Formation of Majorana fermions in finite-size graphene strips

TL;DR

This paper explores how Majorana fermions can form in finite graphene strips with specific boundary conditions, magnetic fields, and superconducting proximity, highlighting the influence of edge type and size on their emergence.

Contribution

It demonstrates that finite-size graphene strips can host Majorana states at low doping levels near Dirac points, depending on edge type and width, under magnetic and superconducting conditions.

Findings

Majorana states can form at small doping near Dirac points in finite graphene strips.

Edge type (armchair vs. zigzag) affects the formation of Majorana states.

Finite size enables Majorana states at different doping levels compared to infinite ribbons.

Abstract

We investigate the formation of Majorana fermions in finite-size graphene strips with open boundary conditions in both directions, in the presence of an in-plane magnetic field and in the proximity of a superconducting substrate. We show that for long enough strips the Majorana states can form in the presence of a Rashba-like spin-orbit coupling, as well as in the presence of an inhomogeneous magnetic field. We find that, unlike infinite graphene ribbons in which Majorana states arise solely close to the bottom of the band and the Van Hove singularities, for finite-size systems this can happen also at much smaller doping values, close to the Dirac points, and depends strongly on the type of the short edges of the systems (e.g. armchair vs. zigzag), as well as on the width of the ribbons.