Majorana-like fermion physics: Emergence of topologically protected vortical states in graphene interacting with an electromagnetic field

Within the framework of a quasi-relativistic model of graphene that admits topologically nontrivial Majorana-like quasiparticle excitations, appearance of such vortex states in the frequency dependencies of the complex dielectric permittivity of the system subjected to an external electromagnetic field has been examined. The vortex graphene states possess topological charges (flavours ) being nonzero Zak phases. Interaction effects of Majorana-like modes have been qualitatively related to the formation of Fano resonances in the optical response. The constructed topological model of graphene may be considered as a toy model of three-flavour mass-neutrino oscillations.