Electrical transport in junctions between unconventional superconductors: Application of the Green’s-function formalism

We present a general Green’s-function-based method that can be used to describe the electrical transport properties of junctions with arbitrary coupling strength involving superconductors with unconventional pairing symmetry and arbitrary band structures. Our method correctly takes into account the midgap surface states that arise in d-wave superconductors due to sign change of the order parameter. In the tunneling limit, we present simple expressions that describe the effect of the midgap states on the dc and ac components of the Josephson current including their temperature dependence. A numerical example is presented for a junction between two d-wave superconductors with arbitrary coupling strength showing a feature originating from the sign change of the order parameter, namely, for some orientations of the d-wave order parameter relative to the surface, the current-phase relation may remain nonsinusoidal even when the coupling is quite weak.