Current flow in inhomogeneous superconductors

The change of normal current flow into supercurrent flow is examined in a number of problems in which the pair potential of the superconductor can vary spatially. We examine approximate solutions to the Bogoliubov equations in the limits that the pair potential, ~('f), varies quickly or slowly compared to a coherence length, ~ (T), to see how well such solutions conserve charge c flux. These solutions are then used to compute the linear current response of a superconductor in these two limits. Scatter'ing is included using the Mattis-Bardeen scattering technique. Using the step-like pair potential the linear current response of a superconducting-normal (SN) junction as well as NSN, SNS, and layered structures SNSN... as occur with a static electric field applied normal to the boundaries is calculated. The results for the self-consistent currents and fields are found to be the same in certain limits as those found by other investigators who used semiphenomenological approaches. The linear current response of a superconductor with a pair potential which varies slowly over a coherence length to an applied alternating electric field is also examined. This result should be useful in describing the current response of very wide superconducting-normal-superconducting (SNS) junctions in which a very small pair potential exists in the "normal" region at very low temperatures in the millidegree range.U of I Onlydissertation/thesi