vacancy States in PbTe

## Abstract

The purpose of this paper is to describe the implementation of the Koster-Slater^{1} 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} Parada^{3} 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 Ferreira^{4} 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 PbTe^{5} 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.

## Keywords

Irreducible Representation Secular Equation Bloch Function Wannier Function Vacancy State## Preview

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## References

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