Fluctuations and the return to the superconducting state in granular microbridges

We observe the effect of thermal fluctuations acting on the critical currents of an ultra-thin granular niobium weak-link in the presence of a critical current hysteresis. We find that the these fluctuation induced variations in the dissipative-superconducting transition in this film can be quantitatively explained by a model whereby the non-equilibrium length associated with the dissipative site shrinks exponentially in time while being modulated by thermally activated fluctuations. Since the nonequilibrium region recovers with a characteristic time τd, the current at which the transition to the superconducting state occurs and its associated fluctuations are rf frequency dependent. Fitting the data to our model we find the characteristic non-equilibrium site length, L0, to be 1900A and τdto be 4.0 nsec, both of which are in good agreement with other determinations of these parameters on other niobium samples.