Strain-modified TDGL modeling of vortex pinning and dynamics in superconductors with nanorods

Abstract

Enhancing the critical current density (J_c) under high magnetic fields remains a central challenge for high-temperature superconductors (HTSs). Introducing nanoscale pinning centers is a proven strategy to immobilize magnetic vortices and improve J_c. In the time-dependent Ginzburg-Landau (TDGL) framework, this process is commonly modeled through a spatially varying function p(r) that represents the local suppression of the critical temperature (T_c). However, conventional TDGL models overlook the influence of local strain generated by lattice mismatch between nanostructures and the superconducting matrix. In this work, a strain-modified TDGL formulation is developed by incorporating the strain-dependent modulation of T_c through a revised pinning function p(r, ε). Based on this framework, the effects of strain, nanorod size, and spatial distribution on J_c are systematically investigated, and the optimal pinning configurations for given magnetic fields are identified. Results show that neglecting strain leads to substantial underestimation of J_c at low defect densities and misrepresentation of its its dependence on doping concentration. Therefore, incorporating strain-induced corrections not only enhances the predictive accuracy of the TDGL model but also provides a more reliable theoretical foundation for the design and optimization of high-performance superconducting materials.