Effect of Resonance Scattering and Impurity Correlations on the Thermodynamic and Transport Properties of Superconducting Alloys

A model due to Anderson is used to investigate the superconducting properties of nonmagnetic alloys of simple metals with transition-metal impurities. The alloys are assumed to be very dilute. The resonance-scattering effects in the alloys are related to the width $\Gamma$ of the bound $d$ state on each impurity, and the physical limit $\Gamma \gg k{T}_c$ is chosen. Here $T_c$ is the superconducting critical temperature of the alloy. The impurity correlations are dependent on the Coulomb interaction $U$ between $d$ electrons on opposite spin, and are included in the superconducting problem by a self-consistent Hamiltonian due to Ratto and Blandin. The order parameter, the electronic density of states $N\left(\omega \right)$, and the specific heat are calculated for the superconducting state of the alloys at temperatures $T$ such that $0\lesssim T\ll T_c$. It is found that $N\left(\omega \right)\sim {(\omega -{\omega }_G)}^{\frac{1}{2}}$ close to the gap edge ${\omega }_G$, and that $U$ has a strong effect on the thermodynamic properties of the alloys in this temperature range. The thermodynamic properties are also investigated in the temperature range $0\ll T\lesssim T_c$. It is found that they depend on the impurity correlations only through $T_c$. However, the transport properties of the alloys are strongly $U$-dependent for these temperatures, in particular the Josephson current. Finally, the relation to the Kondo effect is discussed and the results of the paper are considered in the light of experiment.