Tracking vortices in superconductors: Extracting singularities from a discretized complex scalar field evolving in...

Area of Science:

• Condensed Matter Physics
• Superconductivity
• Computational Physics

Background:

• Magnetic flux vortices are crucial for understanding transport properties in type-II superconductors.
• Vortices are topological defects in the complex order parameter field, as described by Ginzburg-Landau theory.
• Previous work established a method for extracting static vortices from simulated data.

Purpose of the Study:

• To extend the vortex extraction method to track dynamics over time.
• To represent vortices as 2D space-time sheets in 4D space-time.
• To analyze vortex interactions like merging and splitting through graph topology.

Main Methods:

• Extending a previously developed vortex extraction method to incorporate time evolution.
• Representing time-dependent vortices as connected graphs in a discretized space-time field.
• Analyzing the topology of these graphs, specifically the appearance/disappearance of holes, to identify vortex interactions.

Main Results:

• Vortices are now represented as 2D space-time sheets (connected graphs) in 4D space-time.
• Vortex merging and splitting events are identified by changes in graph topology (hole dynamics).
• The method achieves resolution limited only by the field discretization, reconstructing trajectories between time steps.

Conclusions:

• The enhanced method provides unprecedented detail in tracking vortex dynamics in superconducting materials.
• This approach offers a powerful tool for studying complex phenomena in superconductivity.
• The technique is versatile, making no assumptions about vortex scale or behavior.