  We study the effects of disorder on bilayer graphene using four different
microscopic models and directly compare their results. We compute the
self-energy, density of states, and optical conductivity in the presence of
short-ranged scatterers and screened Coulomb impurities, using both the Born
approximation and self-consistent Born approximation for the self-energy. We
also include a finite interlayer potential asymmetry which generates a gap
between the valence and conduction bands. We find that the qualitative behavior
of the two scattering potentials are similar, but that the choice of
approximation for the self-energy leads to important differences near the band
edge in the gapped case. Finally, we describe how these differences manifest in
the measurement of the band gap in optical and transport experimental
techniques.
