Quasi-classical theory of weakly anisotropic superconductors

Abstract

This thesis starts by reviewing superconductivity in one-dimension where fluctuations cause a loss of supercurrent due to an intrinsic resistance. Solved via the Ginzburg-Landau equations, the theory of thermally activated phase slips given by Langer and Ambegaokar is outlined. In turn this leads to the investigation of superconductivity via a microscopic approach, in particular the quasi-classic green’s functions of Eilenberger. The Eilenberger equations are derived and considered in the dirty and weakly anisotropic limits which provides a simple derivation of the Ginzburg-Landau equations near the transition temperature. This prompts an extended derivation which includes the non-linear terms normally removed in deriving the Ginzburg-Landau equations. This is required for calculating effects at temperatures below the transition temperature. These quasi-classic equations of weakly anisotropic superconductors are first written for arbitrary temperature and impurity concentration then limited to the pure and dirty cases. The latter being simplified to zero temperature and solved in the context of thermally activated phase slips.