Thermoelectric effect as a test of exotic superconductivity

Abstract

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.

Thermal conductivity and gap structure of the superconducting phases of UPt3

“…In non conventional superconductors with nodes of the gap, the pair breaking effect of even non magnetic impurities or defects leads to a finite density of states at the Fermi level, due to virtual bound states forming a band of width γ (see Refs. [9][10][11][13][14][15][16][17][18][31][32][33][34]). This band is easier to observe when the impurities are in the unitarity scattering limit (scattering phase shift δ = π/2), and in heavy fermion superconductors, impurity scattering is expected to be in this limit [9].…”

“…[2,3,[5][6][7][8] for experimental and Refs. [9][10][11][12][13][14][15][16][17][18][19] for theoretical work) has already demonstrated that the thermal conductivity (κ) in this compound is of electronic origin at very low temperature, and thus sensitive to the electronic excitations in the superconducting state. Compared to the specific heat C, κ is a directional probe, and it seems [5,6] that the anomaly present in the specific heat below 100mK does not influence κ.…”

Quasiparticle Transport Properties ofd-Wave Superconductors in the Vortex State

“…This represents the contribution to the heat current from a small region of space around R, in which the local superfluid velocity is v s (R), from quasiparticles at the Fermi level. Impurity vertex corrections, which vanish identically at H = 0, [17] are still negligible, of order Hγ 2 /(H c2 ∆ 2 0 ). Here γ ≡ Σ ′′ 0 (0) is the broadening of the nodal quasiparticle states.…”

Thermoelectric effects in the superconducting state

“…Ситуация существенно изменилась после открытия ВТСП, у которых и Т с выше и меньше. Так, при Т с ~ 100 К и ~ 0,1 эВ уже [8] Учитывая грубость оценки (18), вполне может оказаться, что для ка ких то материалов даже Далее, если спаривание является не s спариванием, как в теории БКШ, а р или d спариванием (и, вообще, как говорят, экзотическим спариванием), то возрастает в раз [19,20] и, таким образом, даже при оценке типа (18), ~ 1. Ана логична с ВТСП ситуация для сверхпроводников с тяжелыми фермионами [231.…”

“…Но каковы подлинные значения b n в монокристаллах ВТСП при Т < Т с , мы не знаем. Они могут быть не столь уже малыми даже при S спаривании, а при экзотическом спари вании будут значительны [19,20]. Тем интереснее, очевидно, осуществить соответствующие измерения.…”