Effect of Parallel Transport Currents on the D-wave Josephson junction

In this paper, the nonlocal 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 a mis-orientation and a phase difference. Furthermore, they are subjected to a tangential transport current along the $ab$-plane of d-wave crystals and parallel with interface between superconductors. The effects of mis-orientation and external transport current on the current-phase relations and current distributions are subjects of this paper. It observed that, at values of phase difference close to 0, $\pi$ and $2\pi$ the current distribution may have a vortex-like form in vicinity of the point contact. The current distribution of this junction between d-wave superconductors is totally different from the junction between s-wave superconductors. As the interesting results, spontaneous and Josephson currents are observed for the case of $\phi=0$.