Universal Current Scaling in the Critical Region of a Two-Dimensional Superconducting Phase Transition

The transition to a superconducting state in ultrathin ({~}30 {}) granular niobium nitride is found to obey scaling laws characteristic of critical regions near phase transitions. Dynamic scaling of voltage with current is theoretically suggested in analogy with magnetic phase transitions and is experimentally demonstrated. A universal function of current and temperature involving two independent critical exponents is generated.