Case Studies on Time-Dependent Ginzburg-Landau Simulations for Superconducting Applications

The macroscopic electromagnetic properties of type-II superconductors are mainly influenced by the behavior of microscopic superconducting flux quantum units. Time-dependent Ginzburg-Landau (TDGL) theory is a well-known tool for describing and examining both the statics and dynamics of these superconducting entities. It have been instrumental in replicating and elucidating numerous experimental results over the past decades. This paper provides a comprehensive overview of the progress in TDGL simulations, focusing on three key aspects of superconductor applications. We delve first into vortex rectification in supercon-ductors described within the TDGL framework, specifically highlighting the achievement of superconducting diode effect through asymmetric pinning landscapes and the reversible manipulation of vortex ratchets with dynamic pinning landscapes. In terms of the achievements of TDGL simulations concerning the critical current density of superconductors, we emphasize particularly on the optimization of pinning sites, including vortex pinning and dynamics in polycrystalline Nb 3 Sn with grain boundaries. In the third aspect, we concentrate on numerical modeling of vortex penetration and dynamics in superconducting radio-frequency cavities, including a discussion on superconductor-insulator-superconductor multilayer structures. Finally, we present key findings, insights, and perspectives derived from the discussed simulations.