Thermal Conductivity Anisotropy in Superconducting $UPt_3$

TL;DR

This paper investigates the anisotropic thermal conductivity in the superconductor UPt3, comparing theoretical models with experimental data to constrain its ground state symmetry, and finds that certain candidate states predict isotropic conductivity.

Contribution

It provides a detailed theoretical analysis of thermal conductivity in UPt3's superconducting states, comparing predictions with experiments to identify the most likely symmetry class.

Findings

E2u state predicts isotropic conductivity on simple Fermi surfaces.

Experimental anisotropy constrains the possible superconducting symmetries.

Inelastic scattering and Fermi surface anisotropy influence thermal conductivity predictions.

Abstract

Recent thermal conductivity measurements on $UPt_3$ single crystals by Lussier et al. indicate the existence of a strong b--c anisotropy in the superconducting state. We calculate the thermal conductivity in various unconventional candidate states appropriate for the $UPt_3$ ``B phase" and compare with experiment, specifically the $E_{2u}$ and $E_{1g}$ $(1,i)$ states predicted in some Ginzburg-Landau analyses of the phase diagram. For the simplest realizations of these states over spherical or ellipsoidal Fermi surfaces, the normalized $E_{2u}$ conductivity is found, surprisingly, to be completely isotropic. We discuss the effects of inelastic scattering and realistic Fermi surface anisotropy, and deduce constraints on the symmetry class of the $UPt_3$ ground state.