Disorder-induced temperature-dependent transport in graphene: Puddles,   impurities, activation, and diffusion
  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. 
Qiuzi Li, E. H. Hwang, S. Das Sarma
cond-mat.mes-hall