James M. Gordon

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.

Fractal dimensions and dimensional crossover in superconducting wire networks

Abstract We have fabricated Al wire networks in the form of submicron scale fractals including the Sierpinski Gasket (SG), arrays of SGs, and percolation clusters. Measurements have been made of the superconducting phase boundary, T c ( H ), and the magnetoconductance above T c . From analysis of the SG data we have determined the fracton dimension of that fractal. The gasket arrays show a crossover from fractal behavior at small length scales to two-dimensional behavior over large lengths, or, equivalently, small fields. The percolation networks are also inhomogeneous, but show no crossover. Presumably this is due to the addition of randomness and dead-end bonds in these patterns.

Fabrication of submicron wire networks using electron beam lithography

Abstract We have fabricated and studied superconducting wire networks with various geometrical properties including fractal, periodic, quasi-periodic, and random. We will discuss design and fabrication of these aluminum networks, which consist of nearly one million elements and span a square millimeter. We will present results of several studies of these networks.