Majorana Fermions in Honeycomb Lattices

TL;DR

This paper investigates the emergence of Majorana fermions in honeycomb lattice structures under specific conditions, establishing a mapping to 1D chains and identifying key factors like band inversion.

Contribution

It introduces an exact mapping between honeycomb nanoribbons and 1D chains, predicting Majorana fermions based on band structure analysis.

Findings

Majorana fermions can form at edges of honeycomb nanoribbons.

Existence of Majoranas is linked to band inversion in the bulk.

Similar Majorana formation occurs in isotropic honeycomb lattices.

Abstract

We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a one-dimensional chain, for which the existence of Majorana fermions has been extensively discussed. Consequently we can predict the conditions for the emergence of Majorana fermions at the edges of such ribbon, and relate the existence of Majoranas to a band inversion in the bulk band structure. Moreover we find that similar situations arise in isotropic lattices and we give some examples which show the formation of Majorana fermions in these structures.