Model for large arrays of Josephson junctions with unconventional superconductors

We study large arrays of mesoscopic junctions made out of gapless unconventional superconductors where the tunneling processes of both particle-hole and Cooper pairs give rise to a strongly retarded effective action which, contrary to the standard case, cannot be readily characterized in terms of a local Josephson energy. This action can be relevant, for example, to grain boundary and c-axis junctions in layered high-T-c superconductors. By using a particular functional representation, we describe emergent collective phenomena in this system, ascertain its phase diagram, and compute electrical conductivity.