The second Josephson harmonic in the dirty limit

Abstract

We calculate the Josephson current across a plane interface separating dirty superconductors up to second order in the transparency of the junction. The leading contribution to the second-order correction is caused by the suppression of the superconducting order parameter near the interface. The ratio of the correction to the Josephson current in the first order is about D xi(T)/l, where D is the transparency of the junction, xi(T) is the temperature-dependent coherence length, and l is the mean free path. This correction gives rise to the second harmonic in the current-phase relationship.