  We discuss the effect of disorder on the band gap measured in bilayer
graphene in optical and transport experiments. By calculating the optical
conductivity and density of states using a microscopic model in the presence of
disorder, we demonstrate that the gap associated with transport experiments is
smaller than that associated with optical experiments. Intrinsic bilayer
graphene has an optical conductivity in which the energy of the peaks
associated with the interband transition are very robust against disorder and
thus provide an estimate of the band gap. In contrast, extraction of the band
gap from the optical conductivity of extrinsic bilayer graphene is almost
impossible for significant levels of disorder due to the ambiguity of the
transition peaks. The density of states contains an upper bound on the gap
measured in transport experiments, and disorder has the effect of reducing this
gap which explains why these experiments have so far been unable to replicate
the large band gaps seen in optical measurements.
