Current-voltage characteristics of Nb-carbon-Nb junctions

We report on properties of Nb(/Ti)-carbon-(Ti/)Nb junctions fabricated on graphite flakes using e-beam lithography. The devices were characterized at temperatures above 1.8 K where a Josephson current was not observed, but the differential conductivity revealed features below the critical temperature of Nb, and overall metallic conductivity, in spite of a high-junctions resistance. Since the conductivity of graphite along the planes is essentially two-dimensional (2D), we use a theoretical model developed for metal/graphene junctions for interpretation of the results. The model involves two very different graphene "access" lengths. The shorter length characterizes ordinary tunneling between the three-dimensional Nb(/Ti) electrode and 2D graphene, while the second, much longer length, is associated with the Andreev reflections (AR) inside the junction and involves also "reflectionless" AR processes. The relevant transmission factors are small in the first case and much larger in the second, which explains the apparent contradiction of the observed behaviors.