Regularities of temperature changes in IR reflection spectra of the infrared radiation of the Bi$_{0.8}$Sb$_{1.2}$Te$_{3}$ crystal in the region of excitation of plasma oscillations of free charge carriers and interband transitions

The regularities of the temperature behavior of the reflection spectra of the Bi$_{0.8}$Sb$_{1.2}$Te$_{3}$ crystal obtained in the range of the plasma resonance of free charge carriers and the fundamental absorption edge allow us to trace the changes in the plasmon energy $E_p$ and the optical band gap $E_{g\operatorname{opt}}$. The observed decrease in $E_{g\operatorname{opt}}$ with increasing temperature corresponds to the existing ideas about the redistribution of holes between the nonequivalent extremes of the valence band in (Bi$_{2-x}$Sb$_{x}$)Te$_{3}$ (0 $<x<$ 1) crystals. The dominance of this process in a certain temperature range contributes to the change in plasma frequencies.