Effect of the boundary condition on the vortex patterns in mesoscopic three-dimensional superconductors - disk and sphere

TL;DR

This study investigates how boundary conditions influence vortex configurations in mesoscopic 3D superconductors, revealing bent vortex lines in spheres and boundary-dependent effects on critical fields and magnetization.

Contribution

It provides a detailed analysis of vortex patterns in mesoscopic superconductors with different boundary conditions using Ginzburg-Landau theory, including the impact on critical fields.

Findings

Vortex lines in spheres are bent and closest at the equator.

Boundary properties significantly affect matching fields and $H_{c3}$.

Surface parameter variations can enhance $H_{c3}$ substantially.

Abstract

The vortex state of mesoscopic three-dimensional superconductors is determined using a minimization procedure of the Ginzburg-Landau free energy. We obtain the vortex pattern for a mesoscopic superconducting sphere and find that vortex lines are naturally bent and are closest to each other at the equatorial plane. For a superconducting disk with finite height, and under an applied magnetic field perpendicular to its major surface, we find that our method gives results consistent with previous calculations. The matching fields, the magnetization and $H_{c3}$, are obtained for models that differ according to their boundary properties. A change of the Ginzburg-Landau parameters near the surface can substantially enhance $H_{c3}$ as shown here.