Theory of Josephson effect in unconventional superconducting junctions with diffusive barriers

TL;DR

This paper develops a theoretical framework for the Josephson effect in unconventional superconductor junctions with diffusive barriers, predicting novel behaviors like nonmonotonic temperature dependence and anomalous current-phase relations.

Contribution

It derives generalized boundary conditions for unconventional superconductors and applies them to predict new Josephson effects in various junction configurations.

Findings

Nonmonotonic temperature dependence in D/DN/D junctions

Anomalous current-phase relation in P/DN/P junctions

Second harmonics and double peak structures in critical current

Abstract

We study theoretically the Josephson effect in junctions based on unconventional superconductors with diffusive barriers, using the quasiclassical Green's function formalism. Generalized boundary conditions at junction interfaces applicable to unconventional superconductors are derived by calculating a matrix current within the circuit transport theory. Applying these boundary conditions, we have calculated the Josephson current in structures with various pairing symmetries. A number of predictions are made: (a) nonmonotonic temperature dependence in d-wave superconductor/diffusive normal metal/d-wave superconductor (D/DN/D) junctions, (b) anomalous current-phase relation in $p $-wave superconductor/diffusive normal metal/$p$% -wave superconductor (P/DN/P) junctions, (c) second harmonics in D/DN/D and P/DN/P junctions, (d) a double peak structure of the critical current in D/DF/D junctions, (e) enhanced Josephson current by the exchange field in S/DF/P junctions. We have also investigated peculiarities of the Josephson coupling in D/DF/D, P/DF/P and S/DF/P junctions. An oscillatory behavior of the supercurrent and the second harmonics in the current-phase relation are studied as a function of the length of the diffusive ferromagnet.