Disordered Josephson Junctions of d-Wave Superconductors

TL;DR

This paper investigates how interface roughness affects the Josephson effect in d-wave superconductor junctions, revealing non-monotonic critical current behavior and a transition from sinusoidal to double-frequency current-phase relations.

Contribution

It provides a detailed theoretical analysis of the impact of interface roughness on Josephson junctions of d-wave superconductors, including new insights into current-phase relations and critical current temperature dependence.

Findings

Non-monotonic temperature dependence of critical current in mirror junctions with low roughness.

Transition from sin(φ) to sin(2φ) current-phase relation in large asymmetric junctions.

Good agreement with recent experimental data.

Abstract

We study the Josephson effect between weakly coupled d-wave superconductors within the quasiclassical theory, in particular, the influence of interface roughness on the current-phase relation and the critical current of mirror junctions and $45^\circ$ asymmetric junctions. For mirror junctions the temperature dependence of the critical current is non-monotonic in the limit of low roughness, but monotonic for very rough interfaces. For $45^\circ$ asymmetric junctions with a linear dimension much larger than the superconducting coherence length we find a $\sin(2\phi)$-like current-phase relation, whereas for contacts on the scale of the coherence length or smaller the usual $\sin\phi$-like behavior is observed. Our results compare well with recent experimental observations.