S. K. Yip

Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors

We use the quasiclassical theory of superconductivity to calculate the electronic contribution to the thermal conductivity. The theory is formulated for low temperatures when heat transport is limited by electron scattering from random defects and for superconductors with nodes in the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are universal at low temperature, {ital k}{sub {ital BT}}{lt}{gamma}, where {gamma} is the bandwidth of impurity bound states in the superconducting phase. The components of the electrical and thermal conductivity also obey a Wiedemann-Franz law with the Lorenz ratio {ital L}({ital T})={kappa}/{sigma}{ital T} given by the Sommerfeld value of {ital L}{sub {ital S}}=({pi}{sup 2}/3)({ital k}{sub {ital B}}/{ital e}){sup 2} for {ital k}{sub {ital BT}}{lt}{gamma}. For intermediate temperatures the Lorenz ratio deviates significantly from {ital L}{sub {ital S}}, and is strongly dependent on the scattering cross section, and qualitatively different for resonant vs nonresonant scattering. We include comparisons with other theoretical calculations and the thermal conductivity data for the high-{ital T}{sub {ital c}} cuprate and heavy fermion superconductors. {copyright} {ital 1996 The American Physical Society.}

Nonlinear Meissner effect in unconventional superconductors

We examine the long-wavelength current response in anisotropic superconductors and show how the field dependence of the Meissner penetration length can be used to detect the structure of the order parameter. Nodes in the excitation gap lead to a nonlinear current-velocity constitutive equation at low temperatures that is distinct for each symmetry class of the order parameter. The effective Meissner penetration length is linear in {ital H} and exhibits a characteristic anisotropy for fields in the {ital ab} plane that is determined by the positions of the nodes in momentum space. The nonlinear current-velocity realtion also leads to an intrinsic magnetic torque for in-plane fields that are not parallel to a nodal or antinodal direction. The torque scales as {ital H}{sup 3} for {ital T}{r_arrow}0 and has a characteristic angular dependence. We analyze the effects of thermal excitations, impurity scattering and geometry on the current response of a {ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2} superconductor, and discuss our results in light of recent measurements of the low-temperature penetration length and in-plane magnetization of single-crystals of YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} and LuBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}}.

Models for superfluid 3He in aerogel

Several recent experiments find evidence of superfluidity of 3He in 98%-porous aerogel. The primary effect of the aerogel is that it scatters the quasiparticles of 3He. We find that many experimental findings are quantitatively understood by a relatively simple model that takes into account strong inhomogeneity of the scattering on a length scale of 100 nm.

Weak link between conventional and unconventional superconductors

In this paper we consider the Josephson coupling between a conventional and an unconventional superconductor through a constriction. It is demonstrated that a weak link is very different from a tunnel junction. In particular, in an orientation where the coupling in a tunnel junction vanishes because of symmetry, the Josephson current in the case of a weak link can nevertheless be finite, albeit with the distinctive characteristics of(i) a current phase relationship with a period of 2π/n, (ii) the critical current near but below the transition temperature T1 of the lower transition temperature superconductor is proportional to (1−(T/T1))n/2, where n is an integer determined by the symmetry.

Energy resolved supercurrent between two superconductors

In this paper I study the energy-resolved supercurrent of a junction consisting of a dirty normal metal between two superconductors. I also consider a cross geometry with two additional arms connecting the above mentioned junction with two normal reservoirs at equal and opposite voltages. The dependence of the supercurrent between the two superconductors on the applied voltages is studied.

Thermal conductivity of superconducting UPt3 at low temperatures

We study the thermal conductivity within the E1g and E2u models for superconductivity in UPt3 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/Tc ≈ 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 E1g or E2u order parameter. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum that are reflected in the thermal conductivity at very low temperatures. Significant differences between the E1g and E2u models are predicted to develop at excitation energies below the bandwidth of the impurity-induced Andreev bound states. The zero-temperature limit of the ĉ axis thermal conductivity, limT→0 kc/T, isuniversal for the E2u model, but non-universal for the E1g model. Thus, impurity concentration studies at very low temperatures should differentiate between the nodal structures of the E2u and E1g models.

Circular dichroism and birefringence in unconventional superconductors

We present a theoretical analysis of circular dichroism and birefringe in unconventional BCS superconductors with appropriate broken symmetries. We show that for the effect to exist, that in addition to broken time-reversal and two-dimensional parity symmetries, it is necessary to take into account the weak particle-hole asymmetry of the low-energy excitations of the metallic state. Circular dichroism and birefringence are shown to arise from the order parameter collective mode response of the superconductor; in the clean limit the contribution to the current response from the single-particle excitations does not give rise to circular dichroism or birefringence, even with particle-hole asymmetry. The magnitude of the circular dichroism is found to be small for the classes of superconductors which are thought to be likely candidates to exhibit the requisite broken symmetries, namely the heavy fermions and oxide superconductors. The order of magnitude of the elliptical polarization of a linearly polarized incident wave is Vf/c(ζ/λL) (Δ/Ef) ln(Ef/Δ), which is roughly 10−7−10−8 rad at frequencies of order the gap, and decreases at least as fast as (2Δ/ω)2 at higher frequencies.

Pinhole junctions in d-wave superconductors

Abstract We present a self consistent treatment of pinhole junctions in d x 2 − y 2 superconductors. The current–phase relation j s ( χ ) is studied at different temperatures and at different angles α between the crystal â -axis and the junction (surface) normal. We show that the critical current of a junction can be reduced by pair-breaking effects at the separation. We also study the Josephson energy of a pinhole as a function of the phase difference across the junction. In particular are mapped the positions of the energy minima χ min at different temperatures as functions of ( α L , α R ), the crystal orientations of the left and right superconductors. With decreasing temperature there is an increasing range of crystal orientations where χ min varies continuously from 0 to π .

Conductance anomalies for normal-metal--insulator--superconductor contacts

This paper considers the conductance through a dirty junction between a normal conductor and a superconductor with an insulating barrier. It is shown that for large-barrier resistances there is a relative enhancement of the conductance near zero voltage, whereas for low-barrier resistance this anomaly appears at finite voltage.

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

AbstractWe 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 UPt3. 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, κc/κb, 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 UPt3. The models for the order parameter that fit the experimental data for the ĉ and