Two types of topological transitions in finite Majorana wires

TL;DR

This paper explores two distinct topological transitions in finite Majorana wires, linking the conventional infinite-system transition to a pole-based transition observable in scattering matrix analysis, with implications for conductance measurements.

Contribution

It establishes a universal relationship between pole positions and transition parameters, revealing a new type of topological transition in finite Majorana wires.

Findings

Identifies two types of topological transitions in finite Majorana wires.

Derives a universal dependence of pole positions near the transition.

Discusses how pole transitions affect differential conductance.

Abstract

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.