Topological properties of superconducting junctions

TL;DR

This paper investigates the topological properties of superconducting junctions, revealing that finite junctions are topologically trivial and identifying a different kind of transition related to resonant poles, challenging previous assumptions.

Contribution

It clarifies the topological nature of finite superconducting junctions and introduces a new perspective on resonant pole configurations, resolving prior contradictions.

Findings

Finite junctions are always topologically trivial.

Resonant poles undergo a transition affecting the s-matrix configuration.

No traditional topological transition occurs in finite junctions.

Abstract

Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically trivial. We resolve an apparent contradiction with the previous results by taking into account the low-energy resonant poles of s-matrix. Thus no common topological transition occur in a finite junction. We reveal a transition of a different kind that concerns the configuration of the resonant poles.