Molecular Crystals and Localized Vibrational States

Abstract

The normal modes arising from a simple linear model of a crystalline solid predict many important properties such as the specific heat, the sound velocity, and the Raman and infrared response. Such a model fails, however, to produce thermal expansion and finite thermal conductivity. The introduction of weak non-linear couplings between the normal modes immediately corrects these simpler problems, while preserving the usual phonon representation of the purely linear system as a useful first approximation for small phonon amplitudes. What we wish to consider here is the next step in the process, taken by keeping the weak non-linearities but introducing large phonon amplitudes. Putting aside, for the moment, the question of how to achieve the necessary amplitudes, we can consider the consequences if certain not unusual conditions obtain which put the phonon equation of motion in correspondence with the non-linear Schrodinger equation. We can then be guided by classical solutions of this equation which predict spontaneous symmetry breaking and vibrational localization. To focus our thoughts, we outline in physical terms the processes leading to the localization of vibrational energy. We use the insight gained to guide our choice of materials, and we describe the measurements we have made to begin the establishment of a rigourous connection between real solids and the theoretical constructs related to this problem.