Thermal Conductivity of the Accidental Degeneracy and Enlarged Symmetry Group Models for Superconducting UPt₃

Abstract

We present theoretical calculations of the thermal conductivity for the “accidental degeneracy” and “enlarged symmetry group” models that have been proposed to explain the phase diagram of UPt ₃ . The order parameters for these models possess point nodes or cross nodes, reflecting the broken symmetries of the ground state. These broken symmetries lead to robust predictions for the ratio of the low-temperature thermal conductivity for heat flow along the ĉ axis and in the basal plane. The anisotropy of the heat current response at low temperatures is determined by the phase space for scattering by impurities. The measured anisotropy ratio, κ _c/κ _b, provides a strong constraint on theoretical models for the ground state order parameter. The accidental degeneracy and enlarged symmetry group models based on no spin-orbit coupling do not account for the thermal conductivity of UPt ₃. The models for the order parameter that fit the experimental data for the ĉ and ${\hat c}$ directions of the heat current are the 2D E_1g and E _2u models, for which the order parameters possess line nodes in the ab-plane and point nodes along the ĉ axis, and the A_1g⊕E _1g model of Zhitomirsky and Ueda. This model spontaneously breaks rotational symmetry in the ab-plane below T_c2 and predicts a large anisotropy for the ab-plane heat current.