Distribution of Supercurrent Switching in Graphene under the Proximity Effect

We study the stochastic nature of switching current in hysteretic current-voltage characteristics of superconductor-graphene-superconductor junctions. We find that the dispersion of the switching current distribution scales with temperature as sigma(I) proportional to T-alpha G with alpha(G) as low as 1/3. This observation is in sharp contrast to the known Josephson junction behavior where sigma(I) proportional to T-alpha J with alpha(J) = 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.