| Regular periodic patterns exit widely in nature, and one of their remarkable manifestations is the intermediate state structures of type-â… superconductors. Due to demagnetizing effects, the perfect diamagnetism of a type-â… sample breaks down when the enhanced surface magnetic fields reach the critical filed, and applied magnetic fields penetrate into the body of the sample and form macroscopic flux domains with distinct morphologies immersed into a superconducting matrix. Although numerous studies have been conducted since the pioneering work of Landau in 1930s, the question about the minimum-energy structures of the intermediate state remains open. In experiments, the magnetic system may be trapped into various metastable states due to pinning effects. Thus, the complex magnetic patterns rather than the regular ones could be observed, precluding the clear understanding of the equilibrium structures of the intermediate state. On the other hand, some models have been proposed to explain the experimental observations, including Landau lamina model, Goren-Tinkham spot model and current-loop model. Although these models can be suitable for some specific experiments, an accurate description of all experimental observations based on a single model is still needed. In this work, we attempt to use atomic approach to study the flux physics of type-â… superconductors through constructing a model system consisted of interacting quantized vortices. Our idea is motivated by the recent theoretical and experimental works, revealing that a single quantum vortex is the smallest building block of the intermediate state. Then it is rational to assume that the interaction between flux tubes or flux domains should happen through quantized vortex. In this case, we consider a simple model containing the basic physics of the system, where the vortices interact with each other via a competing long-range repulsion due to the demagnetizing effects and short-range attraction due to superconducting condensation. Based on Langevin dynamics, we numerically study the static magnetic structures depending magnetic field and sample thickness, and moving structures and transport behaviors under driving forces.In chapter 1, we introduce the research background of the intermediate state for Type-â… superconductors. In chapter 2, we describe in detail the model system used to study the intermediate state. This relates to the idea of atomizing, the inducing of the competing vortex-vortex interactions, and Langevin moving equation. In chapter 3, we numerically investigate the equilibrium flux patterns in type-â… . superconducting thin films. For thinner films, the ordered Abrikosov mixed state is found independent of magnetic field. While for thicker films, ordered bubblelike intermediate mixed structure, bubbelike and stripelike flux domains, and ordered bubblelike superconducting domains are obtained with increasing fields. A phase diagram is presented as a function of magnetic field and film thickness. In chapter 4, we study the moving magnetic domain structures for the systems with random pinning centers under driving forces. The simulations show four typical structures or dynamic states:well-pinned state, plastic flow, ordered bubbles and ordered stripes. We obtain a phase diagram as function of magnetic fields and driving forces. In chapter 5, we study the force-velocity characteristic of the magnetic system for type-â… . superconductors. The simulations show that the system displays similar resistance relaxation and memory effect to the vortex systems for type-â…¡ superconductors. Finally, we summery the main results in this work. |
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