On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors

TL;DR

This paper examines the relationship between bulk topological invariants and the presence of Majorana bound states in 2D topological superconductors, revealing that high Chern numbers do not always guarantee Majorana states.

Contribution

It challenges the assumption that the Chern number directly indicates Majorana bound states, using a graphene-based model to demonstrate exceptions.

Findings

High Chern numbers do not necessarily imply Majorana bound states.

The bulk-boundary correspondence can be more complex than previously thought.

The model shows phases with high Chern numbers lacking Majorana states.

Abstract

The bulk-boundary correspondence establishes a connection between the bulk topological index of an insulator or superconductor, and the number of topologically protected edge bands or states. For topological superconductors in two dimensions the first Chern number is related to the number of protected bands within the bulk energy gap, and is therefore assumed to give the number of Majorana band states in the system. Here we show that this is not necessarily the case. As an example we consider a hexagonal-lattice topological superconductor based on a model of graphene with Rashba spin orbit coupling, proximity induced s-wave superconductivity, and a Zeeman magnetic field. We explore the full Chern number phase diagram of this model, extending what is already known about its parity. We then demonstrate that despite the high Chern numbers that can be seen in some phases these do not strictly always contain Majorana bound states.