Calculation of the electromagnetic coherence length in superconductors with magnetic impurities

Abstract

We calculate the electromagnetic coherence length $\xi$ for superconductors with magnetic impurities by using the theory of Shiba and of Rusinov. The expression for $\xi$ is analytically evaluated in several limits, and it is numerically evaluated for a range of values of the variables on which $\xi$ depends. It is found that, over the range of values of the variables for which $\xi$ is calculated, $\xi$ can be fitted with a simple empirical function to an accuracy that is never worse than 6%, and is typically better than 2%, whereas a naive estimate of $\xi$ can be as much as 80% higher than the correct value. We show how to calculate the penetration depth in the London limit and the extreme anomalous limit from the results for $\xi$ and the already calculated local-limit penetration depth.