Nonlinear Reactance of Superconducting Films

The dependence of the imaginary part of the conductivity (${\sigma }_2$) on current has been measured at various temperatures for films of tin, indium, and tin-indium alloys. The samples were thin, narrow films so that both the dc and microwave currents were spatially uniform. The reactance of the samples was measured with a small 23-kMc/sec signal while the direct current in the film was varied from zero to the critical value. At reduced temperatures above 0.6, both the magnitude and the temperature dependence of the nonlinearity were in remarkably good agreement with both the microscopic theory of Parmenter and the phenomenological Ginsburg-Landau theory. The only adjustable parameter was the penetration depth for each sample. The values chosen for the penetration depth were in excellent agreement with values computed from residual resistance ratios. There was also an indication in our data that the boundary scattering in indium films is highly specular, whereas in the tin films it appears to be diffuse.