Motion of magnetic vortices in type-Ⅱ superconductor with randomly distributed pinning centers

Abstract

The dynamic behaviors of the magnetic vortices in a two-dimensional square superconductor with randomly distributed pinning centers of normal state were considered using the Ginzburg-Landau (G-L) model. The pinning centers are randomly distributed as various contents in all the area of the superconductor and a distribution function p(r) defined in a MATLAB is used to determinate the size and sites of normal state pinning centers. Using COMSOL and MATLAB, we analyzed the magnetization curves and the density of superconducting electrons as a function of the external magnetic field applied along the z-axis. Simulation results showed that the vortices configurations and magnetization depend on the content of the pinning centers and the maximum magnetization values decrease exponentially as the content increases. The content of pinning centers with the largest mixed state is determined by modeling the number of the magnetic vortices trapped in the pinning centers. This work will provide good results into understanding the dynamics of the magnetic vortices in a superconductor with randomly distributed pinning centers in view of the circumstance that they are randomly distributed in the superconductor during fabricating it.