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We consider a superconductor proximity coupled to a two-dimensionalferromagnetic film with a skyrmion texture. Using the T-matrix calculations andnumerical modeling we calculate the spin-polarized local density of states inthe superconductor in the vicinity of the skyrmion. We predict the skyrmionbound states (SBS) that are induced in the superconductor, similar to thewell-known Yu-Shiba-Rusinov (YSR) states. The SBS wavefunctions have spatialpower law decay. Presence of the SBS suggests the mechanism by whichsuperconductivity could facilitate an effective long-range interaction betweenskyrmions when their SBS wavefunctions overlap.

Skyrmion-induced bound states in a superconductor