Low-frequency electromagnetic response function for strong-coupling superconductors

Abstract

A simple method for calculating the low-frequency electromagnetic response function from tunneling derived ${\alpha }^2\left(\omega \right)F\left(\omega \right)$ has been developed and applied to Pb, ${\mathrm{Pb}}_{0.90}$ ${\mathrm{Bi}}_{0.10}$, amorphous Bi, amorphous ${\mathrm{Pb}}_{0.45}$ ${\mathrm{Bi}}_{0.55}$, and amorphous ${\mathrm{Sn}}_{0.90}$ ${\mathrm{Cu}}_{0.10}$. The results have been compared with previous calculations and experiments. A correction to the calculation of the $T=0\mathrm{}$ values given by Kerchner and Ginsberg is given. Although the calculations agree with experiment for crystalline Pb, the calculated temperature dependence is much stronger near $T_c$ than that inferred from kinetic inductance measurements for amorphous Bi.