Thermal conductivity anisotropy in superconducting UPt3

Abstract

Recent thermal conductivity measurements on UP t3 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 UP t3 \B phase" and compare with experiment, speci cally the E2u and E1g (1; i) states predicted in some GinzburgLandau analyses of the phase diagram. For the simplest realizations of these states over spherical or ellipsoidal Fermi surfaces, the normalized E2u conductivity is found, surprisingly, to be completely isotropic. We discuss the e ects of inelastic scattering and realistic Fermi surface anisotropy, and deduce constraints on the symmetry class of the UP t3 ground state.PACS Numbers: 74.70T,74.25FThe heavy fermion superconductor UPt 3 is now generally thought to be \unconventional", in the sense that the order parameter exhibits a lower symmetry than that of the Fermi surface. The principal evidence for this conclusion has been the observation of a nontrivial phase diagram for the system in applied magnetic eld and pressure. Earlier hints of unconventional behavior included transport and thermodynamic properties reported to vary as power laws in the temperature for T T c , as well as strong, temperature{dependent anisotropy in superconducting transport properties. 1] Current Ginzburg-Landau (GL) theories of the UPt 3 phase diagram attempt to explain the multiplicity of superconducting phases observed by assuming an order parameter corresponding to 1) a higher dimensional irreducible representation of the normal state symmetry group, weakly split by a symmetry{breaking eld; or 2) a mixture of two accidentally nearly degenerate representations. In most scenarios, the quartic terms in the GL free energy are chosen to reproduce, if possible, the expected nature of the low-temperature, low-eld UPt 3 "Bphase", characterized by a line of gap nodes in the hexagonal basal plane, and possibly point nodes along the caxis. The prejudice in favor of this structure arises from early tranport experiments. 1,2] Qualitatively speaking, these experiments support a picture in which there is, for T T c , a higher density of excited quasiparticles with wave vectors in the basal plane. Attempts to measure this anisotropy in other experiments have not been uniformly successful, however. For example, measurements of the London penetration depth L in geometries chosen to maximize currents along chosen directions found L (T ) T 2 with coe cients depending only weakly on direction. 3] A SR experiment reporting considerable anisotropy in the same quantity 4] may in fact have been dominated by extraneous e ects. 5] Explicit evidence in favor of strong gap anisotropy in the superconducting state involving measurements in di erent directions in the same sample is in fact rather limited. 1,6] The recent thermal conductivity measurements of Lussier et al. are therefore of considerable interest, both as hard qualitative evidence for anisotropy and for the opportunity to make q...

Thermal conductivity of superconducting UPt3 at low temperatures

“…This discrepancy is considerably smaller than the discrepancy reported by several other authors. 11,10,15 Finally, the parameters de ning the excitation gap near the point nodes are adjusted to t c (T )=T at T T c . These values are 1 = 2=3 for the E 1g model and 2 = 4 for the E 2u model.…”

Determination of the gap structure inUPt3by thermal conductivity

“…In particular, it is sensitive to the anisotropy of the gap structure. Motivated by the recent calculations of Fledderjohann and Hirschfeld, 5 we have now measured the thermal conductivity of UPt 3 down to T c /10 and report two new facts: ͑1͒ there is no trace of a residual normal fluid at Tϭ0 ͑at the 1% level͒ and ͑2͒ the gap must go to zero along the c axis, in addition to the well-established line node in the basal plane.…”

“…The calculations so far assume a single ellipsoidal Fermi surface and s-wave scattering, and they require two input parameters: the impurity scattering rate ⌫ 0 and the scattering phase shift ␦ 0 . 5 The assumption of isotropic scattering is supported by the fact that both elastic and inelastic processes give the same anisotropy in normal state transport, i.e., c / b ϭ2.8 and c / b ϭ2.7 from Tϭ0.1 K to 0.8 K, which can therefore be attributed to an anisotropy in the Fermi velocity. 4,5 From de Haas-van Alphen ͑dHvA͒ measurements, 12 the Fermi surface is known to be made of several sheets, and a single ellipsoid is certainly an oversimplification.…”

“…5 The assumption of isotropic scattering is supported by the fact that both elastic and inelastic processes give the same anisotropy in normal state transport, i.e., c / b ϭ2.8 and c / b ϭ2.7 from Tϭ0.1 K to 0.8 K, which can therefore be attributed to an anisotropy in the Fermi velocity. 4,5 From de Haas-van Alphen ͑dHvA͒ measurements, 12 the Fermi surface is known to be made of several sheets, and a single ellipsoid is certainly an oversimplification. However, the usual Dingle plot analysis yields fairly uniform scattering rates, with ϭ 1/⌫ dHvA ϭ2 -4ϫ10 Ϫ11 s, in crystals of a quality comparable to ours.…”

Theory of Tunneling Conductance for Normal Metal/Insulator/ Triplet Superconductor Junction

“…singlet pairing states, 3,4,5) while others suggest triplet pairing states belonging to the onedimensional representation (A u ) 6, 7) and to the two-dimensional representation (E u ). 8, 9) Although theoretical 10,11,12) and experimental 13,14,15,16,17) spectroscopic studies of the thermal conduction and transverse sound attenuation of UPt 3 have been performed, the symmetry of the pair potentialcould not yet been determined.Recently superconductivity has been discovered in Sr 2 RuO 4 , 18) which is the first example of a noncuprate layered perovskite superconductor. Since this compound is isostructual to the cuprate superconductors the electronic properties in the normal state 19) Phase-sensitive measurements provide the most useful information for the determination of the symmetry of the pair potentials.…”