Investigations of two types of superconducting arrays

Abstract

This dissertation has two parts. Part one studies the anisotropy effect on homogeneous superconducting wire-networks, by using the Abrikosov approach. The network s assumed to have an infinite square lattice geometry. An anisotropy parameter R is defined to be the cross sectional area ratio of the vertical and horizontal strands. Many limiting behaviors of the order parameter distribution as R [approaches infinity] are obtained. Many anisotropy-induced vortex configurational transitions are found at several Φ/ Φ[0] values studied, and are investigated in detail. Part two studies the ground-state vortex configurations of the Josephson-coupled arrays of superconducting islands. The Ginzburg-Landau Josephson array model is used. With arrays of Penrose tiling geometry, we have found negative evidences against a proposed mechanism, and positive evidences for a new mechanism for generating commensurate states. But the mechanisms for the majority of the nontrivial commensurate states remain to be investigated. With arrays of infinite square lattice geometry, a temperature-induced vortex configurational transition at Φ/ Φ[0] = 1/6 is found. We discover that the equilibrium vortex ground state of an infinite square-lattice array can occur in a unit cell of size other than q by q, or 2q by 2q, which has been widely accepted and commonly used so far.