Localization and Conductivity of Graphene with Adsorbates

We compute the conductivity of graphene for two models of resonant and non resonant adsorbates. Away from the Dirac point the conductivity is well given by the semi-classical Drude formula and localization lengths are exponentially large. For some energies, near the Dirac point, the conductivity is well represented by $\sigma \simeq $4e$^{2}$/$\pi $h-$\alpha $Log(Li/Le) as a function of the inelastic scattering length Li and the elastic mean free path Le $<$ Li. This implies a magneto-conductivity that varies also linearly with Log(B) where B is the magnetic field. Our results suggest that the divergence of the localization length which is expected close to the Dirac point affects only a narrow energy region.