From vortex molecules to the Abrikosov lattice in thin mesoscopic superconducting disks

TL;DR

This study investigates stable vortex configurations in large thin superconducting disks, revealing the formation of Abrikosov lattices and defect structures using advanced theoretical models and numerical simulations.

Contribution

It extends the London approximation by including order parameter variations and compares it with Ginzburg-Landau results for large vortex numbers.

Findings

Vortex configurations with over 700 vortices are stable.

Abrikosov lattice forms at high vorticity in the disk center.

Defects and grain boundaries are observed near the disk edge.

Abstract

Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50 \xi). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ~ 230 vortices. For large values of the vorticity (typically, L > 100), the vortices are arranged in an Abrikosov lattice in the center of the disk, which is surrounded by at least two circular shells of vortices. A Voronoi construction is used to identify the defects present in the ground state vortex configurations. Such defects cluster near the edge of the disk, but for large L also grain boundaries are found which extend up to the center of the disk.