Detecting vortices in superconductors: Extracting one-dimensional topological singularities from a discretized complex scalar field

TL;DR

This paper introduces a precise method for detecting and visualizing vortex core lines in superconductors from discretized complex scalar fields, enabling higher resolution analysis and efficient data management in large-scale simulations.

Contribution

The paper presents a novel technique for exactly extracting vortex core lines from complex order parameter fields, surpassing previous methods in resolution and scalability.

Findings

Allows vortex core detection at sub-mesh resolution

Reduces data footprint of simulations significantly

Enables detailed visualization and tracking of vortices

Abstract

In type-II superconductors, the dynamics of superconducting vortices determine their transport properties. In the Ginzburg-Landau theory, vortices correspond to topological defects in the complex order parameter. Extracting their precise positions and motion from discretized numerical simulation data is an important, but challenging task. In the past, vortices have mostly been detected by analyzing the magnitude of the complex scalar field representing the order parameter and visualized by corresponding contour plots and isosurfaces. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. Here we present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. By representing the field as the set of vortices, this method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking.