From Andreev bound states to Majorana fermions in topological wires on superconducting substrates: A story of mutation

We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenological study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a nontrivial effect of a quasiparticle broadening term which can take the wire from a topological into a nontopological phase in certain ranges of parameters. Our results also have direct consequences for a nanowire coupled to an inhomogeneous superconductor.