Soft Phonon Mode in SnTe

Abstract

The self-consistent phonon formalism, successful in the description of the quantum crystals ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$, is here applied to a discussion of the soft $k=0\mathrm{}$ TO mode in SnTe. Straightforward considerations allow us to arrive at a simple expression for $\omega _{\mathrm{TO}}^{}{}_{}{}^2\mathrm{}(k=0\mathrm{})\mathrm{}$ in the low-temperature regime. The analysis permits a quantitative fit to the temperature dependence of $\omega _{\mathrm{TO}}^{}{}_{}{}^2\mathrm{}(k=0\mathrm{})\mathrm{}$ over a rather wide range of temperature.