(left) Photograph of a small section of a typical array. Junctions are found

1. Zero Resistance at Discrete Values of Applied Field in Josephson Junction ArraysAllen M. Goldman, University of Minnesota-Twin Cities, DMR 0455121 We have been studying very large Josephson junction arrays (JJAs), with 500,000 and 1,000,000 Nb junctions arranged in a square lattice. The Josephson effect is the phenomenon of current flow without resistance in the junction between two superconductors separated by a very thin insulating barrier. These JJAs have served as model systems for a wide range of phenomena in condensed matter physics including phase transitions in two dimensions,, nonlinear dynamics and vortex dynamics. The arrays were originally produced to serve as models of ultrathin films which constitute the main focus of this program. In studying these arrays we have found that at relatively low temperatures in the presence of significant transport current through the array, but short of driving the array normal, (left) Photograph of a small section of a typical array. Junctions are found At the overlap of the elec- trodes which are crosses. The bar is 80 mm long. (below) Resistance vs. flux, f, in units of the flux quan-tum at T = 1.9 K.

2. Zero Resistance at Discrete Values of Applied Field in Josephson Junction ArraysAllen M. Goldman, University of Minnesota-Twin Cities, DMR 0455121 Superconductivity was found only at magnetic fields corresponding to integer values of the flux in units of the flux quantum, with the array having a high resistance otherwise. This counter-intuitive observation resembles a series of transitions to superconductivity from the insulating state occurring at discrete values of magnetic field. Whether these transitions from nonsuperconducting to superconducting behavior are some type of quantum phase transition is not known at this writing. An account of this work has been published in Physical Review B (Elsayed et al., Phys. Rev. B 80, 052502 (2009)). The broader impact of this work involves the interplay between undergraduate instruction and research. The arrays were made some time ago by Sperry Univac Corporation (now Unisys) using its selective niobium anodization process, as part of an industrial collaboration. They have been used in recent years in the signature upper level experimental course for physics majors. Students have the opportunity to explore various features of the Josephson effect using these robust structures, which also have value as contemporary research tools. This particular work was carried out by a Ph D. student from Egypt, supported by the Egyptian government, who was at Minnesota for a limited time. His presence in the group gave the members exposure to a person from a culture not usually found in the physics department at the University of Minnesota. He also learned low temperature and electrical measure-ments in the course of his work.