Phonon-defect interaction: alternative cause for the low temperature anomaly of the thermal conductivity of high Tc superconductors and of amorphous materials

Abstract We study the phonon relaxation and phonon transport in the isotope defect model using the Green function approach. We find that through the self-consistent calculation of Davies and Langer the inverse of the phonon relaxation time can be a linear function of frequency at low frequencies and the thermal conductivity a quadratic function of temperature at low temperatures for bulk materials containing isotope defects. Thus, we demonstrate that the anomalous T 2 behavior of the thermal conductivity of high T c superconductors and of amorphous materials at low temperatures may result from phonon-defect interaction.