Energy dependence of a vortex line length near a zigzag of pinning centers

TL;DR

This paper investigates how a vortex line's length depends on energy when shaped by a zigzag of insulating pinning centers using Ginzburg-Landau theory in a three-dimensional model.

Contribution

It introduces a 3D model of vortex lines with symmetric pinning centers and calculates free energy density variations based on pinning center size and configuration.

Findings

Energy dependence of vortex line length near zigzag pinning centers

Quantitative analysis of free energy density variations

Impact of pinning center size on vortex configuration

Abstract

A vortex line, shaped by a zigzag of pinning centers, is described here through a three-dimensional unit cell containing two pinning centers positioned symmetrically with respect to its center. The unit cell is a cube of side $L=12\xi$, the pinning centers are insulating spheres of radius $R$, taken within the range $0.2\xi$ to $3.0\xi$, $\xi$ being the coherence length. We calculate the free energy density of these systems in the framework of the Ginzburg-Landau theory.