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Temperature-driven band inversion in Pb$_{0.77}$Sn$_{0.23}$Se: Optical and Hall-effect studies

Optical and Hall-effect measurements have been performed on single crystals of Pb$_{0.77}$Sn$_{0.23}$Se, a IV-VI mixed chalcogenide. The temperature dependent (10--300 K) reflectance was measured over 40--7000 cm$^{-1}$ (5--870 meV) with an extension to 15,500 cm$^{-1}$ (1.92 eV) at room temperature. The reflectance was fit to the Drude-Lorentz model using a single Drude component and several Lorentz oscillators. The optical properties at the measured temperatures were estimated via Kramers-Kronig analysis as well as by the Drude-Lorentz fit. The carriers were p-type with the carrier density determined by Hall measurements. A signature of valence intraband transition is found in the low-energy optical spectra. It is found that the valence-conduction band transition energy as well as the free carrier effective mass reach minimum values at 100 K, suggesting temperature-driven band inversion in the material. Density function theory calculation for the electronic band structure also make similar predictions.