Ferromagnetic impurity induced Majorana zero mode in iron-based superconductors

Recent experiments reported the puzzling zero-energy modes associated with ferromagnetic impurities in some iron-based superconductors with topological band structures. Here, we show that a sufficiently strong exchange coupling between a ferromagnetic impurity and a substrate can trigger a quantum phase transition, beyond which the phase of the topological surface superconducting order parameter around the impurity acquires a sign change. In such a case, we prove that besides a pair of impurity induced trivial Yu-Shiba-Rusinov states, a degenerate pair of Majorana modes can be induced at the boundary separating the two sign-change regimes and trapped around the impurity in the topological surface superconducting state. Furthermore, we show that our theory can explain the controversial observations and confusing features of the zero-energy modes from recent experiments in some iron-based superconductors.