Effect of parallel transport currents on the d-wave Josephson junction

In this paper, the non-local mixing of coherent current states in d-wave superconducting banks is investigated. The superconducting banks are connected via a ballistic point contact. The banks have mis-orientation and phase difference. Furthermore, they are subjected to a tangential transport current along the ab plane of d-wave crystals and parallel to the interface between the superconductors. The effects of mis-orientation and external transport current on the current-phase relations and current distributions are the subjects of this paper. It is observed that, at values of phase difference close to 0, π and 2π, the current distribution may have a vortex-like form in the vicinity of the point contact. The current distribution of the above-mentioned junction between d-wave superconductors is totally different from the junction between s-wave superconductors. The interesting result which this study shows is that spontaneous and Josephson currents are observed for the case of φ = 0.