Steady-state and equilibrium vortex configurations, transitions, and evolution in a mesoscopic superconducting cylinder

TL;DR

This paper introduces a numerical method to analyze vortex configurations and transitions in mesoscopic superconducting cylinders, revealing how vortex states evolve and transition under varying magnetic fields.

Contribution

A new numerical scheme is developed to determine equilibrium vortex configurations in mesoscopic superconductors regardless of symmetry.

Findings

Identified vortex state transitions with contour plots and B-H jumps.

Showed the system passes through metastable states en route to equilibrium.

Demonstrated the scheme's effectiveness in various magnetic field conditions.

Abstract

A numerical scheme to study the mixed states in a mesoscopic type-II superconducting cylinder is described. Steady-state configurations and transient behavior of the magnetic vortices for various values of the applied magnetic field H are presented. Transitions between different multi-vortex states as H is changed is demonstrated by contour plots and jumps in the B vs H plot. Evolving a uniformly-superconducting initial state using the simplest set of relaxation equations shows that the system passes through nearly metastable intermediate configurations, while seeking the final minimum-energy, steady state consistent with the square symmetry of the sample. An efficient scheme to determine the equilibrium vortex configuration in a mesoscopic system at any given applied field, not limited to the symmetry of the system, is devised and demonstrated.