On the nature of a lattice vibrational mode at a frequency of 135 cm$^{-1}$ in Hg$_{1-x}$Cd$_x$Te alloys

The vibrational spectrum of a cadmium impurity atom in the HgTe crystal has been calculated using the microscopic theory of lattice dynamics in the approximation of a low impurity concentration. Within this theory, the behavior of the local and quasi-local modes induced upon substitution of the lighter Cd atom for the Hg atom in the region of the zero or very low one-phonon density of states in the HgTe crystal has been considered. It has been found that, apart from the local mode at a frequency of 155 cm$^{-1}$, the calculated vibrational spectra exhibit a weak (but clearly pronounced) feature at a frequency of 134 cm$^{-1}$, which coincides with the experimentally observed vibrational mode (the “minicluster” mode) at a frequency of 135 cm$^{-1}$ in the Hg$_{1-x}$Cd$_x$Te ($x$ = 0.2–0.3) alloys at 80 K.