Abstract Body

Vortices appear in a type-II superconductor under an external field. Controlling vortices is important for applications of superconductors, e.g high-field magnets or quantum computers. 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 [1-3]. 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. [4]

In order to clarify the origin of such vortex structures, we solve the Giznburg-Landau Equations numerically, using the finite element method. As the origins of strange vortex structures, we consider two points, which are effect of the boundary and vortex-vortex interaction. In order to clarify the boundary affect the vortex structures, we obtained the vortex structures under the slanted uniform magnetic field [5]. In this case vortices are almost parallel to the magnetic field. The effect of the boundary is only that vortices are pushed toward inside of the superconductor due the Meisner current around boundary. So, we focus on the vortex-vortex interaction between non-parallel vortices.

We consider slightly rotated magnetic field where two vortices may have slightly different angle. In fig. 1, we show the example of structure of vortices at low temperature. In this structure, vortices show 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. So, the vortex structure shows phase transition. Moreover, the magnetic vector potential changes with increasing the temperature. These two types of vector potential are connected by a singular gauge transformation [6]. So, it can be said that the gauge field (vector potential) shows phase transition. We will discuss this point in detail.

References

[1] Fukui S, Kato M, Togawa Y 2016 Supercond. Sci. Technol. 29 125008
[2] Fukui S, Kato M, Togawa Y and Sato O 2018 J. Phys. Soc. Jpn 87 084701
[3] Fukui S, Kato M, Togawa Y and Sato O 2018 J. Phys.: Conf. Ser. 1054 012027.
[4] Fukui S, Kato M, Togawa Y and Sato O 2021 Physica C 589 1353918
[5] Yokoji H and Kato M 2021 J. Phys.: Conf. Ser. 1975 012001
[6] Kato M 2023 J. Phys.: Conf. Ser. 2545 012007

Acknowledgment

This work was partly supported by a JSPS KAKENHI (Grant Number 20K03867).