The effect of resonance scattering and d-d correlations on the thermodynamic properties of superconducting alloys

Methods of Quantum Field Theory in Statistical Physics

The depression in critical temperature ${T}_{c}$ of several dilute solid solutions of transition elements in Al, Zn, In, and Sn was measured as a function of residual resistivity and concentration. In Zn-Mn and Zn-Cr, localized moments are present and ${T}_{c}$ decreases linearly with concentration with a slope $\ensuremath{-}\frac{d{T}_{c}}{\mathrm{dc}}$ of 315 and 170\ifmmode^\circ\else\textdegree\fi{}K/at.%, respectively. By comparing these numbers with theory, a value of about 1.4 eV was found for the $s\ensuremath{-}d$ exchange integral. In all other alloys, the critical temperature is still depressed but much less than in Zn-Mn and Zn-Cr, and the depression becomes less rapid with increasing concentration of impurities. However, no saturation is found up to the maximum concentrations reached. The effect here found is different from that taking place in dilute alloys containing nontransition metals in that the depression of ${T}_{c}$ is larger, giving rise to suppression of superconductivity at sufficiently high impurity concentration. An analysis of the data for Al-Mn, Al-Cr, Al-Fe, Zn-Fe, Zn-Co, and Zn-Ni shows that in these systems the observed decrease of ${T}_{c}$ is satisfactorily accounted for by the smoothing out of the gap anisotropy and by the formation of localized virtual states, whose effect on the superconducting properties has been studied theoretically by Zuckermann. In-Mn and Sn-Mn do not fit the foregoing picture; however, the results obtained rule out the presence of magnetic moments in these two systems in bulk form. The apparent contrast with the results obtained in thin films is discussed. Some results on ternary alloys are also reported. It is shown that no effect on the critical temperature of In-Mn dilute solutions is produced by the addition of Pb.

Effect of Transition-Metal Impurities on the Critical Temperature of Superconducting Al, Zn, In, and Sn

A model of Anderson's is used to obtain the effect of transition-metal impurities on simple superconductors due to resonance scattering. If it is assumed that the impurities do not sustain a magnetic moment, then a sharp decrease in the critical temperature is found when $k{T}_{c}\ensuremath{\gg}\ensuremath{\Gamma}\ensuremath{\gg}{E}_{d}$. Here $\ensuremath{\Gamma}$ is the broadening of the bound $d$ state on each impurity due to Anderson's $s\ensuremath{-}d$ interaction and ${E}_{d}$ is the energy displacement of the $d$ state from the Fermi level. This region is, in fact, unphysical since the $s\ensuremath{-}d$ interaction is too small to swamp out the magnetic moment of each impurity. In consequence, the theoretical analysis of Merriam et al. for the In-Mn alloys is incorrect. The decrease in ${T}_{c}$ is much weaker when $\ensuremath{\Gamma}\ensuremath{\gg}k{T}_{c}$. This is the physical region in which the magnetic moments are swamped out by the $s\ensuremath{-}d$ interaction. It is also shown that the superconducting state in such alloys displays a nonzero energy gap at all impurity concentration. When the $s\ensuremath{-}d$ interaction is weak the impurity has a nonzero magnetic moment and the problem is shown to reduce to one already considered by Gor'kov and Rusinov. The results are used to comment on the experimental results of Merriam et al. and of Boato et al. Also, reasonable agreement with Friedel's predictions is found.

The effect of resonance scattering and d-d correlations on the thermodynamic properties of superconducting alloys

References

Methods of Quantum Field Theory in Statistical Physics

Effect of Transition-Metal Impurities on the Critical Temperature of Superconducting Al, Zn, In, and Sn

Resonance scattering in impure superconductors

Effect of 3d transitional impurities on the superconducting transition of aluminium

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