  We study the effect of long-range disorder created by charge impurities on
the carrier density distribution of graphene-based heterostructures. We
consider heterostructures formed by two graphenic sheets (either single layer
graphene, SLG, or bilayer graphene, BLG) separated by a dielectric film. We
present results for symmetric heterostructures, SLG-SLG and BLG-BLG, and hybrid
ones, BLG-SLG. As for isolated layers, we find that the presence of charged
impurities induces strong carrier density inhomogeneities, especially at low
dopings where the density landscape breaks up in electron-hole puddles. We
provide quantitative results for the strength of the carrier density
inhomogeneities and for the screened disorder potential for a large range of
experimentally relevant conditions. For heterostructures in which BLG is
present we also present results for the band-gap induced by the perpendicular
electric field generated self-consistently by the disorder potential and by the
distribution of charges in the heterostructure. For SLG-SLG heterostructures we
discuss the relevance of our results for the understanding of the recently
observed metal-insulator transition in each of the graphene layers forming the
heterostructure. Moreover, we calculate the correlation between the density
profiles in the two graphenic layers and show that for standard experimental
conditions the two profiles are well correlated.
