CRITICAL CURRENTS IN INHOMOGENEOUS TRIANGULAR JOSEPHSON ARRAYS - A MODEL FOR POLYCRYSTALLINE SUPERCONDUCTORS

The current-voltage characteristics of polycrystalline superconducting films are modeled as a triangular array of resistively-shunted Josephson junctions. The variation observed experimentally in YBa2Cu3O7 grain boundary critical currents as a function of the crystallographic misorientation angle has been explicitly taken into account by randomly distributing two different values of the grain boundary critical currents throughout the array. We calculate I-V characteristics for these random systems, obtain a scaling relation for the critical current, and examine some functional forms relating the voltage to the input current. Our finding of a characteristic length scale greater than the average grain diameter for critical currents in superconducting films has implications for other properties of polycrystalline materials.