Simulation Of Vortex Dynamics Based On Time-Dependent Ginzburg-Landau Equations

In this dissertation, I briefly review the history of research on superconductivity and introduce the famous Ginzburg-Landau Theory, which describes the properties of mixed state of Type-II superconductors. We take partial differential with regard to the order parameter and magnetic vector, and get two new G-L equations. Then we carry on the procedures of nondimensionalization and discretization, and a model based on an auxiliary linking variable is obtained. After we work out boundary conditions of the system, it becomes available to compute and simulate the process of evolution of vortices and properties at equilibrium state in a two-dimensional superconductor, under different external conditions.Firstly, we simulate the vortices distribution of a clean two-dimensional superconductor without any pinnings or current in the system. We find that the vortices distribute as the quasi-triangle lattice. Then we compare with the changes of the magnetisability and free energy by altering one of the parameters. Secondly, we apply the factor of temperature into the system and simulate its effect on the disturbance of vortices and critical current. Finally, we bring in different pattern of pinnings and make a comparison in terms of the intensity of magnetization and critical current, and find that under the circumstance of equal intensity and density of pinning, a system with comformal pinning possesses higher level of critical current than that of triangle pinning.