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Vortex chains due to nonpairwise interactions and field-induced phase transitions between states with different broken symmetry in superconductors with competing order parameters

We study superconductors with two order components and phase separation driven by intercomponent density-density interaction, focusing on the phase where only one condensate has non-zero ground-state density and a competing order parameter exists only in vortex cores. We demonstrate there, that multi-body intervortex interactions can be strongly non-pairwise, leading to some unusual vortex patterns in an external field, such as vortex pairs and vortex chains. We demonstrate that, in external magnetic field, such a system undergoes a field-driven phase transition from (broken) $U(1)$ to (broken) $U(1)\times U(1)$ symmetries, when the subdominant order parameter in the vortex cores acquires global coherence. Observation of these characteristic ordering patterns in surface probes may signal the presence of a subdominant condensate in the vortex core.