Magneto-optical studies of PbTe in the far infrared

Far-infrared magneto-optical studies have been carried out on bulk PbTe with the 10.4- and 3.7-meV lines of a ${\mathrm{H}}_2$O and an HCN gas laser. Both $n$- and $p$-type samples were studied in fields up to 100 kG oriented along the major symmetry axes. Most of the measurements were made in the Voigt geometry. Field modulation permitted high-resolution reflection derivative spectra in which cyclotron resonances, magnetoplasma resonances, and dielectric anomalies were identified by comparison with line shapes predicted from classical magnetoplasma theory in the local limit. In the 10.4-meV data the deviations of the observed line shapes from the classical theory can be interpreted in terms of nonparabolicity of the bands. The observed transitions were fit to a six-band $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ model, and a set of band parameters was deduced which gave a consistent interpretation of all the 10.4-meV data. The resulting band-edge masses are $m^{*}\mathrm{}\left(0\right)=0.0190\mathrm{}\pm 0.0003$ for $n$-type and $m^{*}\mathrm{}\left(0\right)=0.0200\mathrm{}\pm 0.0003$ for $p$-type samples. In the 3.7-meV data, where conditions are far more classical, the line shapes are well represented by a classical calculation but with a mass 15% higher than that predicted by the 10.4-meV data. There is, however, a weak feature in the spectra which corresponds to the lower mass. It is demonstrated that the 15% splitting cannot be interpreted in terms of nonparabolicity or sample inhomogeneities. An interpretation in terms of excitonic modes arising from the phonon-mediated electron-electron interaction is discussed.