Critical currents and the Ambegaokar-Baratoff to Ginsburg-Landau crossoverin granular superconductors

A simple expression for the transport critical current, which describes rat her well the Ambegaokar-Baratoff (A-B) to Ginsburg-Landau (G-L) crossover, is obtained from an elementary analysis of a Josephson junction subject to external magnetic fields within the Ginsburg-Landau theory. We show that th e order parameter in the intergrain region depends crucially on the interpl ay of two characteristic lengths: the superconducting coherence length xi p roportional to(1-T/T-c)(-1/2) and the junction-induced superconducting deco herence length zeta(q)proportional to(1 - T/T-c)(-alpha). Data for the tran sport critical current in granular YBCO samples are presented, and the A-B to G-L crossovers successfully described.