Generalized Landau level representation: Effect of static screening in the quantum Hall effect in graphene

Abstract

By making use of the generalized Landau level representation (GLLR) for the quasiparticle propagator, we study the effect of screening on the properties of the quantum Hall states with integer filling factors in graphene. The analysis is performed in the low-energy Dirac model in the mean-field approximation, in which the long-range Coulomb interaction is modified by the one-loop static screening effects in the presence of a background magnetic field. By utilizing a rather general ansatz for the propagator, in which all dynamical parameters are running functions of the Landau level index $n$, we derive a self-consistent set of the Schwinger-Dyson (gap) equations and solve them numerically. The explicit solutions demonstrate that static screening leads to a substantial suppression of the gap parameters in the quantum Hall states with a broken $U(4)$ flavor symmetry. The temperature dependence of the energy gaps is also studied. The corresponding results mimic well the temperature dependence of the activation energies measured in experiment. It is also argued that, in principle, the Landau level running of the quasiparticle dynamical parameters could be measured via optical studies of the integer quantum Hall states.

18 pages, 6 multi-panel figures; v2: published version with extended discussions and several new references

References in corpus (31)

• The electronic properties of graphene
• Unconventional Integer Quantum Hall effect in graphene
• Quantum Hall Ferromagnetism in Graphene
• Landau Level Splitting in Graphene in High Magnetic Fields
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Landau level spectroscopy of ultrathin graphite layers
• Infrared spectroscopy of Landau levels in graphene
• Interactions and phase transitions on graphene's honeycomb lattice
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Theory of interacting electrons on the honeycomb lattice
• The zero-energy state in graphene in a high magnetic field
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Dirac electronic states in graphene systems: Optical spectroscopy studies
• Theory of integer quantum Hall effect in graphene
• Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field
• Excitations from Filled Landau Levels in Graphene
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Charge and Spin Transport at the Quantum Hall Edge of Graphene
• Metal to insulator transition on the N = 0 Landau level in graphene
• Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects
• Intrinsic Zeeman Effect in Graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Dynamical polarization of monolayer graphene in a magnetic field
• Supersymmetry and Correlated Electrons in Graphene Quantum Hall Effect
• Toward theory of quantum Hall effect in graphene
• Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field

Cited by in corpus (5)

• Many-particle effects in the cyclotron resonance of encapsulated monolayer graphene
• Many-body effects of Coulomb interaction on Landau levels in graphene
• The fermion self-energy and damping rate in a hot magnetized plasma
• Many-body filling-factor dependent renormalization of Fermi velocity in graphene in strong magnetic field
• Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction