What happens in Josephson junctions at high critical current densities

The impressive advances in material science and nanotechnology are more and more promoting the use of exotic barriers and/or superconductors, thus paving the way to new families of Josephson junctions. Semiconducting, ferromagnetic, topological insulator and graphene barriers are leading to unconventional and anomalous aspects of the Josephson coupling, which might be useful to respond to some issues on key problems of solid state physics. However, the complexity of the layout and of the competing physical processes occurring in the junctions is posing novel questions on the interpretation of their phenomenology. We classify some significant behaviors of hybrid and unconventional junctions in terms of their first imprinting, i.e., current-voltage curves, and propose a phenomenological approach to describe some features of junctions characterized by relatively high critical current densities J(c). Accurate arguments on the distribution of switching currents will provide quantitative criteria to understand physical processes occurring in high-J(c) junctions. These notions are universal and apply to all kinds of junctions.