Many-body corrections to cyclotron resonance in monolayer and bilayer graphene

Abstract

Cyclotron resonance in graphene is studied with focus on many-body corrections to the resonance energies, which evade Kohn's theorem. The genuine many-body corrections turn out to derive from vacuum polarization, specific to graphene, which diverges at short wavelengths. Special emphasis is placed on the need for renormalization, which allows one to determine many-body corrections uniquely from one resonance to another. For bilayer graphene, in particular, both intralayer and interlayer coupling strengths undergo infinite renormalization; as a result, the renormalized velocity and interlayer coupling strength run with the magnetic field. A comparison of theory with the experimental data is made for both monolayer and bilayer graphene.

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

“…17,60,61 At even integers in the central Landau band (ν = ±2, 0) orbital degeneracy does not play a similar role, and the intra-level excitations are still magnetoexcitons. 35,62 For inter-LL excitations, the many-body corrections to cyclotron resonance has been calculated by renormalization 55 including the possi-ble particle-hole symmetry-breaking terms but using the unscreened Coulomb interaction, with partial agreement with experiments. 10 To complement these studies, here we address the issue of the inter-Landau level excitations of bilayer graphene in the quantum Hall regime.…”

“…55 The wave-vector dependence of the excitations have not been observed so far. Theoretically, the intra-Landau level excitations in bilayer graphene are well understood.…”

“…Sometimes the magnetoexciton spectra are obtained using a screened model interaction instead of the bare Coulomb, not letting LL transitions mix. 55,69 We believe such an approach is suitable in the q = 0 limit, where an additional quantum number l z also restricts LL mixing, and for intra-LL modes. At finite wave vector the mean-field theory with LL mixing removes spurious level crossings in the excitation spectra and provides insight into the orbital structure of the excitations.…”

“…68 For monolayer graphene, a proper renormalization procedure is required. 50,55 The shift ∆(N, N ′ ) is analogous to the Lamb shift in quantum electrodynamics. 68 The next term is the direct dynamical interaction between the electron and the hole:…”

“…52 Many-body corrections to cyclotron resonance due to the interaction with the Dirac sea were calculated by Shizuya. 55 Infrared absorption data by Jiang et al 56 and Henriksen et al 57 indicate a contribution from many-body effects to the interLandau level transitions in these states.…”