Vortex Lattice and Matching Fields for a Long Superconducting Wire

TL;DR

This paper models flux penetration and vortex lattice formation in a long superconducting wire using London theory and Monte Carlo simulations, revealing finite size effects and matching fields.

Contribution

It introduces a detailed theoretical and computational approach to analyze vortex patterns and matching fields in cylindrical superconducting wires, aligning with experimental observations.

Findings

Finite size effects delay vortex penetration.

Vortex accumulation occurs at the center.

Vortex patterns agree with experiments.

Abstract

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner state, with boundary conditions appropriate for this geometry. Using the Monte Carlo Simulated Annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed state provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results.