Phonon mode potential and its contribution to anharmonism

We present systematic ab-initio study on the phonon mode potential as a source of anharmonicity in the crystal. As an example, the transverse optical (TO) mode potential in PbTe has been fitted to density-functional-theory calculated energies of phonons excited with different amplitudes of mode displacements. The corresponding equation of motion has been analytically and numerically solved in 1D and 2D space, respectively. The solution is used for constructing the ensemble of 10,000 systems with potential and kinetic energies selected according to the thermal equilibrium distributions. The velocity auto-correlation function derived from the computed trajectories is then used to calculate the profile of the phonon spectrum for the TO an LA modes at three temperatures of 100, 300, and 600 K. This technique allows for determination of the contribution of non-quadratic potential of the phonon mode to the anharmonicity in the crystal and its effect on the phonon spectrum.