We study, within the tight-binding approximation, the electronic properties of a graphenebilayer in the presence of an external electric field applied perpendicular to the system—abiased bilayer. The effect of the perpendicular electric field is included through aparallel plate capacitor model, with screening correction at the Hartree level.The full tight-binding description is compared with its four-band and two-bandcontinuum approximations, and the four-band model is shown to always be a suitableapproximation for the conditions realized in experiments. The model is applied toreal biased bilayer devices, made out of either SiC or exfoliated graphene, andgood agreement with experimental results is found, indicating that the model iscapturing the key ingredients, and that a finite gap is effectively being controlledexternally. Analysis of experimental results regarding the electrical noise and cyclotronresonance further suggests that the model can be seen as a good starting point forunderstanding the electronic properties of graphene bilayer. Also, we study the effect ofelectron–hole asymmetry terms, such as the second-nearest-neighbour hopping energiest′ (in-plane) andγ4 (inter-layer), andthe on-site energy Δ.
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