Landau Ginzburg theory of the d-wave Josephson junction

TL;DR

This paper develops a Landau Ginzburg theoretical framework for d-wave Josephson junctions, revealing how anisotropy and imperfections influence the current-phase relationship and local time reversal symmetry breaking.

Contribution

It introduces a symmetry-based Landau Ginzburg model for d-wave Josephson junctions, analyzing the effects of anisotropy and imperfections on the current-phase relation.

Findings

The Josephson current includes both sin(φ) and sin(2φ) components.

Anisotropy and imperfections can significantly alter the current-phase relationship.

Local time reversal symmetry breaking can occur under certain conditions.

Abstract

This letter discusses the Landau Ginzburg theory of a Josephson junction composed of on one side a pure d-wave superconductor oriented with the $(110)$ axis normal to the junction and on the other side either s-wave or d-wave oriented with $(100)$ normal to the junction. We use simple symmetry arguments to show that the Josephson current as a function of the phase must have the form $j(\phi) = j_1 \sin(\phi) + j_2 \sin(2 \phi)$. In principle $j_1$ vanishes for a perfect junction of this type, but anisotropy effects, either due to a-b axis asymmetry or junction imperfections can easily cause $j_1 / j_2$ to be quite large even in a high quality junction. If $j_1 / j_2$ is sufficiently small and $j_2$ is negative local time reversal symmetry breaking will appear. Arbitrary values of the flux would then be pinned to corners between such junctions and occasionally on junction faces, which is consistent with experiments by Kirtley et al.