Thermal conductivity of systems with a gap in the phonon spectrum

An original theoretical model for describing the low-temperature thermal conductivity in systems with a region of forbidden values (a gap) in the phonon spectrum is proposed. The model is based on new experimental results on the temperature dependence of the phonon diffusion coefficient in nanoceramics and dielectric glasses which showed a similar anomalous behavior of the diffusion coefficient in these systems that may be described under the assumption of a gap in the phonon spectrum. In this paper, the role of the gap in low-temperature behavior of the thermal conductivity, κ (T), is analyzed. The plateau in the temperature dependence of the thermal conductivity is shown to correlate with the position and the width of the gap. The temperature dependence of thermal conductivity of such systems when changing the scattering parameters related to various mechanisms is studied. It is found that the umklapp process (U-processes) involving low-frequency short-wavelength phonons below the gap forms the behavior of the temperature dependence of thermal conductivity in the plateau region. A comparison of the calculated and experimental results shows considerable possibilities of the model in describing the low-temperature thermal conductivity in glass-like systems.