In-plane surface impedance of epitaxial YBa2Cu3O7−δ films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity

Abstract

We have measured the temperature dependence of both the surface resistance and the change of the penetration depth in two optimized epitaxial c-axis oriented YBa2Cu3O7−δ (YBCO) films at 87 GHz by incorporating each film as an end plate in a cylindrical copper cavity. A high frequency is used in order to increase losses in the superconducting samples relative to the losses in the copper cavity. It is found that our measuring frequency is of a magnitude comparable to the relevant low-temperature scattering rates, so that the real part of the conductivity would be expected to display significant frequency dependence. The two films investigated were both 350 nm thick, but prepared by different techniques. The experimental results are compared to weak-coupling d- and s-wave models of superconductivity which incorporate both inelastic and elastic scattering, with the latter forming a small part of the total scattering. The sizable surface resistance at low temperatures and the approximately linear temperature variation can be accounted for without subtracting an extrinsic residual surface resistance, if d- or anisotropic s-wave order parameters with nearly vanishing Fermi surface averages and scattering phase shifts close to 0.4π are assumed. Large low-temperature losses are obtained theoretically in spite of the fact that order parameter amplitudes must be in the range of 2Δ0(0)/kBTc=6.0–7.5, considerably larger than the corresponding weak-coupling values, in order to describe the data at higher temperatures. When inelastic scattering is represented by a phenomenological temperature-dependent scattering rate, a quantitative fit to the experimental data for both the surface resistance and the penetration depth of YBCO over the whole measured temperature range from 4.2 to 145 K can be obtained within a single model. Some discrepancy between theory and experiment remains near the transition temperature where fluctuation effects, not treated in this paper, are clearly visible. While very different parameter sets can be found that would fit the real part of the conductivity, having to explain both penetration depth and surface resistance puts severe constraints on the available parameter space. A description of the inelastic scattering on the basis of spin fluctuation exchange within the nested Fermi-liquid model with full frequency dependence taken into account still gives reasonable fits to the data, even though only a single parameter, fixed by the normal-state resistivity, is involved. For s-wave states, whose Fermi surface average is a sizable fraction of the order-parameter amplitude, scattering rates drop well below the experimental frequency at sufficiently low temperatures for the whole range of scattering phase shifts. Thermally excited quasiparticles still present then act as a nearly ideally conducting system which results in losses too low to be compatible with the experimental observations.

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