Pair-breaking parameter

On + 7TTck -2 where the pair breaking parameters are given by... 

We start from the Abrikosov-Gorkov theory and its predictions for Tc. In that theory the effect of the randomly distributed magnetic scattering centers of concentration m is characterized by a pair-breaking parameter o which is given by... 

Hereby 4o is the superconducting order parameter at T = 0 in the absence of any impurities. Furthermore an isotropic exchange interaction has been assumed. The dependence of Tc as function of n or a is shown in fig. 17.13. acrit denotes the critical value of the pair-breaking parameter a beyond which superconductivity can no longer exist. It is a it = i The functional dependence of (nO is described by... 

Fig. 17.13. TJT as function of the pair-breaking parameter a a as predicted by the theory of Abrikosov and Gorkov (1960).

Fig. 17.14. Pair-breaking parameter y versus x = SI2T for inelastic exchange scattering (from Fulde et al., 1970).

Special cases For an isotropic order parameter, t/m+4/ 2 has to be replaced by um and pair breaking from defect scattering is absent, irrespective of the exact form of the scattering potential. For 5-functions scatterers, only uo 0. Then the pair breaking is equally effective whatever the exact form of the dxi-yi order parameter k4e 2 =... 

We have seen that the quark mass dependence of ferromagnetism should be important, while we have treated it as an input parameter. When we consider the realization of chiral symmetry in QCD, the quark mass should be dynamically generated as a result of the vacuum superconductivity qq pairs are condensed in the vacuum. We consider here SU(2)l x SU(2)r symmetry. Then Lagrangian should be globally invariant under the operation of any group element with constant parameters, except the symmetry-breaking term... 

The range of coherence follows naturally from the BCS theory, and we see now why it becomes short in alloys. The electron mean free path is much shorter in an alloy than in a pure metal, and electron scattering tends to break up the correlated pairs, so dial for very short mean free paths one would expect die coherence length to become comparable to the mean free path. Then the ratio k i/f (called the Ginzburg-Landau order parameter) becomes greater than unity, and the observed magnetic properties of alloy superconductors can be derived. The two kinds of superconductors, namely those with k < 1/-/(2T and those with k > l/,/(2j (the inequalities follow from the detailed theory) are called respectively type I and type II superconductors. 

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