Abstract
Using three-dimensional (3D) numerical discretization of the Ginzburg–Landau (GL) equations, we investigate the superconducting state of a sphere with a piercing hole in the presence of a magnetic field. In the case of samples with central perforation, in axially applied homogeneous magnetic field, we realized unconventional vortex states of broken symmetry due to complex, 3D competing interactions, which depend on the GL parameter κ. For certain sizes of the sample, non-hysteretic multi-vortex entry and exit is predicted with the non-existence of some vorticities as stable states. In a tilted magnetic field, we studied the gradual transformation of 3D flux patterns into 1D vortex chains, where vortices align along the perforation, and the evolvement of the multi-vortex entry as well. We analyze the flux-guiding ability of the hole in a tilted field, which leads to fractional flux response in magnetization M(H) curves.
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