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 $\mathrm{\Delta }$ 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 $\mathrm{\Delta }(n)$. We discuss the influence of a finite asymmetry gap $\mathrm{\Delta }(0)$ at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect.