Thermal Conductivity of Superconducting UPt$_3$ at Low Temperatures

TL;DR

This paper compares theoretical models of superconductivity in UPt3 with experimental thermal conductivity data, highlighting how impurity effects can distinguish between E1g and E2u pairing symmetries at very low temperatures.

Contribution

It provides a detailed comparison of E1g and E2u models for UPt3's superconductivity, predicting distinct impurity-dependent thermal conductivity behaviors.

Findings

Both models fit the data down to T/Tc≈0.1.

E2u model predicts universal zero-temperature thermal conductivity.

E1g model predicts non-universal behavior depending on impurities.

Abstract

We study the thermal conductivity within the E$_{1g}$ and E$_{2u}$ models for superconductivity in UPt$_3$ and compare the theoretical results for electronic heat transport with recently measured results reported by Lussier, Ellman and Taillefer. The existing data down to $T/T_c\approx 0.1$ provides convincing evidence for the presence of both line and point nodes in the gap, but the data can be accounted for either by an E$_{1g}$ or E$_{2u}$ order parameter. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum that are reflected in the thermal conductivity at very low temperatures. Significant differences between the E$_{1g}$ and E$_{2u}$ models are predicted to develop at excitation energies below the bandwidth of the impurity-induced Andreev bound states. The zero-temperature limit of the $\bf \hat c$ axis thermal conductivity, $\lim_{T\to 0} \kappa_c/T$, is \underline{universal} for the E$_{2u}$ model, but non-universal for the E$_{1g}$ model. Thus, impurity concentration studies at very low temperatures should differentiate between the nodal structures of the E$_{2u}$ and E$_{1g}$ models.