Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

TL;DR

This study uses three-dimensional Ginzburg-Landau simulations to analyze how a vortex line in a superconductor follows a zigzag pattern of pinning spheres and identifies the critical displacement where the vortex detaches.

Contribution

It introduces a detailed 3D Ginzburg-Landau simulation approach to study vortex pinning by a zigzag of insulating spheres and determines the critical displacement for vortex detachment.

Findings

Vortex lines can follow zigzag pinning centers up to a critical displacement.

The critical displacement depends on the geometry and size of the pinning spheres.

The free energy analysis reveals the conditions for vortex pinning stability.

Abstract

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.