The first part of my dissertation work involved the design, construction, and operation of a scanning microscope that uses a superconducting quantum interference device (SQUID) as a probe. This system can produce two-dimensional (2D) images of the magnetic flux above samples as large as 1cm by 1cm. The microscope has a spatial resolution on the order of 40µm and a flux resolution on the order of a micro flux quantum.
Next, I used this scanning SQUID microscope system to study the distribution of currents in 2D arrays of SNS Josephson junctions and attempt to estimate the penetration depth for perpendicular magnetic fields, λ⊥. λ⊥ is an important parameter in that it is a determining factor for the possibility of a Kosterlitz-Thouless phase transition in arrays. Raster scanned images of the flux above an array were produced for various temperatures and currents. The first method I used to determine λ⊥ was transforming the 2D flux images into images of current distribution. Intrinsic problems with the transforation algorithm led to a second approach of fitting a single flux scan to the Biot-Savart law. For the samples studied, λ⊥ was determined to be on the order of the array lattice constant.
Finally, we investigated the usefulness of Fisher, Fisher, and Huse dynamical scaling to determine the occurrence of a Kosterlitz-Thouless transition in 2D systems. We simulated current-voltage (IV) curves for a 2D Josephson junction array using appropriate parameters and expressions above and below the Kosterlitz-Thouless-Berezinskii transition temperature (TKT). We also included a contribution arising fromfinite-size induced free vortices. The curves were scaled for different voltage cutoffs to simulate the minimum sensitivity of a voltmeter. We found that the value of the dynamical scaling exponent, z, for the best scaling fit and the optimal value of the transition temperature, depended upon the voltage cutoff level chosen; in effect the fit depended upon how much of the finite-sized linear portion of the IV curve that we included.