Phase Transition of Strange Vortex State in a Superconductor under a Rotated Magnetic Feld

Vortices appear in a type-II superconductor under an external field. Under a uniform field, vortices are parallel to the field and form usually a triangular lattice. However, if the magnetic field is not uniform, it is not clear how vortex structure changes.

Previously, we considered the bilayer system with a superconductor and chiral helimagnet Using the numerical simulations, in two-dimensional system, we found that vortices and anti-vortices appear according to the direction of the field [1,2]. In the three-dimensional system, under a helical magnetic field, vortices are not parallel to the local field. They are slanted but slanted directions are almost perpendicular to that of the external field. [3]

In order to clarify the origin of such vortex structures, we solve the Giznburg-Landau Equations numerically, using the finite element method.

We consider slightly rotated magnetic field where two vortices may have slightly different angle. We found a strange structure in which vortices form some entangled state and also cutting and reconnection of vortices occur. Increasing the temperature, this structure changes to the structure where vortices are parallel to the local field. We will discuss this structure in detail.