Anisotropy of the Fermi Surface of $p$-Type PbTe

We have studied the angular dependence of Shubnikov-de Haas oscillations in a sample of $p$-type PbTe having a hole concentration of 3.0 × ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Orientations of the magnetic field in a {110} plane and temperatures between 4.2 and 1.2°K were used. For the first time in this material, the component frequencies were determined by Fourier analysis. The angular dependence of the corresponding extremal areas was precisely fitted by four $〈111〉$-oriented ellipsoids of revolution having a "mass anisotropy" of 13 and containing the same number of holes as that determined from the high-field Hall coefficient. These results, which are considerably different from those previously reported by Cuff et al. for material with the same hole concentration, suggest that the anisotropy is constant, at least up to the hole concentration studied here. A $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ band model, consistent with this behavior and with other results presented here, is considered. From the temperature dependence of the oscillations with $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$, the transverse effective mass at the Fermi level $m_{\perp }\left({\epsilon }_F\right)$ is $(0.\mathrm{}036\pm 0.002)m$. Longitudinal and transverse effective $g$ values at the Fermi level were determined from the spin splitting of peaks in the oscillations. For $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[111\right]\mathrm{}$, the ratio of spin splitting to Landau-level separation is 0.58 ± 0.01, and $g_{\parallel }\left({\epsilon }_F\right)=32\mathrm{}\pm 2$. For ${\overrightarrow{\mathrm{H}}}_{\perp }\mathrm{}\left[111\right]\mathrm{}$, this ratio is 0.27 ± 0.01, and $g_{\perp }\left({\epsilon }_F\right)=7\mathrm{}\pm 2$.