Identifying trivial and Majorana zero-energy modes using the Majorana polarization

TL;DR

This paper demonstrates that Majorana polarization can effectively distinguish Majorana zero modes from trivial zero-energy states in superconductor-semiconductor hybrids, providing a real-space topological indicator even amidst disorder.

Contribution

It introduces the use of Majorana polarization as a tool to identify topological phases and Majorana modes in complex experimental scenarios with trivial states.

Findings

Majorana polarization characterizes topological phase transitions.

It distinguishes Majorana from trivial zero-energy states.

Effective in normal-superconductor and Josephson junctions.

Abstract

In this work we consider superconductor-semiconductor hybrids containing both trivial and Majorana zero modes and explore their signatures in the Majorana polarization. In particular, we consider trivial zero energy states due to confinement and disorder, which seem to be very likely experimental scenarios. We show that the Majorana polarization is able to characterize the topological phase transition as well as the emergence of Majorana zero modes even when trivial zero-energy states proliferate. Notably, the Majorana polarization inherits direct information about spatial correlations which are then the key for distinguishing Majorana and trivial zero-modes. We demonstrate the utility of the Majorana polarization in normal-superconductor junctions and superconductor-normal-superconductor Josephson junctions. Our results support the interpretation of the Majorana polarization as a real space topological indicator.