Graphene-based Planar Josephson Junction in Short and Ballistic Regime

Planar graphene-based Josephson junctions are prepared by the atomic edge contact of two closely arranged Al superconducting electrodes to h-BN encapuslated graphene. We first confirm the ballisticity of our junctions by the Fabry-Perot interference in both the normal and Josephson-coupled states. The I_cR_N product, a quality factor of Josephson coupling, almost reaches the theoretical limit (~2.4Δ₀/e) of the short-and-ballistic Josephson coupling. But the T dependence of the junction I_c does not fit the conventional Kulik-Omel’yanchuk (KO) prediction in the short-and-ballistic regime. No exponentially decaying I_c(T) is observed with increasing temperature near T_c, which excludes the long-junction characteristics. Since the KO model is valid for a one-dimensional point-contact junction it is not relevant to our planar junctions. We confirm that I_c(T) fits well the short-and-ballistic Josephson coupling proposed by a recent theoretical model [1], which takes account of the spatial carrier inhomogeneity in graphene induced by the electronic doping near the superconducting electrodes.
[1] Y. Takane, K.-I. Imura, J. Phys. Soc. Jpn. 81, 094707 (2012).