Interface size dependence of the Josephson critical behaviour in pyrolytic graphite

We have studied the transport properties of TEM lamellae obtained from a pyrolytic graphite sample with electrical contacts at the edges of the embedded interfaces. The temperature dependence of the resistance as well as the current-voltage characteristic curves are compatible with the existence of Josephson coupled superconducting regions. The transition temperature at which the Josephson behavior sets in, decreases with the interface width and vanishes for width below 200~nm. This unexpected behavior is apparently due to the influence of weak localization effects on the superconducting critical temperature.