Vortices in superconductors with a columnar defect: finite size effects

TL;DR

This paper analyzes vortex behavior in superconducting cylinders with a central columnar defect, deriving magnetic field and energy distributions, and determining vortex capacity and flux entry barriers for various size limits.

Contribution

It provides general formulas for vortex behavior in finite-sized superconductors with a defect, including specific limits and vortex capacity calculations.

Findings

Maximum vortex number depends on cavity and cylinder sizes.

Surface barrier field for flux entry is quantified.

Finite size effects significantly influence vortex dynamics.

Abstract

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated.