Critical currents in graphene ribbon Josephson's junctions

The rapidly advancing technology of nanodevices has led to the production of smaller and smaller structures often called mesoscopic systems. These devices are large on the atomic scale, but sufficiently small that the electron wave function is coherent over the entire sample: the condition for coherence is that the electron traverses the wire without undergoing any collision with phonons or other electrons. Because the electron can lose energy and equilibrate with heat bath only via inelastic collisions, it is necessary to re-examine the conventional concept of energy dissipation in a resistor. We study the way in which the superconducting correlations are induced in graphene ribbon when it is placed between two superconductors, how such correlations may depend on complex edge structure of the ribbon, on the geometry of the experimental set-up and what is the role of Andreev's reflection in Josephson's effect at superconducting contacts.