Distribution of supercurrent switching in graphene under proximity effect

We study the stochastic nature of switching current in hysteretic current-voltage characteristics of superconductor-graphene-superconductor (SGS) junctions. We find that the dispersion of the switching current distribution scales with temperature as a power law with the power close to 1/3. This observation is in sharp contrast with the known Josephson junction behavior where switching current dispersion is expected to scale with the power 2/3. We propose an explanation using a generalized version of Kurkijarvi's theory for the flux stability in rf-SQUID and attribute this anomalous effect to the temperature dependence of the critical current which persists down to low temperatures.