Boundary spin polarization as robust signature of topological phase transition in Majorana nanowires

TL;DR

This paper demonstrates that boundary spin polarization can serve as a robust, disorder-resistant indicator of topological phase transitions in Majorana nanowires, independent of Majorana zero modes.

Contribution

It introduces boundary spin as a new, reliable signature of topological phase transitions that does not depend on Majorana zero-energy modes.

Findings

Boundary spin peaks at the topological transition point.

Signatures are observable at boundaries between topological and trivial regions.

Boundary spin signatures are stable against disorder.

Abstract

We show that the boundary charge and spin can be used as alternative signatures of the topological phase transition in topological models such as semiconducting nanowires with strong Rashba spin-orbit interaction in the presence of a magnetic field and in proximity to an $s$-wave superconductor. We identify signatures of the topological phase transition that do not rely on the presence of Majorana zero-energy modes and, thus, can serve as independent probes of topological properties. The boundary spin component along the magnetic field, obtained by summing contributions from all states below the Fermi level, has a pronounced peak at the topological phase transition point. Generally, such signatures can be observed at boundaries between topological and trivial sections in nanowires and are stable against disorder.