Pairbreaking effect of correlated impurities in a superfluid Fermi liquid

Abstract

The conventional theory of superconducting alloys does not take into account the discrete character of impurities. Experimental data for superfluid 3He in aerogel and for some high-Tc superconductors reveal a significant discrepancy between the observed temperatures, Tc, of their transitions in the superfluid or superconducting states and those predicted theoretically. Here a theoretical scheme is presented for finding corrections to the Tc originating from spatial correlations between impurities. Analysis is limited to the Ginzburg and Landau temperature region. The shift of Tc with respect to the pure material is represented as a series in concentration of the impurities, x. In the first order on x, the conventional mean-field result for lowering Tc is recovered. The contribution of correlations enters the second-order term. It is expressed via the structure factor of the ensemble of impurities. For superfluid 3He in a silica aerogel, the sign of the correction corresponds to an enhancement of the Tc, so that the resulting pair-breaking effect of impurities is weakened. When the correlation radius of the impurities, R, exceeds the coherence length of the superfluid, the contribution of correlations to the shift of Tc acquires a factor, and the weakening of the pair-breaking effect becomes appreciable. The presented scheme is applied to the superfluid 3He in aerogel.