k→·p→ Model for the Magnetic Energy Levels in PbTe and Pb1−xSnxTe

Abstract

A $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ band model is developed for the magnetic energy levels of the valence- and conduction-band extrema in PbTe and ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$. The model, similar in approach to that of Cohen for bismuth, extends the six-band model of Dimmock for ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ to the case of an arbitrarily directed magnetic field, and includes calculation of the eigenfunctions. These eigenfunctions, which depend on field orientation, are used in the formal development of a theory of the Knight shift for subsequent comparison with experiment. An observed maximum in the Knight shift as a function of carrier concentration is correctly accounted for, and one component of the inhomogeneous broadening of the NMR lines is explained in terms of the orientation dependence of the spin admixture of the Landau-level wave functions.