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We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction betweenmagnetic impurities on the surface of a three-dimensional topological insulatorwith proximity induced superconductivity. A superconductor placed on the top ofthe topological insulator induces a gap in the surface electron states andgives rise to a long-ranged in-plane antiferromagnetic RKKY interaction. Thisinteraction is frustrated due to strong spin-orbit coupling, decays as $1/r$for $r<\xi$, where $r$ is the distance between two magnetic impurities and$\xi$ the superconducting coherence length, and dominates over theferromagnetic and Dzyaloshinskii-Moriya type interactions for $r>\xi$. We findthe condition for the Yu-Shiba-Rusinov intragap states that are bound to themagnetic impurities.

RKKY Interaction On Surfaces of Topological Insulators With Superconducting Proximity Effect