  We theoretically study the transport properties of both monolayer and bilayer
graphene in the presence of electron-hole puddles induced by charged impurities
which are invariably present in the graphene environment. We calculate the
graphene conductivity by taking into account the non-mean-field two-component
nature of transport in the highly inhomogeneous density and potential
landscape, where activated transport across the potential fluctuations in the
puddle regimes coexists with regular metallic diffusive transport. The
existence of puddles allows the local activation at low carrier densities,
giving rise to an insulating temperature dependence in the conductivity of both
monolayer and bilayer graphene systems. We also critically study the
qualitative similarity and the quantitative difference between monolayer and
bilayer graphene transport in the presence of puddles. Our theoretical
calculation explains the non-monotonic feature of the temperature dependent
transport, which is experimentally generically observed in low mobility
graphene samples. We establish the 2-component nature (i.e., both activated and
diffusive) of graphene transport arising from the existence of potential
fluctuation induced inhomogeneous density puddles. The temperature dependence
of the graphene conductivity arises from many competing mechanisms, even
without considering any phonon effects, such as thermal excitation of carriers
from the valence band to the conduction band, temperature dependent screening,
thermal activation across the potential fluctuations associated with the
electron-hole puddles induced by the random charged impurities in the
environment, leading to very complex temperature dependence which depends both
on the carrier density and the temperature range of interest.
