Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability

TL;DR

This paper demonstrates the creation of flat Majorana bands in 2D lattices with inhomogeneous magnetic fields, analyzing their topological properties and stability under various perturbations.

Contribution

It introduces specific configurations of inhomogeneous magnetic fields that produce stable flat Majorana bands in 2D lattices, expanding understanding of topological Majorana states.

Findings

Majorana bands can be formed in 2D lattices with inhomogeneous magnetic fields.

These Majorana bands are stable under various perturbations.

The study provides phase diagrams indicating conditions for weak topology.

Abstract

In this paper we show that for a range of configurations of inhomogeneous magnetic fields it is possible to create flat bands of Majorana states localized on the edges of 2-d lattices. Majorana bound states have been predicted to exist in both one dimensional and two dimensional systems with Rashba spin-orbit coupling, magnetic fields, and placed in proximity to a superconductor. For the proposed systems we present the bulk topological phase diagrams, and we study the conditions for weak topology which predicts the formation of bands of Majorana states. The Majorana bands are demonstrated to be relatively stable with respect to a variety of different perturbations on both square and hexagonal lattices.