  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.
