Energy Bands in PbTe

The augmented-plane-wave method for calculating the band structure of a solid has been extended to include the relativistic terms of the two-component Hamiltonian which is obtained by two successive applications of the Foldy-Wouthuysen transformation to the Dirac Hamiltonian. Basis functions for the secular equation which are basis partners for the irreducible representations of the double group are constructed from the eigenfunctions of the nonrelativistic Hamiltonian. Expressions for the relativistic matrix elements between these basis functions are found and numerically evaluated, and the resulting Hamiltonian matrix is diagonalized to give the energy levels for PbTe. The calculated bands, with only slight modification, appear to be consistent with available experimental information.