Realization of short ballistic vertical graphene Josephson junction

We realized short ballistic vertical graphene Josephson junctions (vGJJs), where a monolayer graphene sheet is sandwiched between two superconducting electrodes along the c-axis of graphene. To enhance the transparency between electrodes and graphene layer we thermally deposited aluminum superconducting electrodes on both surfaces of the graphene sheet by using a ``flip-transfer'' scheme instead of transferring graphene onto the bottom electrode. With the highly transparent contacts and atomically short channel length, vGJJ shows a very large value of I$_c$R$_N$ product (2.2$\Delta_{Al}$). This value is in sharp contrast to much suppressed value of $I_cR_N$$ < \Delta_{Al}$, observed in planar graphene Josephson junctions. Surprisingly, $I_c$ decreases superlinearly with increasing temperature ($T$) from 50 mK up to the junction critical temperature, which is a typical character of a short ballistic Josephson junction. To our best knowledge, this feature has long been predicted but never been reported in proximity-coupled Josephson junctions. $I_c$-$T$ curve fits well to the short ballistic Josephson junction model (KO-2)\footnote[1]{K. K. Likharev, Rev. Mod. Phys. \textbf{51}, 101 (1979)} with the transparency of 0.94.