  Motivated by recent experiments on suspended graphene showing carrier
mobilities as high as 200,000 cm^2/Vs, we theoretically calculate transport
properties assuming Coulomb impurities as the dominant scattering mechanism. We
argue that the substrate-free experiments done in the diffusive regime are
consistent with our theory and verify many of our earlier predictions including
(i) removal of the substrate will increase mobility since most of the charged
impurities are in the substrate, (ii) the minimum conductivity is not
universal, but depends on impurity concentration with cleaner samples having a
higher minimum conductivity. We further argue that experiments on suspended
graphene put strong constraints on the two parameters involved in our theory,
namely, the charged impurity concentration n_imp and d, the typical distance of
a charged impurity from the graphene sheet. The recent experiments on suspended
graphene indicate a residual impurity density of 1-2 \times 10^{10} cm^{-2}
which are presumably stuck to the graphene interface, compared to impurity
densities of ~10^{12} cm^{-2} for graphene on SiO_2 substrate. Transport
experiments can therefore be used as a spectroscopic tool to identify the
properties of the remaining impurities in suspended graphene.
