Regular Article

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

¹ Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180 Urca, RJ, Brazil
² Universidade Federal de Viçosa (UFV), Departamento de Física, Campus Universitário, Avenida Peter Henry Rolfs s/n, 36570-900 Viçosa, MG, Brazil
³ Ibitipoca Institute of Physics (IbitiPhys), 36140-000 Conceição do Ibitipoca, MG, Brazil

^a e-mail: oswaldo.delcima@ufv.br

Received: 10 December 2019
Received in final form: 18 July 2020
Accepted: 24 August 2020
Published online: 5 October 2020

Abstract

The parity-preserving U(1) × 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 K and K′ points in the Brillouin zone might exhibit attractive interaction, while two electron–polarons (p-wave state) lying both either in K or in K′ points experience repulsive interaction.