Order Parameter and Magnetic Field of a Vortex Line Pinned at a Point Defect: Ginzburg-Landau Theory

TL;DR

This paper applies the Ginzburg-Landau theory to analyze the effects of a point defect on a vortex line in a superconductor, deriving analytic solutions for the order parameter and magnetic field near the defect.

Contribution

It develops coupled differential equations and provides analytic solutions for vortex pinning effects, extending previous theoretical models with numerical evaluations.

Findings

Derived analytic solutions for order parameter and magnetic field near a defect.

Compared numerical results with Clem's approximate solutions.

Enhanced understanding of vortex pinning in superconductors.

Abstract

Recent theoretical work has derived the correct form of the Ginzburg-Landau differential equations, for the superconducting order parameter and vector potential, in the presence of a small defect. Here, these equations are applied to the case of a single vortex line pinned on such a defect. We develop the coupled set of partial differential equations, and show how to derive analytic solutions for the order parameter and magnetic field perturbations in the region of space near the defect. Certain properties of the unperturbed vortex solution are needed to totally specify our result; these are evaluated numerically, and compared with those deduced from Clem's approximate solution.