Yao, NormanGlazman, Leonid IDemler, EugeneLukin, MikhailSau, Jay D.2014-11-242014Yao, N. Y., L. I. Glazman, E. A. Demler, M. D. Lukin, and J. D. Sau. 2014. “Enhanced Antiferromagnetic Exchange Between Magnetic Impurities in a Superconducting Host.” Physical Review Letters 113 (8) (August). doi:10.1103/physrevlett.113.087202.0031-9007http://nrs.harvard.edu/urn-3:HUL.InstRepos:13421142It is generally believed that superconductivity only weakly affects the indirect exchange between magnetic impurities. If the distance r between impurities is smaller than than the superconducting coherence length \((r \lesssim \xi)\) , this exchange is thought to be dominated by RKKY interactions, identical to the those in a normal metallic host. This perception is based on a perturbative treatment of the exchange interaction. Here, we provide a non-perturbative analysis and demonstrate that the presence of Yu-Shiba-Rusinov bound states induces a strong \(1/r^2\) anti-ferromagnetic interaction that can dominate over conventional RKKY even at distances significantly smaller than the coherence length \((r\ll \xi )\). Experimental signatures, implications and applications are discussed.en-USJournal Article2014-11-2410.1103/PhysRevLett.113.087202