Mesoscopic fluctuations of the Josephson current of an S-I-S junction with weak structural disorder

It is shown that in the range of tunneling resonance energies of an S-I-S (superconductor-insulator-superconductor) junction with weak (low impurity concentrations) structural disorder in the I-layer, the average critical current and the magnitude of its mesoscopic fluctuations are determined by tunneling along quantum resonance-percolation trajectories. For a “small” junction situated in a parallel magnetic field at temperature T = 0 conditions for smallness of the mesoscopic fluctuations are obtained and an estimate is made of the range of parameters in which the resonance mechanism for supercurrent propagation predominates.