Anharmonic resonant modes and the low-temperature specific heat of glasses

Abstract

For disordered solids it is shown that anharmonic resonant modes can contribute both a linear and a cubic term to the temperature-dependent specific heat. The linear dependence is associated with resonant-mode diffusion while the excess cubic term comes from the stationary resonant-mode component. Both features are derived from the vibrational anharmonicity of the solid with the resonant mode frequency as the one important model parameter. When its value is fixed with the measured linear term then the enhanced resonant mode density of states has the correct order of magnitude and frequency position to account for the excess $T^3$ specific heat observed in a number of glasses. The same mechanism also can account for both the presence and absence of the observed linear specific-heat contribution in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.