Infrared reflection spectra of Pb$_{1-x}$Sn$_{x}$Se ($x$ = 0.2, 0.34) topological insulator films on a ZnTe/GaAs substrate and the vibrational modes of multilayer structures

The reflectance spectra of the topological insulator Pb$_{1-x}$Sn$_{x}$Se ($x$ = 0.2, 0.34) films grown by molecular-beam epitaxy on a ZnTe/GaAs substrate are measured in the range of 12–2500 cm$^{-1}$ at room temperature. Using dispersion analysis, the frequencies of transverse optical phonons, plasma frequencies, highfrequency permittivities, and layer thicknesses are determined. In the quasi-steady-state approximation, the interface mode frequencies of the four-layer structure are calculated as a function of the overlap parameter $\chi_{1}$ (0 $\le\chi_{1}\le$ 1). The parameter describes the degree of overlap of two interface modes localized at planes bounding the layer to the right and left. The existence of interacting interface modes in the structure makes its spectrum different from the sum of component spectra. These differences manifest themselves in the experiment. The conditions of the interaction of interface modes with IR radiation are discussed.