Skyrmion formation due to unconventional magnetic modes in anisotropic multiband superconductors

Multiband superconductors have a sufficient number of degrees of freedom to allow topological excitations characterized by skyrmionic topological invariants. In the most common, clean s-wave multiband systems, the interband Josephson and magnetic couplings favor composite vortex solutions, without a skyrmionic topological charge. It was discussed recently that certain kinds of anisotropies lead to hybridization of the interband phase difference (Leggett) mode with magnetic modes, dramatically changing the hydromagnetostatics of the system. Here we report this effect for a range of parameters that substantially alter the nature of the topological excitations, leading to solutions characterized by a nontrivial skyrmionic topological charge. The solutions have a form of a coreless texture formed of spatially separated but bound excitations in each band, namely fractional vortices, each carrying a fraction of the flux quantum. We demonstrate that in this regime there is a rich spectrum of skyrmion solutions, with various topological charges, that are robust with respect to changes of parameters of the system and present for a wide range of anisotropies.