Discrete-lattice model approach to the tunneling between d-wave superconductors: interference of tunnel bonds

Abstract

The Josephson current between d-wave superconductors is investigated in the framework of tight-binding lattice model. The junction is modelled by a small number of connecting bonds. It is obtained that the Josephson current through one bond vanishes when at least one of the superconductors has $(110)$ interface-to-crystal orientation. Interference between the nearest bonds is appeared to be very important. In particular, it is the interference term that leads to the nonzero Josephson current for $(110)$ orientation. Also, interference of two connecting bonds manifests itself in non-monotonic behavior of the critical Josephson current in dependence on the distance between the bonds.