Finite Element Treatment of Vortex States in 3D Mesoscopic Cylindrical Superconductors in a Tilted Magnetic Field

Abstract

The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for the mesoscopic superconducting samples with cylindrical shape in a uniform axial magnetic field. We obtain the different vortex patterns as a function of the applied field perpendicular to its surface. We find that multi-vortex states are ground state in three-dimensional mesoscopic cylinders. These results show that our approach is an effective and useful to interpret experimental data on vortex states in the mesoscopic superconductors.

Formation and Rearragement of Vortex Tubes in a 3D Mesoscopic Superconductor with a Central Weak Link

“…A direct observation of vortex states in small superconducting disks for vorticity L = 0 to 40 was also reported [13]. Theoretically, it has been shown that many different kinds of superconducting states can exist in mesoscopic samples [2,[5][6][7][8][9][10][11]. Vortices also show very rich static and dynamic behavior in the presence of a weak link [7,10,14].…”

“…Mesoscopic superconductor exhibit very peculiar magnetic properties when their size is comparable to the coherence length ξ [1]. The mesoscopic samples of different shapes surrounded by vacuum or an insulator medium have been considered extensively both experimentally and theoretically [2][3][4][5][6][7][8][9][10]. In experiment, the measured superconducting phase boundary for the mesoscopic Al square shows the direct experimental evidence for these symmetry-induced vortex-antivortex pairs [11].…”

Dynamic Behavior of Vortices under Applied Current Drive in Mesoscopic Superconducting Strip with Two Magnetic Dots

“…Numerical simulations will be performed in the framework of the time-dependent Ginzburg-Landau (TDGL) model. The finite-element method (FEM) [14][15][16] was used due to its ability to handle complex geometries and complicated boundary conditions, and the additional benefit of less computing time. The TDGL equations are numerically solved to obtain the dynamic properties of the superconducting strips.…”