Nonuniform vortex distributions in superconductors: from critical state to conformal crystals - MENEZES, Raí Maciel de (2017)
In this dissertation, we study through numerical simulation, properties of the vortex matter in superconductors. In non-homogeneous superconductors, the penetration of magnetic flux (provided by the vortex entry) within the sample is theoretically described by the macroscopic critical state models, where due to interaction with material impurities (pinning centres), the vortex density is high near the edges and decreases as we approach the center of the sample. Although extensively studied, the critical state models do not explain in detail how the microscopic events lead to the global behavior predicted by the macroscopic models , especially nearby the surfaces, where the vortex currents are deformed to satisfy the boundary conditions. We simulate through molecular dynamics methods the penetration and the microscopic dynamics of vortices in a superconducting slab subjected to a parallel applied magnetic field. We explicitly take into account the often neglected vortex-surface interaction and analyse how this can influence the dynamics and the critical state configurations. We then verify which of the various critical state models best describes the system. Nearby the surfaces, we observed regions with zero density of vortices, which arise due to the energetic barrier that hinders the vortex entry and exit. Such regions, known as flux free regions, have a thickness which depends on the strength of the applied magnetic field and the level of pinning forces in the material. We also analyse the temporal evolution of the flux front inside the superconductor and the hysteresis cycles of the magnetization due to an external field variation, and compare with results known in the literature. Another topic of broad interest concerns the possible ordered structures that the vortex lattice can form. In situations of uniform density the system of vortices converges to a minimum of energy and tends to be ordered as a triangular lattice (Abrikosov lattice). However, in situations where the vortices may form nonuniform distributions, due to variations in sample thickness, interactions with material inhomogeneities, among other ways, the triangular Abrikosov lattice will not satisfy the minimum energy condition. The question is whether the nonuniform distribution of vortices presents a structure of small domains of different densities, i.e., a nonuniform glass, or a new ordered structure emerges. We obtain evidences of conformal crystals as possible, stable nonuniform vortex configurations in a superconductor. Such configuration is an example of ordered crystallization in a nonuniform particle distribution. These ordered structures, although can present local inhomogeneities, preserve the topological order and can be mathematically mapped into a triangular lattice through a conformal transformation. We propose a simple method to obtain the particle density required to observe such structures and suggest possible experimental realizations in which conformal (or quasiconformal) vortex crystals could be observed in bulk superconductors or thin films.