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We numerically study the vortex-vortex interaction in multi-componenthomogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskiitheory. We provide strong evidences that pairwise vortex interaction capturesthe underlying mechanisms which determine the geometric configuration of thevortices, such as different lattices in many-vortex states, as well as thebound vortex states with two (dimer) or three (trimer) vortices. Specifically,we discuss and apply our theoretical approach to investigate intra- andinter-component vortex-vortex interactions in two- and three-componentBose-Einstein condensates, thereby shedding light on the formation of theexotic vortex configurations. These results correlate with current experimentalefforts in multi-component Bose-Einstein condensates, and the understanding ofthe role of vortex interactions in multiband superconductors.

Bound vortex states and exotic lattices in multi-component Bose-Einstein condensates: The role of vortex-vortex interaction