Asymmetry gap in the electronic band structure of bilayer graphene

A tight-binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap Delta between the conduction and valence bands. In particular, a self-consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density n of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap Delta(n). We discuss the influence of a finite asymmetry gap Delta(0) at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect.