Persistent ferromagnetism and topological phase transition at the interface of a superconductor and a topological insulator

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At the interface of an s-wave superconductor and a three-dimensional topological insulator, Ma- jorana zero modes and Majorana helical states have been proposed to exist respectively around magnetic vortices and geometrical edges. Here we first show that a single magnetic impurity at such an interface splits each resonance state of a given spin channel outside the superconducting gap, and also induces two new symmetric impurity states inside the gap. Next we find that an increase in the superconducting gap suppresses both the oscillation magnitude and period of the RKKY inter- action between two interface magnetic impurities mediated by BCS quasi-particles. Within a mean field approximation, the ferromagnetic Curie temperature is found to be essentially independent of the superconducting gap, an intriguing phenomenon due to a compensation effect between the short-range ferromagnetic and long-range anti-ferromagnetic interactions. The existence of persis- tent ferromagnetism at the interface allows realization of a novel topological phase transition from a non-chiral to a chiral superconducting state at sufficiently low temperatures, providing a new platform for topological quantum computation.