Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping

We report on short ballistic (SB) Josephson coupling in junctions embedded in a planar heterostructure of graphene. Ballistic Josephson coupling is confirmed by the Fabry-Perot-type interference of the junction critical current I_{c}. The product of I_{c} and the normal-state junction resistance R_{N}, normalized by the zero-temperature gap energy Δ_{0} of the superconducting electrodes, turns out to be exceptionally large close to 2, an indication of strong Josephson coupling in the SB junction limit. However, I_{c} shows a temperature dependence that is inconsistent with the conventional short-junction-like behavior based on the standard Kulik-Omel'yanchuk prediction. We argue that this feature stems from the effects of inhomogeneous carrier doping in graphene near the superconducting contacts, although the junction is in fact in the short-junction limit.