Designing Stable Vortex Pinning with Time-Dependent Ginzburg–Landau

Reducing flux-flow dissipation in current-carrying superconductors requires effective control of vortex dynamics and pinning. Patterned domains that locally suppress the superconducting order parameter establish a fixed pinning landscape capable of immobilizing vortices without altering the device geometry. Our goal is to establish quantitative geometry–pinning criteria—including a critical-gap rule that links inter-domain spacing to core and screening length scales—and to provide layout guidance for planar 2D transmission lines and current-carrying 3D wires. Using Time-Dependent Ginzburg–Landau simulations, we identify when these domains act as stable pinning sites and characterize the associated vortex morphology. Systematic variations of transport current, magnetic field, and domain geometry (size, spacing, shape) reveal distinct regimes of vortex entry, capture, and escape governed by penetration-depth and coherence-length–scale effects. These results establish quantitative design criteria linking geometry to reliable immobilization and delineate thresholds for depinning.