  We investigate a hybrid heterostructure with magnetic skyrmions (Sk) inside a
chiral ferromagnet interfaced by a thin superconducting film via an insulating
barrier. The barrier prevents the electronic transport between the
superconductor and the chiral magnet, such that the coupling can only occur
through the magnetic fields generated by these materials. We find that Pearl
vortices (PV) are generated spontaneously in the superconductor within the
skyrmion radius, while anti-Pearl vortices (\(\overline{\mathrm{PV}}\))
compensating the magnetic moment of the Pearl vortices are generated outside of
the Sk radius, forming an energetically stable topological hybrid structure.
Finally, we analyze the interplay of skyrmion and vortex lattices and their
mutual feedback on each other. In particular, we argue that the size of the
skyrmions will be greatly affected by the presence of the vortices offering
another prospect of manipulating the skyrmionic size by the proximity to a
superconductor.
