When a pair of coils is positioned on opposite sides of a superconducting thin film, measurement of their mutual inductance may in principle be used to infer the penetration depth λ in the superconductor. We have studied how to optimize this measurement with respect to coil design, and have found that the approach that has been generally used is far from the optimum. Useful simplifications to the expression relating mutual inductance to penetration depth are derived. An analysis of the sources of uncertainty in determining λ is presented. For an optimized coil set, the major source of uncertainty often is uncertainty of the thickness of the film. The sensitivity to changes in λ is also studied; it is shown that this can approach 1 pm for a typical high temperature superconductor sample. Finally, it is shown that the analysis may be extended to normal metal films, with the skin depth playing a role similar to that of the penetration depth in superconductors. Measurement of a high conductivity normal metal foil can be used to check calculated calibration factors for a coil set or to determine the skin depth.
The temperature dependence of the penetration depth of superconductornormal-metal multilayered metals has been calculated from Eliashberg theory. The results reported here focus on YBa2Cu307~, but the conclusions apply to any system of proximity-coupled bilayers. Our calculations show that depleting the chains of oxygen, and, consequently the appearance of gaplessness, leads to a transition from an exponential dependence to a power law, initially linear, then quadratic. Different analytical dependences have been measured by various groups, and conflicting conclusions have been made about the pairing state in the cuprate superconductors. We emphasize that our calculations exhibit all of the qualitative features of available experimental data within a single formalism.
The superconducting density of states for the cuprates, particularly for the Y-Ba-Cu-O compound, has been evaluated, and its dependence on temperature and the oxygen content has been analyzed. The analysis is based on the two-gap model. Moreover, the magnetic scattering and corresponding pair-breaking effect, correlated with the oxygen depletion, is taken into account as a key factor. The temperature dependencies of the energy gaps are calculated. Intensive magnetic scattering leads to gaplessness. The calculation allows us to describe various experimental data. ͓S0163-1829͑97͒01237-X͔
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