Superconducting impurity terms in the Ginzburg-Landau equations and supercurrent: A microscopic theory

Finding the correct way to include small defects in the Ginzburg-Landau (GL) theory of superconductivity requires a microscopic analysis. In the presence of a single impurity, we compute terms which must be added to the GL free energy, supercurrent, and the GL differential equation for the order parameter. Our calculation is very general, covering any (k) over cap-dependent order parameter Delta((k) over cap) which transforms according to a one-dimensional irreducible representation of the crystalline point group.