Disappearance of Ensemble-Averaged Josephson Current in Dirty SNS Junctions of d-wave Superconductors

We discuss the Josephson current in superconductor / dirty normal conductor / superconductor junctions, where the superconductors have $d_{x^2-y^2}$ pairing symmetry. The low-temperature behavior of the Josephson current depends on the orientation angle between the crystalline axis and the normal of the junction interface. We show that the ensemble-averaged Josephson current vanishes when the orientation angle is $\pi/4$ and the normal conductor is in the diffusive transport regime. The $d_{x^2-y^2}$-wave pairing symmetry is responsible for this fact.Comment: 8 pages, 5 figure

DC Josephson Effect in SNS Junctions of Anisotropic Superconductors

A formula for the Josephson current between two superconductors with anisotropic pairing symmetries is derived based on the mean-field theory of superconductivity. Zero-energy states formed at the junction interfaces is one of basic phenomena in anisotropic superconductor junctions. In the obtained formula, effects of the zero-energy states on the Josephson current are taken into account through the Andreev reflection coefficients of a quasiparticle. In low temperature regimes, the formula can describe an anomaly in the Josephson current which is a direct consequence of the exsitence of zero-energy states. It is possible to apply the formula to junctions consist of superconductors with spin-singlet Cooper pairs and those with spin-triplet Cooper pairs