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 meanfield 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.

Many-body effects of Coulomb interaction on Landau levels in graphene

“…where v F ≈ 10 6 m/s is the Fermi velocity, l H = c/|e|B is the magnetic length (hereafter we set ≡ 1). Contrary to the case of a non-relativistic electron gas, the energies of cyclotron transitions between Landau levels in graphene are not protected by Kohn's theorem [27] against interaction induced corrections, as both predicted theoretically [7][8][9][10][11][12][13][14][15] and reported in experimental works [17][18][19][20][21][22][23][24][25][26].…”

“…Most theoretical models of Coulomb many-body effects in graphene [7][8][9][10][11][12][13][14][15]26] take into account three major contributions to the inter-Landau level transition energies: single-particle exchange self-energies of electron and hole, an excitonic shift due to electron-hole Coulomb attraction (also referred to as a vertex correction) and an electron-hole exchange energy. The latter contribution is principal in calculating dispersions of collective magneto-plasmon excitations [3,[7][8][9][29][30][31][32][33][34], but vanishes for optically excited nearly zero-momentum electron-hole pairs, therefore we will not include it in our calculations.…”

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

“…The conventional approach [25][26][27][28][29][30][31][32][33][34][35][36][37] to treat the interaction-induced renormalization of Landau level energies is based on the Hartree-Fock approximation, where the renormalized energy…”

“…where F nn ′ (q) are the Landau level form factors (see the details in [5,[38][39][40][41][42]). Note that the statically screened interaction was also used in [34][35][36] to analyze possible spontaneous symmetry breaking and gap generation scenarios. Generally, full dynamical treatment of the screening can provide more accurate results than in the static approximation, although the computational procedure in this case becomes very demanding.…”

Many-body filling factor dependent renormalization of Fermi velocity in graphene in strong magnetic field

“…While the former one, v F , should be close to 0.85 × 10 6 m/s, as indicated by fitting theoretical calculations to various experimental data on graphene (see, e.g., [29][30][31][32]), the latter one, v * F , range from 10 6 m/s to 1.4 × 10 6 m/s depending on carrier density, magnetic field and substrate material [9][10][11][12][13][14][15][16]. The existing theory describes renormalization of Fermi velocity in magnetic field with reasonable accuracy in the Hartree-Fock [15,[22][23][24] and static random-phase [26,29,33] approximations.…”