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The phonon contribution to the thermal conductivity at low temperature insuperconductors with line nodes is calculated assuming that scattering by bothnodal quasiparticles and the sample boundaries is significant. It is determinedthat, within the regime in which the quasiparticles are in the universal limitand the phonon attenuation is in the hydrodynamic limit, there exists a widetemperature range over which the phonon thermal conductivity varies as $T^2$.This behaviour comes from the fact that transverse phonons propagating alongcertain directions do not interact with nodal quasiparticles and is thus foundto be required by the symmetry of the crystal and the superconducting gap,independent of the model used for the electron-phonon interaction. The$T^2$-dependence of the phonon thermal conductivity occurs over a well-definedintermediate temperature range: at higher $T$ the temperature-dependence isfound to be linear while at lower $T$ the usual $T^3$ (boundary-limited)behaviour is recovered. Results are compared to recent measurements of thethermal conductivity of Tl2201, and are shown to be consistent with the data.Comment: 4 page

physical review. b, condensed matter and materials physics

Low-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>phononic thermal conductivity in superconductors with line nodes

Low-Tphononic thermal conductivity in superconductors with line nodes