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 ${\mathit{I}}_{\mathit{c}}$ and of the normal-state resistance R scales with the critical current density ${\mathit{J}}_{\mathit{c}}$. This behavior is different from that of conventional Josephson junctions, for which the product ${\mathit{I}}_{\mathit{c}}$R is independent of ${\mathit{J}}_{\mathit{c}}$. We show that the observed scaling can be well understood within the framework of short-coherence-length effects in the high-${\mathit{T}}_{\mathit{c}}$ oxides.