The Study Of Vortex Dynamics Based On Time-Dependent Ginzburg-Landau Model For Superconductors

Since the discovery of high-Tc superconductors, vortex dynamics, which is an important key to understand superconductivity, becomes a central problem, and especially the time-dependent Ginzburg-Landau (TDGL) model that describes the dynamical properties of superconductors has been a subject of theoretical and experimental work. This thesis focuses on various studies into the dynamical behaviors of magnetic vortices in type-II superconductors by using the TDGL model, specifically the high-Tc superconductors. Some major results are listed as follow.First, we present numerical solutions of the periodic TDGL model for the type-II superconductors by a finite-difference approximation. Both the static and dynamical properties of a single vortex are studied as the external magnetic field varies. Vortex and anti-vortex can coexist and annihilate with time in the case of no external magnetic field, while the vortex will approach a steady state in the presence of magnetic field. We also compare the different effects about the periodic boundary conditions and the natural boundary conditions on vortex distribution.Second, we apply the periodic TDGL model to study vortex dynamical behaviours while pinning centres exist in the sample and find that the pinning site, which has a significant potential to keep the vortex from moving, may trap the vortex. The maximum length over which an attractive interaction between a pinning center and a vortex extends is estimated to be about 6.0 æ‹¢ We also derive spatial distribution expressions for the order parameter, vector potential, magnetic field and supercurrent induced around a point defect. Theoretical results and numerical simulations are compared with each other and they are consistent.Third, we apply the periodic TDGL model to simulate vortex dynamics in a type-II superconductor with square or triangular pinning arrays. A pinning array, which has been designed to be periodic in advance, can pin vortices regularly and periodically, and shapes various vortex lattices depending on the applied magnetic fields. At the matching fields, vortex lattices are commensurate with defect lattices,and the pinning effects are enhanced. The results are consistent with those obtained by considering large-scale simulated annealing as well as flux-gradient-driven molecular dynamics. Estimation about the critical current density Jc is made.Fourth, based on averaging process across the film thickness and power series expansion expression, we develop a time-dependent GL model for thin film with periodic variable thickness in type-II superconductors. Moreover, we have applied the finite-difference approximation to simulate the vortex dynamics, showing that a single vortex will be pinned in thinner regions. The result manifests the suggested model reasonable and applicable.Fifth, we study, using a finite-different method, single vortex structure of a s+id-wave superconductor by solving a TDGL model for high-Tc superconductors. We find that, below a phase transition temperature, the order parameters indicate a twofold symmetry, whereas a fourfold symmetry appears beyond the temperature. We have also investigated the effects of thermal fluctuations on the pairing symmetry while existing an additive noise or a multiplicative noise in the TDGL models. The regular vortex pattern will be distorted and disordered steadily as the noise level increases. And, it becomes no longer recognizable as a sufficiently high magnitude of noise exists.