Impurities and electronic localization in graphene bilayers

We analyze the electronic properties of bilayer graphene with Bernal stacking and a low concentration of adatoms. Assuming that the host bilayer lies on top of a substrate, we consider the case where impurities are adsorbed only on the upper layer. We describe non-magnetic impurities as a single orbital hybridized with carbon's pz states. The effect of impurity doping on the local density of states with and without a gated electric field perpendicular to the layers is analyzed. We look for Anderson localization in the different regimes and estimate the localization length. In the biased system, the field induced gap is partially filled by strongly localized impurity states. Interestingly, the structure, distribution and localization length of these states depend on the field polarization.