We study structures of vortices in a type II superconductor under spatially varying fields. Because in application of superconductors, such as an electromagnet, spatially varying fields appear. In previous study, it is found that directions of vortices are not parallel to the field in a chiral helimagnet /superconductor bilayer structure [1,2]. The origin of this behavior may come from interaction between vortices.

In this study, in order to clarify the origin of previous results, we investigate structures of vortices in a superconductor under spatially varying fields by solving the Ginzburg-Landau equation. We obtain an interesting result like an entanglement structure as stable state under spatially varying field (Fig.1). We will explain how this structure appears and show other structures of vortices under various spatially varying fields.

Figure1: Structure of the order parameter which show an entanglement vortex structure(arrows show vortex direction)

[1] S.Fukui, M. Kato, Y. Togawa, Supercond. Sci. Technol., 29, 125008 (2016).
[2] S.Fukui, M. Kato, Y. Togawa, O. Sato, J.Phys. Soc. Jpn., 87, 084701 (2018).

Keywords: Vortex, Ginzburg-Landau Equation, Vortex entanglement, Finite Element Method