Mesoscopic fluctuations of the DC Josephson current in a dirty SNS junction

We present theoretical studies on mesoscopic fluctuations of the dc Josephson current in superconductor (S)-dirty normal conductor (N)-superconductor junctions. The analytical expression for the Josephson-current fluctuation delta J(2) is obtained by using the thermal Green's function method, which is shown to he valid when the separation between two superconductors is much lager than the coherence length of the dirty superconductor. The effects of temperature and inelastic scattering on delta J(2) are examined. The results show that the characteristic temperature (size) for the reduction of delta J(2) is of the order of the Thouless correlation energy E(c) (the phase choherence length). From the current correlation function, the energy correlation range is estimated to be at about E(c). In order to prepare a specific reference for the system under our consideration, we numerically examine the critical-current fluctuations delta J(c)(2) in the long-junction limit in a model system. Numerical results show that the magnitude of delta J(c)(2) and energy correlation range agree with our analytical result. The effect of the barrier potential at the NS interfaces is numerically investigated. We find that the experimental result by Takayanagi et al. can be explained quantitatively within the frame work of our theory.