Transverse magnetization and torque in asymmetrical mesoscopic superconductors

We show that asymmetrical mesoscopic superconductors bring new insight into vortex physics, where we found the remarkable coexistence of long and short vortices. We study an asymmetrical mesoscopic sphere that lacks one of its quadrants, and obtain its three-dimensional vortex patterns by solving the Ginzburg-Landau theory. We find that the vortex patterns are asymmetric, and their effects are clearly visible and detectable in the transverse magnetization and torque.

Figure 1

(Color online) Three-dimensional isodensity plots taken at 20% of the maximum density ${\mid \psi \mid }^2$. Each isocontour is a single surface made of the vortices and the superconductor surface. The magnetic field is directed from bottom to top with $H∕H_{c2}=0.16$ (a), 0.29 (b), 0.35 (c), 0.27 (d), 0.39 (e), 0.49 (f), 0.35 (g), 0.48 (h), and 0.54 (i). The figures correspond to the full sphere (a)–(c) and to the minus-quarter sphere, positioned in two ways, (d)–(f) and (g)–(i), with respect to the field.

Figure 2

(Color online) Magnetization for a full field cycle (a) for the full and (b), (c) for the minus-quarter sphere. The ascending (red) and descending (blue) branches are labeled for the first nine vortex states. Selected isoplots obtained in ascending and descending fields show the degeneracy of state 5. The full nonintersecting magnetization branches are shown just for the full sphere.

Figure 3

(Color online) Ascending (red) and descending (blue) torque branches (a) and the corresponding misalignment angle (b).

Figure 4

(Color online) Torque upon rotation of the fixed applied field $(H=0.40)$ in 5° increments. The inset shows the angle between $\mathit{M}$ and $\mathit{H}$ versus the applied field angle. Selected isoplot configurations for 110°, 130°, 150°, and 180° are also displayed here.