Asymmetry gap in the electronic band structure of bilayer graphene

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