Strong-coupling correction to the low-frequency electrical conductivity of superconductors and Josephson junctions

Abstract

Values of the strong-coupling correction to the low-frequency local-limit conductivity of a number of superconductors are given. These values also describe the strong-coupling correction to the critical current of a Josephson tunnel junction. The correction is given for indium, amorphous gallium, $\beta$-phase gallium, amorphous bismuth, ${\mathrm{Pb}}_{0.8}$ ${\mathrm{Bi}}_{0.2}$, ${\mathrm{Pb}}_{0.7}$ ${\mathrm{Bi}}_{0.3}$, amorphous ${\mathrm{Pb}}_{0.45}$ ${\mathrm{Bi}}_{0.55}$, ${\mathrm{Tl}}_{0.9}$ ${\mathrm{Bi}}_{0.1}$, ${\mathrm{Pb}}_{0.8}$ ${\mathrm{Tl}}_{0.2}$, and previously published values are listed for tin, lead, mercury, thallium, and indium-thallium alloys. It is shown that there is a simple empirical relation between these values and the effective electron-electron coupling parameter ($\lambda -{\mu }^{*}$).