The effect of pinning on vortex states with attractive and repulsive interactions

Abstract: Recently there has been renewed interest in understanding vortex patterns in superconductors and Bose–Einstein condensates, where the repulsive vortex–vortex interactions have an additional intermediate or long range attractive component. These states can arise in low-κ materials and may occur in multi-band superconductors. A combination of repulsive and attractive pairwise interactions can also occur in certain types of Bose–Einstein condensates and in magnetic superconductors. We show that when the pairwise interaction includes a long range attractive term, the ground state consists of a single vortex cluster. In the presence of pinning there is a well defined transition to a fragmented state as a function of pinning strength and density. We also demonstrate that in systems with intermediate range attraction and long range repulsion, ordered stripe and bubble phases occur. [Copyright &y& Elsevier]