Pairbreaking effect of correlated impurities in a superfluid Fermi liquid

TL;DR

This paper develops a theoretical framework to account for impurity correlations in superfluid Fermi liquids, revealing that such correlations can weaken impurity pairbreaking effects, especially when the impurity correlation radius exceeds the superfluid coherence length.

Contribution

It introduces a correction scheme for $T_c$ considering impurity correlations, extending conventional theory to include spatial correlations between impurities.

Findings

Correlation effects can enhance $T_c$ in superfluid $^3$He in aerogel.

When impurity correlation radius exceeds superfluid coherence length, pairbreaking effects are significantly weakened.

The correction to $T_c$ scales with the square of the ratio of correlation radius to coherence length.

Abstract

The conventional theory of superconducting alloys does not take into account a discreet character of impurities. Experimental data for superfluid $^3$He in aerogel and for some of high-$T_c$ superconductors reveal a significant discrepancy between the observed temperatures $T_c$ of their transitions in the superfluid or superconducting state and that predicted by the theory. Here a theoretical scheme is presented for finding corrections to the $T_c$ originating from spatial correlations between impurities. Analysis is limited to the Ginzburg and Landau temperature region. The shift of $T_c$ 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 the lowering of $T_c$ is recovered. Contribution of correlations enters the second order term. It is expressed via the structure factor of the ensemble of impurities. For superfluid $^3$He in silica aerogel the sign of the correction corresponds to an enhancement of the $T_c$ so that the resulting pairbreaking effect of impurities is weakened. When correlation radius of impurities $R$ exceeds the coherence length of the superfluid $\xi_0$ the contribution of correlations to the shift of $T_c$ acquires a factor $\sim(R/\xi_0)^2$ and the weakening of the pairbreaking effect becomes appreciable. The presented scheme is applied to the superfluid $^3$He in aerogel.