Magnetic interaction between spatially extended superconducting tunnel junctions

A general description of magnetic interactions between superconducting tunnel junctions is given. The description covers a wide range of possible experimental systems, and we explicitly explore two experimentally relevant limits of coupled junctions. One is the limit of junctions with tunneling distance much smaller than the London penetration depth of the superconductors, the other is the limit where the tunneling distance is much larger than the London penetration depth. The former case has previously been studied in the context of adjacent conventional Josephson junctions, while the latter has been considered through arrays of superconducting weak links based on semiconductor quantum wells with superconducting electrodes. We use the model to make direct interpretations of the published experiments and thereby propose that long-range magnetic interactions are responsible for the reported experimental signatures of coupling between tunnel junctions.