Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization

TL;DR

This paper introduces a generalized Majorana polarization measure that universally characterizes Majorana states in 1D and 2D systems, enabling precise topological phase identification.

Contribution

It develops a universal pseudo-spin quantity extending Majorana polarization to diverse models, providing a necessary and sufficient criterion for Majorana state identification.

Findings

The generalized MP accurately identifies Majorana states in 1D and 2D systems.

The MP criterion effectively maps the topological phase diagram.

Application to Kitaev systems confirms the measure's robustness.

Abstract

We study the solutions of generic Hamiltonians exhibiting particle-hole mixing. We show that there exists a universal quantity that can describe locally the Majorana nature of a given state. This pseudo-spin like two-component quantity is in fact a generalization of the Majorana polarization (MP) measure introduced in Sticlet et al. 2012, which was applicable only for some models with specific spin and symmetry properties. We apply this to an open two-dimensional Kitaev system, as well as to a one-dimensional topological wire. We show that the MP characterization is a necessary and sufficient criterion to test whether a state is a Majorana or not, and use it to numerically determine the topological phase diagram.