Abstract Mesoscopic or nanoscale superconductors are extensively applied in various superconducting devices, and their superconducting properties, along with internal physical processes, are significantly influenced by external fields and structural characteristics. An extremely significant factor is the geometrically dependent demagnetization effect. We implemented a three-dimensional superconductor-vacuum (3D S-V) model that integrates Time-Dependent Ginzburg-Landau (TDGL) equations with Maxwell’s equations to systematically investigate the impact of the demagnetization effect on the superconducting properties of type I and type II mesoscopic superconductors. The 3D S-V model inherently incorporates the demagnetization effect through self-consistent coupling with the surrounding vacuum, achieving high accuracy. The maximum relative error between numerical solutions of the 3D S-V model and analytical solutions of the Maxwell-London equations is only 1.39%, compared to an average relative error of 20% for the traditional 3D model ignoring the vacuum (referred to as the 3D S model). The 3D S-V model also demonstrated good reproducibility for different Ginzburg-Landau parameters. Our investigation of the geometric dependence of the local magnetic field in type I and type II mesoscopic superconductors reveals that systems exhibiting the demagnetization effect require precise modeling via the 3D S-V model, whereas those without this effect can be accurately simulated using the more computationally efficient two-dimensional S model. Furthermore, we systematically compared type I and type II mesoscopic superconductors with varying geometric configurations, analyzing the magnetic field dependence of free energy, magnetization, average magnetic induction, and average Cooper pair density, as well as vortex configurations, phase distribution, and supercurrent distribution. The observed differences are primarily attributed to the influence of the demagnetization effect. This work provides valuable guidance for selecting an appropriate TDGL numerical simulation framework, which is beneficial for our fundamental understanding of the response of mesoscopic superconductors to external fields.
Jin et al. (Wed,) studied this question.