Two-Dimensional Braiding of Two-Dimensional Majorana Fermions : Manifestation in Band Structure of Graphene

Abstract

We construct a gauge theory of two-dimensional topological semimetals with exotic nonabelian Majorana-like gapless fermion excitations, in which Dirac crossings are protected by the existence of the confinement for Majorana states. We demonstrate the existence of zero-energy Majorana modes in Dirac points of graphene Brillouin zone and chiral braiding Majorana-like massless modes outside the neighborhood of the Dirac points. The braiding of Majorana-like states turns out to be due to relativistic electron–hole exchange interactions. The deconfined Majorana fermions reveal themselves through a set of gapped sequence of Fermi arcs. The relativistic exchange is able, through the spin-orbital coupling, to change the symmetry of the Dirac band to octagonal one and, accordingly, hexagonal symmetry of the electron density distribution changes to square one.