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

TL;DR

This paper models pristine graphene-like quantum electrodynamics using a massless U(1)×U(1) QED3 framework, analyzing quasiparticle spectra, Landau levels, and electron-polaron interactions, revealing phenomena similar to experimental graphene observations.

Contribution

It introduces a graphene-like QED3 model that captures Landau level degeneracy breaking, zero-energy levels, and detailed electron-polaron scattering potentials, providing new insights into quasiparticle interactions.

Findings

Four-fold Landau level degeneracy breaking observed.

Zero-energy Landau level indicating anomalous quantum Hall effect.

Electron-polaron interactions depend on wave state and Brillouin zone points.

Abstract

The parity-preserving $U(1)\times U(1)$ massless QED$_3$ 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 N\'eel 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 N\'eel 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.