Does the existence of Majorana zero mode in superconducting vortices imply the superconductivity is topologically non-trivial?

TL;DR

The paper demonstrates that Majorana zero modes in vortex cores do not necessarily indicate topologically non-trivial superconductivity, challenging common assumptions in the field.

Contribution

It clarifies the relationship between Majorana modes and topological superconductivity, showing their presence is neither sufficient nor necessary for topological classification.

Findings

Majorana zero modes are not definitive indicators of topological superconductivity.

Presence of Majorana modes can occur in trivial superconductors.

Implications for interpreting experiments on topological insulator surfaces.

Abstract

We show that the presence of Majorana zero modes (2D), and chiral-dispersing Majorana modes (3D), in the vortex cores of superconductors are neither sufficient nor necessary conditions for one to conclude the superconductivity is topologically non-trivial. We discuss the relevance of this result to the proximity-induced superconductivity, in the presence of magnetic field, on the surface of topological insulators.