Abstract.
We describe the quantum Hall effect (QHE) and far infra-red (FIR) absorption properties of bilayer graphene in a strong magnetic field and contrast them with the weak field regime. This includes a derivation of the effective low energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: The form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model ground states of the bilayer quantum Hall effect system based on the different absorption characteristics of right-handed and left-handed polarisation of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture.
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The true value of the gap between the conduction and valence band, occuring at p ≠0, is \(\tilde{{\rm \Delta}} = |{\rm \Delta} |\gamma_1 / (\gamma_1^2 + {\rm \Delta}^2)^{1/2} \). For huge asymmetry |Δ | ≫γ1, the gap saturates at \(\tilde{{\rm \Delta}} \approx \gamma_1\) although for modest asymmetry |Δ | ≪γ1, as considered throughout this paper, we have \(\tilde{{\rm \Delta}} \approx |{\rm \Delta} |\)
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Abergel, D., McCann, E. & Fal'ko, V. QHE and far infra-red properties of bilayer graphene in a strong magnetic field. Eur. Phys. J. Spec. Top. 148, 105–115 (2007). https://doi.org/10.1140/epjst/e2007-00230-8
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DOI: https://doi.org/10.1140/epjst/e2007-00230-8