  Motivated by a recent experiment reporting on the possible application of
graphene as sensors, we calculate transport properties of 2D graphene
monolayers in the presence of adsorbed molecules. We find that the adsorbed
molecules, acting as compensators that partially neutralize the random charged
impurity centers in the substrate, enhance the graphene mobility without much
change in the carrier density. We predict that subsequent field-effect
measurements should preserve this higher mobility for both electrons and holes,
but with a voltage induced electron-hole asymmetry that depends on whether the
adsorbed molecule was an electron or hole donor in the compensation process. We
also calculate the low density magnetoresistance and find good quantitative
agreement with experimental results.
