Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

Abstract

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.

22 pages, 5 figures; Final version published in the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matter

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• Classification of massive and gapless phases in bilayer graphene
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Chiral asymmetry in QED matter in a magnetic field
• The influence of a weak magnetic field in the Renormalization-Group functions of (2+1)-dimensional Dirac systems
• Lattice Field Theory Study of Magnetic Catalysis in Graphene
• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Many-body effects of Coulomb interaction on Landau levels in graphene
• D3-D7 Holographic dual of a perturbed 3D CFT
• The fermion self-energy and damping rate in a hot magnetized plasma
• Chiral asymmetry in cold QED plasma in a strong magnetic field
• Gap generation and phase diagram in strained graphene in a magnetic field
• Electrified magnetic catalysis in three-dimensional topological insulators
• Many-body filling-factor dependent renormalization of Fermi velocity in graphene in strong magnetic field
• Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene
• Integer Quantum Hall Effect of Interacting Electrons in Graphene
• Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction
• Exciton-driven quantum phase transitions in holography
• Classical features, Anderson-Higgs mechanism, and unitarity in Lee-Wick pseudo-electrodynamics
• Projected Proca Field Theory: a One-Loop Study
• Effective potential of scalar Lee-Wick pseudo-electrodynamics
• Remarks on classical pseudo-electrodynamics
• The Lee-Wick-Chern-Simons pseudo-quantum electrodynamics