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

In type-II superconducting material, the dynamics of the vortices play a critical role in determining the performance of the material. ~In Ginzburg-Landau simulations of superconducting materials, vortices correspond to topological singularities in a discretized complex scalar field. Visualizing the vortices to understand their behavior is a key step in using simulations to engineer optimized pinning landscapes. ~In the past, vortices have been visualized by examining contour plots and isosurfaces of the magnitude of the field. ~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. ~We present a method for exactly finding the vortex core lines from a complex order parameter field. With this method, the 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. ~