Scaling behavior of the critical current of grain-boundary junctions

It has been recently determined experimentally that in Y-Ba-Cu-O grain-boundary junctions the product of the critical current Ic and of the normal-state resistance R scales with the critical current density Jc. This behavior is different from that of conventional Josephson junctions, for which the product IcR is independent of Jc. We show that the observed scaling can be well understood within the framework of short-coherence-length effects in the high-Tc oxides.