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

TL;DR

This paper models Josephson current between d-wave superconductors using a lattice approach, revealing how bond interference affects current flow, especially in specific crystal orientations, and showing non-monotonic behavior with bond separation.

Contribution

It introduces a lattice model with multiple connecting bonds to analyze interference effects on Josephson current in d-wave superconductor junctions, highlighting orientation-dependent phenomena.

Findings

Josephson current vanishes for (110) orientation with a single bond.

Interference between bonds enables nonzero current in (110) orientation.

Critical current exhibits non-monotonic dependence on bond separation.

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.