Numerical approach for vortex dynamics in the presence of mesoscopic pining centers

The efficient and accurate description of superconducting vortex dynamics is required for a number of technological applications extending from microelectronics to dissipationless power transmission lines and powerful magnets.

In the limit of low magnetic fields, it is reasonable to use the Langevin approach for the vortex dynamics, which does not take into account vortex-vortex interaction and thereforeis extremely effective from numerical point of view.

In the limit of high fields, the dynamics of vortices is largely determined by their interaction, and a model that correctly describes this interaction is required. In the vicinity of the critical temperature, Ginzburg-Landau (GL) approach is suitable to acquire the statistics of vortex dynamics. However, since the data for the statistical analysis is roughly proportional the number of vortices, the GL approach becomes numerically inefficient in low field limit.

In the present work we propose the efficient and accurate method for vortex dynamics description in low field limit. We combine (i) GL solver to extract effective energy potential for single vortex and (ii) Langevin approach to acquire statistical data for vortex dynamics. We check the applicability of the combined method by comparison results with time-dependent GL solver.