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Conductance Fluctuations in a Superconductor-Dirty Normal Conductor-Superconductor Junction

We obtain an analytical expression for the conductance fluctuation in a superconductor-dirty normal conductor-superconductor (SNS) junction using the Green's function method. It is shown that the magnitude of the fluctuation is enhanced by a factor of ( L φ / L x ) (4- d )/2 compared with the universal value of the order of \(e^{2}/\hbar\) ( L φ : the phase coherence length, L x : the separation between two superconductors, d : the effective dimension of the normal region). It is also shown that the energy correlation range is of the order of the inverse of the phase relaxation time, in contrast to ordinary cases where the energy correlation range is of the order of the Thouless energy. We calculate the phase coherence length L φ as a function of the sample size and find that L φ becomes longer with the reduction of the sample size. This indicates that the conductance fluctuation in an SNS junction can be strongly enhanced beyond the universal value.