Studies of the phase transition in a model of tin telluride

Abstract

We have constructed a fully-specified model of a diatomic crystal showing a soft-mode phase transition, loosely patterned on tin telluride. The model can be used to test the accuracy of different techniques for studying the phase transition. Here we apply the self-consistent phonon theory (SCI). Using this theory, we do find a soft mode in the high-temperature, cubic phase, and the free energy shows the Landau form, consistent with a mean-field theory of a second-order phase transition. However, the frequency of the soft mode calculated in the self-consistency iterations does not go to zero at the phase transition. It is pointed out that, even within the SC1 approximation, the frequencies associated with the response functions of the crystal should include additional contributions, corresponding to cubic and bubble-diagram shifts. With these contributions included, the frequency does go to zero at the transition. The shape of the spectral function is also discussed.