Properties of Superconducting Alloys Containing Paramagnetic Impurities

We have made some additional calculations on the effects of paramagnetic impurities in superconductors, using the Abrikosov-Gor'kov theory as our starting point and taking full advantage of the information contained in the Green's function of the system. The density of states in energy has been computed for different values of the inverse collision time for exchange scattering $\Gamma$. The (half) excitation energy gap ${\Omega }_G$ (as distinguished from the order parameter $\Delta$) is defined to be the energy at which the density of states vanishes. The temperature-dependent order parameter has been computed for different values of $\Gamma$, and from this, the behavior of ${\Omega }_G$ ($T$) is determined. A comparison with tunneling experiments shows a disagreement of about 30%. The thermodynamic properties of the system follow from the density of states; the critical field and the discontinuity in the specific heat at the critical temperature are calculated in considerable detail. Expressions for the penetration depth and complex conductivity are obtained, and numerical results are presented for the case $T=0\mathrm{}°$. The real part of the conductivity at $T=0\mathrm{}°$ is shown to be zero for frequencies less than $2{\Omega }_G$ and proportional to the square of the density of states for vanishingly small frequencies in the gapless region of impurity concentrations.