Strong-pinning regimes by spherical inclusions in anisotropic type-II superconductors (1708.01653v3)

Abstract: The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current $j_c$ decays with the magnetic field following a power-law $B^{-\alpha}$ with $\alpha \approx 0.66$, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to $\alpha \approx 0.3$. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than $B^{-1}$ as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in $j_c(B)$-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.

• The paper presents a detailed numerical investigation of vortex pinning by spherical inclusions in anisotropic type-II superconductors using large-scale TDGL simulations.
• Key findings show different pinning behaviors for small vs. large inclusions, revealing critical current dependencies and non-monotonic pin forces that deviate from traditional strong-pinning theories.
• The results highlight the complex interplay of pin size, density, and lattice disorder, providing crucial insights for designing high-performance superconducting materials with optimized pinning landscapes.

Insights into Strong Pinning Regimes by Spherical Inclusions in Anisotropic Type-II Superconductors

The paper at hand presents a detailed numerical investigation of vortex pinning phenomena in type-II superconductors with a focus on the role of spherical inclusions as pinning sites. Using large-scale simulations of the time-dependent Ginzburg-Landau (TDGL) equations, the authors aim to elucidate the fundamental mechanisms of strong vortex pinning in anisotropic superconductors, presenting results for various inclusion densities and sizes.

The paper is significant in the context of enhancing the critical currents in high-temperature superconductors, by providing insights into the design of artificial pinning landscapes at the microstructural level. The results are situated within the framework of both standard 1D and 3D strong-pinning theories, delineating their limits of applicability and offering corrections where these models fall short.

Simulation Methodology

The authors employ a sophisticated TDGL solver running on GPU architectures to simulate superconducting states within a substantial three-dimensional volume—allowing them to model realistic physical systems with high fidelity. This approach accounts for complex order parameter fields and captures phenomena that simplified models, such as Langevin dynamics, might overlook. Notably, the simulation includes anisotropic effects, which are crucial for understanding the behavior in high-temperature superconductors.

Key Findings and Strong-Pinning Phenomena

1. Small vs. Large Inclusion Dynamics: The authors contrast the pinning behavior between small ($a \approx 2\xi$) and large ($a \approx 4\xi$) spherical inclusions. Small inclusions show characteristics consistent with strong-pinning regimes, transitioning from 1D to 3D pinning behavior as field and inclusion density change. Notably, the system exhibits the expected $j_c \propto n_p^{1/2}$ scaling at small fields and $j_c \propto n_p$ in a 3D regime at higher fields.
2. Field Dependence Insights: For small inclusions, the critical current $j_c$ exhibits a notable field dependence even in low-field regimes, suggesting that vortex-vortex interactions remain significant at levels where traditional strong-pinning theory predicts saturation. This may suggest the presence of mesoscopic effects not captured by conventional theories or indicate the finite system effects in the simulations.
3. Non-monotonic Pinning Force: Large inclusions present a significant departure from traditional pinning models, with a non-monotonic field dependence of the pin-breaking force $f_p$. The inclusions start interacting minimally with vortices but gain significance as the field increases, eventually reverting to accommodate multiple vortex lines—introducing a distinct "peak" effect in $j_c(B)$ not predicted by simple models.
4. Disorder and Lattice Effects: The simulations reveal that randomly distributed inclusions result in a disordered vortex lattice over a broad parameter space. For small inclusion densities, even a low defect density is sufficient to destroy the lattice's order, challenging assumptions about the elastic response of the lattice captured in classical models.

Implications and Future Directions

The findings underscore the importance of detailed numerical simulations in exploring the parameter space of vortex pinning in complex superconductors. The identification of non-trivial zones of disorder and novel phenomena such as multiple vortex occupations opens new questions about the physics underpinning these effects and how they may be leveraged in materials engineering.

The results have practical implications for the design and optimization of high-performance superconductors, particularly in how pinning landscapes are constructed during the material manufacturing process. Looking forward, further exploration—experimentally and theoretically—of the intermediate pinning regimes and the impact of pinning landscape's heterogeneity could lead to tailored superconducting materials with superior properties. In particular, extending models to include realistic pin-size distributions and their implications on vortex dynamics could provide more holistic design strategies.

Overall, the research provides substantial evidence that enhances the understanding of vortices dynamics in type-II superconductors, highlighting the subtle interplay between lattice disorder, pin size, and pin density in defining the critical current characteristics.