Proximity superconductivity in ballistic graphene, from Fabry-Perot oscillations to random Andreev states in magnetic field

Graphene-based Josephson junctions have attracted significant interest as a novel system to study the proximity effect due to graphene's unique electronic spectrum and the possibility to tune junction properties by gate voltage. Here we describe graphene junctions with the mean free path of several micrometers, low contact resistance and large supercurrents. Such devices exhibit pronounced Fabry-Perot oscillations not only in the normal-state resistance but also in the critical current. The proximity effect is mostly suppressed in magnetic fields of <10 mT, showing the conventional Fraunhofer pattern. Unexpectedly, some proximity survives even in fields as high as 1 T. Superconducting states randomly appear and disappear as a function of field and carrier concentration, and each of them exhibits a supercurrent carrying capacity close to the universal limit of eD/h where D is the superconducting gap, e the electron charge and h Planck's constant. We attribute the high-field Josephson effect to individual Andreev bound states that persist near graphene edges. Our work reveals new proximity regimes that can be controlled by quantum confinement and cyclotron motion.