Low-$T$ Phononic Thermal Conductivity in Superconductors with Line Nodes

TL;DR

This paper calculates the low-temperature phonon thermal conductivity in superconductors with line nodes, revealing a broad temperature range where it varies as T^2 due to symmetry and scattering effects, aligning with experimental data.

Contribution

It demonstrates that phonon thermal conductivity exhibits a T^2 dependence over a wide temperature range in nodal superconductors, independent of electron-phonon interaction models.

Findings

T^2 dependence of phonon thermal conductivity over a broad temperature range

Consistency with experimental measurements of Tl2201

Identification of symmetry-driven phonon behavior

Abstract

The phonon contribution to the thermal conductivity at low temperature in superconductors with line nodes is calculated assuming that scattering by both nodal quasiparticles and the sample boundaries is significant. It is determined that, within the regime in which the quasiparticles are in the universal limit and the phonon attenuation is in the hydrodynamic limit, there exists a wide temperature range over which the phonon thermal conductivity varies as $T^2$. This behaviour comes from the fact that transverse phonons propagating along certain directions do not interact with nodal quasiparticles and is thus found to 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-defined intermediate temperature range: at higher $T$ the temperature-dependence is found to be linear while at lower $T$ the usual $T^3$ (boundary-limited) behaviour is recovered. Results are compared to recent measurements of the thermal conductivity of Tl2201, and are shown to be consistent with the data.