The Superconducting Phase Transition in Million Josephson Tunneling Element Arrays

Square arrays of one million Josephson junctions have been fabricated using the Selective Niobium Anodization Process (SNAP). Such arrays are nearly ideal examples of systems which can be described by the 2D X-Y model. In zero magnetic field we find clear evidence of the expected Kosterlitz-Thouless transition in the power law dependence of the voltage on current in the vicinity of and immediately below the transition temperature. In the regime above the transition, where the temperature-dependent resistance is determined by the free vortex density, only activated behavior is observed. This finding is in contrast with the results of measurements on thin films and proximity-coupled arrays where an exp [-A(T-Tc)^1/2] dependence of resistance on temperature is found.