Complex Conductance Measurements of Two-Dimensional Superconductors

At the forefront of current discussions in superconductivity is the debate over the effects of dimension on the vortex lattice and vortex dynamics. Using the mutual inductance technique, we have performed measurements of the complex conductance of ultra-thin superconducting films in an effort to provide a coherent picture of superconductivity in two dimensions. We studied ultra-thin films of amorphous Mo -Ge, which served as a simple, model system of two-dimensional physics. By measuring the temperature dependence of the complex conductance of these films, we were able to extract information about the magnetic coherence length, the areal density of superconducting pairs, and the sheet resistance of the films. Our studies indicate that at temperatures below the mean field transition temperature in a-Mo-Ge, there exists several dissipative processes that can be attributed to the two-dimensional nature of the films. First, we show evidence of a Kosterlitz-Thouless transition in zero applied magnetic field and fit our data to existing theories of vortex dynamics. Second, we provide details of the vortex state of the films in an applied magnetic field. We examine field and frequency dependent data that show a crossover to a dissipative state in the films. Finally, we consider the effects of disorder on the measurements and try to modify existing theories to include inhomogeneities in the materials.