Topology protection-unprotection transition: an example from multi-terminal superconducting nanostructures

TL;DR

This paper theoretically investigates how topological protection in superconducting nanostructures can transition between protected and unprotected states depending on design parameters, using a Landau theory framework.

Contribution

It introduces a general theoretical model describing protection-unprotection transitions in topological states of superconducting nanostructures.

Findings

Protection-unprotection transition depends on structure design parameters.

A Landau theory approach models the transition.

Potential for similar transitions in other topological systems.

Abstract

We show theoretically that in the superconducting nanostructures the gapped states of different topology are not always protected by separating gapped states. Depending on the structure design parameters, they can be either protected or not, with a protection-unprotection transition separating these two distinct situations. We build up a general theoretical description of the transition vicinity in the spirit of Landau theory. We speculate that similar protection-unprotection transitions may also occur for other realizations of topological protection in condensed matter systems.