On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics

The parity-preserving U(1)times U(1) massless QED₃ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole-polaron, photon and Néel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of anomalous quantum Hall effect. The electron-polaron--electron-polaron scattering potentials in s- and p-wave states mediated by photon and Néel quasiparticles are computed and analyzed. Finally, the model foresees that two electron-polarons (s-wave state) belonging to inequivalent mathbf{K} and mathbf{K^prime} points in the Brillouin zone might exhibit attractive interaction, while two electron-polarons (p-wave state) lying both either in mathbf{K} or in mathbf{K^prime} points experience repulsive interaction.