Ballistic graphene Josephson junctions from the short to the long regime

Abstract

We investigate the critical current, $I_C$, of ballistic Josephson junctions made of encapsulated graphene/boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, $I_S$ is found to scale as $\propto \exp (-k_{b}T/\hat{I}´E)$. The extracted energies $\hat{I}´E$ are independent of the carrier density and proportional to the level spacing of the ballistic cavity, as determined from Fabry-Perot oscillations of the junction normal resistance. As $T\to 0$ the critical current of a long (or short) junction saturates at a level determined by the product of $\hat{I}´E$ (or $\hat{I}”$) and the number of the junction's transversal modes.

Main text: 4 pages, 4 figures. Supplementary: 2 pages, 4 figures