Vortex in superconducting thin-film strips of arbitrary width

TL;DR

This paper analyzes the magnetic field and current distributions of a vortex in thin superconducting strips of arbitrary width, revealing unique field line behaviors and flux suppression effects near edges.

Contribution

It provides a detailed theoretical analysis of vortex fields in finite-width superconducting strips, highlighting differences from infinite films and the flux suppression phenomenon.

Findings

Magnetic field lines in strips return through edges and outside regions.

Vortex flux is less than the flux quantum and depends on vortex position.

Flux suppression is significant in narrow strips with W << Lambda.

Abstract

The currents and field distributions of a vortex in a thin superconducting strip of a width $W$ is considered. It is shown that unlike infinite films where the vortex field crosses the film only in one direction (say, from the half-space under the film to the half-space above it), in strips (as well as in finite size film samples of any shape) the field lines go back to the lower half-space not only out of the sample but also through certain strip parts. The strip patches where the magnetic lines ``dive" back to the space under the strip are situated mostly near the strip edges at the strip and out of it. The magnetic flux through the strip associated with the vortex is shown to be less than the flux quantum and depends on the vortex position. The suppression of the vortex flux is strong in narrow strips with $W<<\Lambda=2\lambda^2/d$ where $\lambda$ is the bulk London penetration depth and $d$ is the film thickness. The vortex energy scales roughly with $W/\Lambda$ and depends on vortex position.