Rotational transition, domain formation, dislocations and defects in vortex systems with combined six- and 12-fold anisotropic interactions

We introduce a new model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed six- and 12-fold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through 30 degrees as the ratio of the six- and 12-fold anisotropy amplitudes is varied. The transition causes the VL to split into domains that have rotated clockwise or counter-clockwise, with domain boundaries that are "decorated" by dislocations consisting of five- and seven-fold coordinated vortices. We also find intra-domain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.