Effects of chiral helimagnets on vortex states in a superconductor

We have investigated vortex states in chiral helimagnet/superconductor bilayer systems under an applied external magnetic field $H_{appl}$, using the Ginzburg–Landau equations. Effect of the chiral helimagnet on the superconductor is taken as a magnetic field $H_{CHM}$, which is perpendicular to the superconductor and oscillates spatially. For $H_{appl}=0$ and weak $H_{CHM}$, there appear pairs of up- and down-vortices. Increasing $H_{appl}$, down-vortices gradually disappear, and the number of up-vortices increases in the large magnetic field region. Then, up-vortices form parallel, triangular, or square structures. (paper)