Effect of Transparency on the D-wave Josephson Junction

In this paper, a dc Josephson junction between two singlet superconductors (d-wave and s-wave) with arbitrary reflection coefficient has been investigated theoretically following the famous paper [ Y. Tanaka and S. Kashiwaya 1996 \textit{Phys. Rev. B} {\bf 53}, R11957]. For the case of High $T_c$ superconductors, the $c$-axes are parallel to an interface with finite transparency and their $ab$-planes have a mis-orientation. The effect of transparency and mis-orientation on the currents is studied both analytically and numerically. It is observed that, the current phase relations are totally different from the case of ideal transparent Josephson junctions between d-wave superconductors and two s-wave superconductors. This apparatus can be used to demonstrate d-wave order parameter in High $T_c$ superconductors.