Electron and Phonon Thermal Conduction in Epitaxial High-T_c Superconducting Films

Electrons and phonons are the carriers of heat in the a-b plane of the high-T_c superconductor YBa₂Cu₃O₇. In the absence of boundary scattering, the a-b plane thermal conductivity and the mean free path of each carrier type are calculated as functions of temperature using kinetic theory, the two-fluid model of the superconducting state, and experimental data for the thermal conductivity and electrical resistivity of a single crystal. The reduction by boundary scattering of the effective a-b plane thermal conductivity along an epitaxial YBa₂Cu₃O₇ film is predicted as a function of temperature and film thickness. The size effect on the phonon conductivity dominates over the size effect on the electron conductivity. The predicted electron mean free path is limited by scattering on defects and is in very good agreement with experimental data from infrared spectroscopy.