Abstract
The optical conductivity of graphene in quantizing magnetic fields is studied. Both dynamical conductivities, longitudinal and Hall’s, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. The optical transitions obey the selection rule with Δn = 1 for the Landau number n. The light transmission and Faraday rotation in the quantizing magnetic fields are calculated.
Highlights
Comprehensive literature on the graphene family is expressed usually in terms of the Dirac gapless fermions
There are two bands at the K hexagon vertexes of the Brillouin zone without any gap between them, and the electron dispersion can be considered as linear in the wide wave-vector region. This region should be small compared with the size of the graphene Brillouin zone, i.e., less than 10−8 cm−1, providing the small carrier concentration n 1016 cm−1
The “constant” parameter v was found to be no longer constant, but at low carrier concentrations n ∼ 109 cm−2, it exceeds its usual value v = 1.05 ± 0.1 × 108 cm/s by a factor of three. This is a result of electron-electron interactions, which becomes stronger at low carrier concentrations
Summary
Comprehensive literature on the graphene family is expressed usually in terms of the Dirac gapless fermions According to this picture, there are two bands at the K hexagon vertexes of the Brillouin zone without any gap between them, and the electron dispersion can be considered as linear in the wide wave-vector region. The following problem appears: how do Coulomb electron-electron interactions renormalize the linear dispersion, and does graphene become an insulator with a gap?. The trigonal warping described by the effective Hamiltonian with a relatively small parameter γ3 provides an evident effect Another important parameter is the gate-tunable bandgap U in bilayer graphene. In this situation, the quantization problem cannot be solved within a rigorous method.
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