Microwave transmission and reflection measurements are performed simultaneously on thin films (approximately 1800 angstrom) of YBa2Cu3O7-x having their c axis perpendicular to the LaAlO3 substrate. We determine power transmission and reflection fractions, T(T, H) and R(T, H), as functions of temperature and static magnetic field (0 < H < 5.4 T), the latter being applied perpendicular to the film. A guided-wave model, which we develop for our experimental situation, is the basis of a computational algorithm that extracts quantitative values of the complex penetration depth lambda, or alternatively the complex surface impedance Z(s), from T and R data. This inversion algorithm is successful when applied to test data generated from a phenomenological theory describing the electrodynamic response of a type-II superconductor. The procedure is applied to T(T, H) and R(T, H) measurements to infer the temperature- and field-dependent complex penetration depth lambda(T, H) that completely characterizes the superconductive film's electromagnetic response.

Microwave transmission and reflection measurements were carried out simultaneously on thin films ( approximately 2000 AA) of YBa/sub 2/Cu/sub 3/O/sub 7-x/ with their c axes perpendicular to the LaAlO/sub 3/ substrate. Power transmission and reflection fractions (T,R) were determined as functions of temperature and magnetic field (0>

We present microwave magneto-dissipation measurements (12.95 GHz) as a function of temperature (5 less-than-or-equal-to T less-than-or-equal-to 90 K) and applied static field (0 less-than-or-equal-to H \H\ less-than-or-equal-to 1.9 T) for single-crystal BSCCO and for melt-textured YBCO. In all instances, induced current densities J(rf) are nearly parallel to the CuO2 layers. Our survey yields characteristic trends in dissipation that depend on the nominal angle between H and c, and between H and J(rf). Nominal angles are inferred from the applied field direction and the sample orientation. One trend that YBCO and BSCCO share is the occurrence of substantial magneto-dissipation even when H and H(rf) are nominally parallel and the nominal Lorentz force is zero. The likely inference is that - over a broad frequency range - local angles between transport currents and flux bundles differ substantially from the nominal (global) value. Finally, we provide definitive evidence for pronounced flux pinning by YBCO twin boundaries.

Thick, clean Zn films, when backed by clean Pb films of sufficient thickness, produce first-derivative tunneling spectra that differ markedly from the predictions of Wolfram's theory in the central virtual-state region. Gallagher has recently extended Wolfram's theory to allow for quasiparticle geometrical resonances in both metal layers, and, using his results, we are able to explain the anomalous portions of our spectra, as well as those portions which continue to agree with Wolfram's theory. For the $c$-axis orientation of Zn and the [111] orientation of Pb, we obtain Fermi velocities of (1.31 \ifmmode\pm\else\textpm\fi{}0.020) \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ and (0.78 \ifmmode\pm\else\textpm\fi{} 0.04) \ifmmode\times\else\texttimes\fi{} ${10}^{6}$ m/s, respectively. Our estimate of the Zn electron-phonon coupling parameter, $\ensuremath{\lambda}={Z}_{N}(0)\ensuremath{-}1=0.42$, agrees with theoretical estimates by Tomlinson and Swihart, but away from the Fermi surface our estimates of the complex renormalization function generally exceed theirs.

Experiments with thin Ag layers (${d}_{N}\ensuremath{\sim}100\ensuremath{-}700$ \AA{}) backed by thicker Pb (${d}_{S}\ensuremath{\sim}3500$ \AA{}) have led Khim and Tomasch to infer large effective renormalizations for Ag that increase with decreasing ${d}_{N}$, even though the electron-phonon interaction presumably retains its bulk character. Arnold has recently shown that dirty proximity superconductors violate Anderson's theorem and that, in this regime, the usual treatment of elastic scattering is inappropriate for Andreev interference phenomena. He finds that both the pairing potential, ${\ensuremath{\Delta}}_{N}(E)$, and the effective layer renormalization, ${Z}_{N}(E)$, are influenced strongly by scattering. Our reanalysis, based on Arnold's theory and on Gallagher's compound-resonance theory, assumes bulk behavior for the Ag electron-phonon interaction. We obtain successful quantitative agreement with the Ag-Pb data when the Ag mean free path nearly equals the Ag film thickness. Our best estimates of the dressed Fermi velocities are ${v}_{\mathrm{FS}}^{*}(\mathrm{Pb})=(0.72\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ m/s and ${v}_{\mathrm{FN}}^{*}(\mathrm{Ag})=(1.07\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ m/s.

By virtue of their sensitivity to incoherent scattering, virtual-state resonances observed by tunneling into thick-film elemental superconductors provide a superior probe of the electron-phonon interaction at low energies where relatively few phonon modes participate. In strong-coupling and intermediate-coupling systems, spontaneous phonon emission progressively limits quasi particle mean-free-paths with increasing energy, causing resonance amplitudes to fall below those predicted for the weak-coupling limit. Accelerated damping of virtual-state oscillations at higher junction biases provides a practical basis for experimental determination of Im{Z(ω)[ ω2−Δ2(ω)]1/2} which in turn permits α2F(ω), Im{Z(ω)} and Im{Δ(ω)} to be inferred by means of the ELIASHBERG equations. This approach has proven considerably more sensitive than the familiar tunneling method of ROWELL and McMILLAN, and generally tends to augment the latter at low energies. Experimental results obtained with very thick In films exhibit substantial phonon damping compared to those obtained with thick Al films. The coefficinet g0 appearing in α2F(ω)≐g0 ω2 determined for In by the present method is found to be substantially smaller than that inferred from earlier tunneling studies, as are the quantities Im{Z(ω)} and Im{Δ(ω)}.

We consider tunneling between two superconductors, SA and SB, in the approximation that SA is a BCS superconductor and that thermal excitations are unimportant. Inversion formulas are developed which permit numerical evaluation of the tunneling density of states for SB when the ac conductance, or its voltage derivative, is known as a function of bias voltage. The method is applied to finely spaced (∼30 μV) conductance structure produced by quasiparticle interference phenomena in a thick (∼30 μm) In film at 0.3 K (so-called Tomasch effect).

Observed persistence of bulk superconductivity in the presence of intense defect scattering precludes a significant role for multiple-band effects in lanthanum's superconductivity. Implications with regard to interpreting earlier surface resistance measurements are discussed.

Bound- and virtual-state structure has been observed in the tunneling characteristics of thick Cd films deposited over Pb. We observed amplitude effects displaying a temperature dependence not previously reported. An important point is made concerning basic spacings of bound and virtual levels. Amplitudes and level spacings appear to contain retrievable proximity-effect information. Taking nonlinear effects into account, a value of ${v}_{\mathrm{F}}=1.30\ifmmode\times\else\texttimes\fi{}{10}^{8}$ cm/sec is obtained for the $c$ direction.

Geometrical resonances have been observed in the tunneling characteristics of Sn films 2.4 – 4.3μ thick. Results are interpreted in terms of quasiparticle standing waves. Crystallite texture, multiple-gap behavior, and a new aspect of the overlay effect are also described.

Received 3 September 1965DOI:https://doi.org/10.1103/PhysRevLett.15.672©1965 American Physical Society