Thermal conductivity of superconducting UPt3 at low temperatures

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 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 re ected in the thermal conductivity at very low temperatures. Signi cant di erences 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 theĉ axis thermal conductivity, lim T !0 c =T , is universal for the E 2u model, but non-universal for the E 1g model. Thus, impurity concentration studies at very low temperatures should di erentiate between the nodal structures of the E 2u and E 1g models.

Transport and the order parameter of superconductingUPt3

“…This indicates that the fit for the E 2u model is somewhat questionable. Our fitting procedure differs from that of Graf et al [8,13]. These authors used revised order parameters…”

Impurity scattering in f-wave superconductor UPt3

“…First the thermal conductivities with the heat current parallel to the c axis and within the basal plane decrease linearly in T the temperature at low temperature [2]. This is consistent with E 2u but inconsistent with the then prevailing model E 1g [3,4]. Almost at the same time 195 Pt Knight shift measurement in UPt 3 finds the spin triplet pair [5].…”

Universality in transport processes of unconventional superconductors

“…Thus, our order parameter model depends on angle (p f ) and the nodal parameters ({µ i }), ∆(p f ; {µ i }). The advantage of this approach is that we can quantitatively determine the phase space contributing to the low temperature transport coefficients and then examine in more detail the effects of impurity scattering and order parameter symmetry on the current response [3], without having to know the overall shape of the Fermi surface or basis functions.The number of nodal parameters is fixed by the minimal number of symmetry unrelated point and line nodes. These parameters define the slope or curvature of the gap near a line or point node in a spherical coordinate system (uniaxial anisotropy is included by mapping an ellipsoidal Fermi surface onto a sphere).…”

“…Instead of examining the effects of the multi-sheeted Fermi surface on the heat current, charge current, and momentum current, we model the excitation spectrum by an excitation gap that opens at line and point nodes on the Fermi surface, and by the Fermi surface properties in the vicinity of the nodes (i.e., the Fermi velocities, v f , and the density of states, N f , near the nodes) [3]. Crystal symmetry determines the positions of the nodal regions of the excitation gap on the Fermi surface, but not the prefactors for the gap opening.…”

“…Thus, our order parameter model depends on angle (p f ) and the nodal parameters ({µ i }), ∆(p f ; {µ i }). The advantage of this approach is that we can quantitatively determine the phase space contributing to the low temperature transport coefficients and then examine in more detail the effects of impurity scattering and order parameter symmetry on the current response [3], without having to know the overall shape of the Fermi surface or basis functions.…”