Magneto-optical investigations of phase-transition-induced band-structure changes of ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$Te

The structural phase transition in semiconducting ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{\mathrm{x}}$Te from a high-temperature cubic structure to a low-temperature rhombohedral structure was studied by investigating the temperature dependence of the electronic properties. The reduction of symmetry below the phase-transition temperature $T_c$ changes the electronic band structure. Experimentally, these changes were studied by magneto-optical intraband and interband transmission for samples with Ge content up to 1 at. % and $T_c$ values below 50 K. Theoretically the energy-versus-momentum relationships for the T and L points of the Brillouin zone are deduced by the method of invariants and by a k→⋅p→ calculation. Below $T_c$, the main result is the occurrence of k-linear terms described by one additional momentum matrix element. The magnetic field dependence of Landau states was derived and electric dipole intraband and interband transition elements were calculated. New transitions like spin-flip, and combined spin-flip and cyclotron-resonance harmonics appear in the low-temperature phase. Based on a linear-response formalism for the conductivity, the magnetic field dependence of the intraband transmission for far-infrared frequencies is calculated and quantitatively compared with the experimental data. The relevant band parameters were determined. An additional matrix element plays the role of a secondary order parameter evidenced by its temperature dependence. This parameter is closely related to the optical interband deformation potential which is determined for the T and L points of the Brillouin zone.