Novel vortex structures in a three-dimensional superconductor under a helical magnetic field from a chiral helimagnet

We have investigated vortex structures in three-dimensional superconductors under a helical magnetic field from a chiral helimagnet numerically. In order to obtain vortex structures, we solve the three-dimensional Ginzburg-Landau equations with the finite element method. A spatial distribution of the helical magnetic field corresponds to a spatial distribution of magnetic moments in the chiral helimagnet. Then, the magnetic field is parallel to a yz-plane and helical rotation along a helical axis (x-axis). An arrangement of the vortex is different from the spatial oscillation in each component of the magnetic field. In this calculation, two-types of vortex structures appear. One is an appearance of vortices perpendicular to a xy-plane and a zx-plane of the superconductor. The other arrangement is that vortices are tilted toward the helical axis, although the magnetic field along the helical axis is zero. The arrangement of the tilted vortex depends on a direction of a rotation in the helical magnetic field.