Belarusian State University, Belarus

Within the quasi-relativictic graphene model for which it has been shown the existence of topologically nontrivial Majorana-like quasiparticles we investigate the reveal of this non-triviality in frequency dependence of the complex conductivity of the system in an external electromagnetic field. Vortex graphene states are demonstrated to possess topological charges (flavours ) being nonzero Zak phases. Interaction effects of Majorana-like modes are qualitatively associated with a formation of Fano resonances in optical response of the system. Some known experimental results are in a good agreement with predictions of the proposed model.