We calculate the electronic thermal conductivity in a d-wave superconductor, including both the effect of impurity scattering and inelastic scattering by antiferromagnetic spin fluctuations. We argue that phonons dominate heat transport near T c , but that electrons are responsible for most of the peak observed in clean samples, The peak position is predicted to vary nonmonotonically with disorder, in good agreement with experiments on YBa 2 ͑Cu 12x Zn x ͒ 3 O 72d . [S0031-9007(96)01535-9] PACS numbers: 74.72. Bk, 74.25.Fy, 74.62.Dh Analysis of transport experiments in the superconducting state of the high-temperature cuprate superconductors has already provided the most compelling evidence for electronic pairing in these materials. The collapse of the quasiparticle relaxation rate below T c , as observed in optical [1,2] and microwave [3] measurements, is not observed in classic superconductors, and is most naturally interpreted in terms of a gapping of the spectral density of electronic excitations responsible for inelastic scattering just above T c . This collapse is now understood to be responsible, e.g., for the peak at intermediate temperatures in the microwave conductivity of YBa 2 Cu 2 O 6.95 [3].Thermal conductivity measurements provide information on order parameter symmetry and quasiparticle relaxation and have the advantage that they are bulk probes not subject to extrinsic surface effects which have hampered the interpretation of the low-T microwave conductivity [3]. They have the disadvantage that the electronic contribution to the heat current must be separated from the phononic one. As pointed out by Yu et al. [4], the similarity between the microwave conductivity peak and measurements of the thermal conductivity k͑T ͒ in YBa 2 Cu 3 O 72d single crystals suggests that at least part of the thermal conductivity peak should be due to the electronic thermal conductivity k el ͑T ͒, in contrast to earlier analyses of this peak in terms of a phonon conductivity k ph ͑T ͒ alone [5,6]. In the work of Yu et al., the phononic mean free path ᐉ ph is assumed to vary only weakly with T , T c , whereas in the Peacor et al. approach [5], ᐉ ph is assumed to be dominated by phonon-electron relaxation, leading via the pair correlations in the electronic system to an exponential behavior below T c . In Ref.[5] it is assumed that k ph ¿ k el over the entire temperature range, whereas Yu et al. deduce k ph ͑T c ͒ Ӎ 2 2 3k el ͑T c ͒ using the measured s 1 ͑T c ͒ on similar quality crystals, and assuming the Wiedemann-Franz law k el L 0 T s 1 with the free electron Lorenz number L 0 .In this paper, we adopt a theoretical model of electronic transport in a d-wave superconductor limited by impurity and spin fluctuation scattering which has proven successful in describing many of the systematics of mi-crowave measurements, and apply it to calculate the electronic thermal conductivity. We analyze experiments on Zn doped YBa 2 Cu 3 O 72d to argue that (a) phonons do in fact dominate heat conduction at T c ; (b) a peak in ...
I show that measurements of thermoelectric effects can provide a simple criterion for distinguishing between ordinary superconductivity and superconductivity characterized by an order parameter with symmetry less than that of the underlying Fermi surface. An externally imposed temperature gradient gives rise generally to circulating currents and magnetic 6elds which vanish only if the thermoelectric and electromagnetic responses of the superconductor are isotropic. An estimate of the magnitude of this effect suggests that, while in ordinary superconductors these effects are extremely small, a signal in a heavy-fermion superconductor should be detectable. The heavy-fermion superconductors CeCu2Si2, UBet3, and UPt3 have attracted a great deal of experimental and theoretical attention, largely because of thermodynamic and transport properties dramatically different from those predicted by Bardeen-Cooper-Schrieffer (BCS) theory. ' While a number of measurements have pointed to the existence of a highly anisotropic order parameter in these systems,it has proven surprisingly difficult to distinguish experimentally between superconducting order with the symmetry of the underlying Fermi surface and an "exotic" type of order corresponding to a higher order, possibly degenerate representation of this symmetry group. A definitive proof that the order in heavy-fermion superconductors is of the latter type would be of extreme interest, particularly in light of suggestions that the pairing in these systems is mediated by virtual electronic spin or charge fluctuations rather than phonons.~Such a system would be less likely to condense in a state with trivial or "s-wave" symmetry.Similarities in responses predicted for various anisotropic states, coupled with experimental uncertainties regarding, among other things, the exact form of the true Fermi surface, have led to a search for unambiguous tests of "exotic" ordering. Josephson tunneling between known even-parity and candidate odd-parity superconductors was initially proposed as a potential method of determining the parity of the heavy-fermion order parameter;s it has recently been observed, however, that the large differences in spin-orbit interaction on both sides of the interface may complicate interpretation of these experiments.Gorkov has shown that the slope of the upper critical field at T, will exhibit anisotropy in a cubic system only if the order parameter corresponds to a degenerate representation of the Fermi-surface symmetry group.However, the huge measured H, 2 slope in the UBet3 system unfortunately renders such an experiment impracticable.
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