Two types of topological transitions in finite Majorana wires

Motivated by the recent advances in studying Majorana states in nanowires under conditions of superconducting proximity effect, we address the correspondence between the common topological transition in infinite system and the topological transition of other type that manifests itself in the positions of the poles of the scattering matrices. We establish a universal dependence of the pole positions in the vicinity of the common transition on the parameter controlling the transition, and discuss the manifestations of the pole transitions in the differential conductance.