C. T. Rieck

Quasiclassical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering

A theory of the upper critical field is developed which is sufficiently general to incorporate strong coupling effects, anisotropy of both Fermi surface and pairing interaction, and momentum dependent scattering, including exchange and spin-orbit scattering. It is not necessary to assume that spin-orbit scattering is a small fraction of the total scattering. An important improvement in this theory is the correct treatment of the spatial dependence of the anomalous Green function and the order parameter in the mixed state. In the presence of anisotropy this is, in general, not described with sufficient accuracy by the Abrikosov vortex lattice. Application of this theory to anisotropy effects, with the clean limit taken in most cases, have been published elsewhere and additional studies will appear in the near future. In this paper we concentrate on the effects arising from the momentum dependence of the elastic scattering. If spin-orbit scattering forms a sizeable fraction of the total scattering it is necessary to take its explicit momentum dependence into account. When this is done we find that spin-orbit scattering is actually less effective in reducing paramagnetic limiting.p- andd-wave scattering have a marked effect on the upper critical fieldHc2 at low reduced temperatures, partially cancelling each other.d-wave scattering raisesHc2(O), but for physically acceptable parameter value is not sufficient to explain the apparent absence of paramagnetic limiting in some high-field superconductors. For a complete description of the upper critical field, other effects mentioned above need to be taken into account, but for superconductors of intermediate purity the momentum dependence of the scattering cannot be ignored. The greatest problem remaining in our quest for a complete understanding of the upper critical field appears to be an accurate determination of the relevant normal state properties.

Coherent versus incoherent c-axis Josephson tunneling between layered superconductors.

We calculate I{sub c}(T) and R{sub n} for both coherent and incoherent electron tunneling across a {ital c}-axis break junction between two {nu}=s,d{sub x{sup 2}{minus}y{sup 2}}-wave layered superconducting half spaces, each with {ital c}-axis bandwidth 2J. Coherent quasiparticle tunneling only occurs for voltages V{lt}2J/e, leading to difficulties in measuring R{sub n} for underdoped samples. The coherent part of I{sub c}(0) is independent of {Delta}{sub {nu}}(0) for J/{Delta}{sub {nu}}(0){lt}1, and can be large. Our results are discussed with regard to recent experiments. {copyright} {ital 1998} {ital The American Physical Society}

Re-entrant superconductivity due to Landau level quantization?

Abstract Conditions are examined under which superconductivity in type-II superconductors can persist in magnetic fields far above the upper critical field calculated from the semiclassical approximation. While orbital diamagnetism will not destroy superconductivity when only a few Landau levels are occupied, magnetic moments of the charge carriers together with scattering by impurities will strongly suppress this phase transition, rendering its observation in real singlet superconductors highly unlikely.

Time-domain Terahertz spectroscopy as a diagnostic tool for the electrodynamic properties of high temperature superconductors

Abstract Time-domain Terahertz transmission spectroscopy (TDTTS) has proved to be a unique method for the experimental study of electromagnetic properties of high temperature superconducting thin-films at THz-frequencies in basic and applied research. We have improved the analysis of TDTTS-measurements by numerically extracting the complex index of refraction from the measured complex transmission of the superconducting thin film. Based on this other important figures as surface resistance and dielectric function are derived. We have applied this method to study the surface resistance and the dielectric function of YBa2Cu3Ox thin films between 10K and 120K in the frequency range between 0.15THz and 2.4THz. The temperature and frequency dependence of our surface resistance data is successfully explained by a weak coupling model of d-wave superconductivity which incorporates inelastic and elastic scattering at temperatures above 50K. At lower temperatures a deviation of the experimental data from theory is observed which is due to a resonance of the dielectric function.

Upper critical fields of superconductors with anisotropic fermi surfaces

Abstract It is shown how the temperature dependence of the upper critical field H c2 and that of the vortex state at the phase boundary can be calculated exactly for superconductors with arbitrary Fermi surfaces. Effects of isotropic impurity scattering are included. The theory is applied to nearly cylindrical model Fermi surfaces appropriate for the high- T c superconductors.

Surface impedance of epitaxial YBCO thin films — Comparison of experimental data with a d-wave theory of superconductivity

The surface impedance of two 350nm thick YBCO films was measured for temperatures between 4.2K and 150K in a copper cavity at 87 GHz. Both films, one grown by electron beam evaporation on MgO, the other one by high oxygen-pressure dc sputtering from a stoichiometric target on LaAlO3, provide critical temperatures of about 91K, low residual surface resistances of Rs(4.2K) < 1mΩ and low specific resistivities in the normal state of ϱ(100K) < 85μΩcm. The experimental data obtained on these two films are compared to a d-wave model of superconductivity which incorporates elastic and inelastic scattering. Good agreement between theory and the experimental results for both the surface resistance and the penetration depth in the whole temperature range is achieved for scattering phase shifts near 0.4π and order parameter amplitudes in the range of 2Δ0(0)/kBTc = 6.0 – 7.5 without subtracting an extrinsic residual surface resistance.

Raman scattering in unconventional superconductors: Vertex corrections in the Hubbard and Coulomb models

The electronic Raman spectrum for the experimentally relevant polarizations is calculated within a Hubbard-type model for anisotropic superconductors and compared with the results for the standard Coulomb model. The requirement of gauge invariance is shown to play an especially important role. The Raman A1g response depends rather sensitively on band structure.

Exchange enhancement of the electron-phonon pair interaction

Abstract The critical temperature of high-Tc superconductors is determined, at least in part, by the electron-phonon coupling. We include the effect of an exchange interaction between the electrons and calculate the renormalization of the bare phonon frequencies and the electron-phonon verticies in a random phase approximation and obtain a strongly enhanced attractive phonon-induced electron-electron interaction. Using Fast Fourier Transform techniques, the weak-coupling selfconsistency equation for the order parameter is solved in the 2D first Brillouin zone for the Emery tight-binding band with different band fillings. The enhancement of Tc arises primarily from the softening of the phonon frequencies rather than the vertex renormalization.

Theory of NMR and specific heat for extended s-wave and d-wave pairing states in high Tc superconductors

We solve the Eliashberg equations exactly for anisotropic interactions projected onto extended s-wave and d-wave states. The resulting density of states for a gap with nodes (s- or d-wave) yields a nuclear spin relaxation rate which has almost no Hebel-Slichter peak. We calculate ΔF, Hc, and ΔC for different coupling constants and Einstein spectra of the isotropic and anisotropic interactions. The specific heat jump ΔC can be large and sharp compared to BCS theory. We conclude that gaps having nodes yield better agreement with experiments on high-Tc superconductors.

Inelastic light scattering in clean d-wave superconductors

Abstract We have calculated the Raman response function in the weak-coupling limit for a clean d-wave superconductor below T c using various approaches for the bare coupling between the incident light and the electronic excitations. Within a one-band description, it turns out that the A 1g and B 2g scattering intensities depend strongly on bandstructure effects. Thus, a simultaneous explanation of the Raman data for optimally doped cuprates for all three relevant polarization geometries remains difficult.