Surface Impedance in the Surface Superconducting State

To enable a simple calculation of the microwave surface resistance, the surface superconducting state is approximated by a model in which a layer of uniform order parameter is considered superposed on the normal bulk. Appropriate values for the order parameter and thickness of this layer were chosen with the use of the numerical solutions of the Ginsburg-Landau equations by Fink and Kessinger. A Gorter-Casimir temperature dependence was used for the order parameter and the Maki temperature dependence for $\kappa$. Our experiments on Pb-In alloys at frequencies of 9.5, 23, and 55 Gc/sec are in good agreement with the calculations.