Impurity-induced bound states in superconductors with topological order

The study of classical spins in topological insulators (Liu and Ma 2009 Phys. Rev. B 80 115216) is generalized to topological superconductors. Based on the characteristic features of the so-called F-function, the Bogoliubov-de Gennes Hamiltonian for superconductors is classified to positive, negative, and zero 'gap' categories for topologically trivial and nontrivial phases of a topological superconductor as well as a BCS superconductor, respectively. It is found that the F-function determines directly the presence or absence of localized excited states, induced by bulk classical spins and nonmagnetic impurities, in the superconducting gap and their persistence with respect to impurity strength. Our results provide an alternative way to identify topologically insulating and superconducting phases in experiments without resorting to the surface properties.