Masses and Majorana fermions in graphene

TL;DR

This paper reviews the possible gap-opening instabilities in graphene's Dirac Hamiltonian and demonstrates the potential to realize an odd number of Majorana fermions attached to vortices under specific conditions.

Contribution

It classifies all 36 relativistic masses in graphene and shows how to realize Majorana fermions through specific mass hierarchies.

Findings

Identified 36 possible gap-opening masses in graphene.

Showed conditions for realizing odd numbers of Majorana fermions.

Proposed a hierarchy of mass scales for Majorana fermion realization.

Abstract

We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.