Carrier Transport in Two-Dimensional Graphene Layers

Carrier transport in gated 2D graphene monolayers is considered in the presence of scattering by random charged impurity centers with density $n_i$. Excellent quantitative agreement is obtained (for carrier density $n>{10}^{12}{\mathrm{cm}}^{-2}$) with existing experimental data. The conductivity scales linearly with $n/n_i$ in the theory. We explain the experimentally observed asymmetry between electron and hole conductivities, and the high-density saturation of conductivity for the highest mobility samples. We argue that the experimentally observed saturation of conductivity at low density arises from the charged impurity induced inhomogeneity in the graphene carrier density which becomes severe for $n\lesssim n_i\sim {10}^{12}{\mathrm{cm}}^{-2}$.

Figure 1

Graphene conductivity limited by Coulomb scattering calculated using different approximation schemes with dielectric constant $\kappa =2.5$. The complete screening approximation (Ref. 8) does not depend on dielectric constant and overestimates the conductivity, whereas using the unscreened Coulomb interaction would have conductivity less than $4e^2/h$ for the entire range of gate voltages used in the experiment. RPA is the main approximation that we use in this Letter.

Figure 2

The effect of remote scatters. Here $d$ is the distance between the 2D graphene layer and the 2D impurity layer.

Figure 3

Graphene conductivity calculated using a combination of short and long range scatterers. One finds that sublinear conductivity at high density is likely to be seen in samples with a small Coulomb impurity density and high mobility.

Figure 4

Figure shows comparison of theory (Eq. (1)) with experimental data of Ref. 2 (up and down triangles, $n_i=2.3\times {10}^{12}{\mathrm{cm}}^{-2}$), Ref. 5 (circles and squares, $n_i=3.4\times {10}^{12}{\mathrm{cm}}^{-2}$), and Ref. 4 (diamonds and crosses, $n_i=0.43\times {10}^{12}{\mathrm{cm}}^{-2}$) for electrons and holes, respectively. Solid lines (from bottom to top) show the minimum conductivity of $4e^2/h$, theory for $d=0$, and $d=2\AA$. The inset shows Ref. 2 data on a linear scale assuming that the impurity shifts by $d=2\AA$ for positive voltage bias.