The surface impedance of superconductors

Abstract

New measurements of the surface impedance of superconducting tin and tin-indium alloys at 3 kMc/s, obtained by measuring the bandwidth and characteristic frequency of a resonator containing the specimen, are reported. The results are compared in detail with the microscopic theory, those on the low temperature surface reactance being reduced to values of d.c. penetration depth. At the lowest temperatures the penetration depth, λ, shows slight downward curvature when plotted against y(Τ/Τ_C = (1 − Τ_C ⁴)^−½ for yλ by about 5 × 10⁻⁷ cm. For samples containing more than 2% indium λ(y) appears to be linear at all temperatures. The slope, dλ/dy, agrees with the predicted values for large y. The low temperature surface resistance follows the usual empirical rule with A(θ) only weakly dependent on purity. A new method of obtaining λ at absolute zero, free from zero error, by analysis of the resistance and reactance data together is presented. The extension of the theory to anisotropic metals is discussed, and applied to the results for pure specimens. Good agreement is found, provided that allowance is made for a rather complex anisotropy of the energy gap, with a total range of about 30%; and a new method of measuring anisotropy of the energy gap is proposed. The simple relations between the Pippard parameters, G ₁ and G ₂, and the normal state skin depth discovered by Pippard and Fawcett is shown to be essentially accidental. In considering the surface impedance of pure specimens very near T _c, it is shown that the coherence length is certainly finite at T _c in tin, and a new interpretation is given for the results of Williams on pure aluminium near T _c. Finally, the small disagreements between experiment and theory are analysed, and ascribed to a slightly wrong form for the energy gap as a function of temperature used by the theory; it is suggested that this itself may be explained if different pieces of the Fermi surface have different energy gaps in tin. The general conclusion is that, if modified to allow for the anisotropy of the Fermi surface and the energy gap, the theory is very successful when applied to the known data on tin at frequencies up to 40 kMc/s.