Figure 1

(Color online) The conductivity $\left(\sigma \right)$ versus gate voltage $\left(V_{\text{g}}\right)$ curves for different potassium concentrations for BLG (a) and SLG (b). For BLG, $\sigma \left(V_{\text{g}}\right)$ is measured at a temperature of 10 K in UHV. Data in (b) are from Ref. 14.Reuse & Permissions

Figure 2

(Color online) (a) Inverse of electron mobility $1/\mu$ versus potassium concentration $n_{\text{K}}$. Line are linear fits to all data points used to extract the slope $1/C$. $\mu$ is the maximum field-effect mobility for SLG (data from Ref. 14) and is shown at two different carrier densities for BLG. (b) The inverse slope $C$ from (a) versus effective gate voltage (solid black squares). Also shown is a second set of data from a different sample measured in a two-probe configuration (solid black circles). Solid lines show the theoretical predictions for $C$ within the Thomas-Fermi approximation for a parabolic dispersion relation assuming complete screening (black line) and finite TF screening wave vector with impurity graphene distance $d=0$ (red/gray with an open circle) and $d=0.43\text{nm}$ (purple/dark gray with an open upward-pointing triangle). The green/gray with an open downward-pointing triangle line shows the theoretical results for a hyberbolic dispersion relation with finite TF screening wavevector and $d=0.43\text{nm}$. The SLG value is also shown (blue dashed line) for comparison (Ref. 14).Reuse & Permissions

Figure 3

(Color online) Minimum conductivity ${\sigma }_{\text{min}}$ and residual carrier density $n^{\ast }$ of bilayer graphene as a function of potassium concentration $n_{\text{K}}$. The blue (dashed) and black (solid) lines show fits to $n^{\ast }={\left[\left(n_{\text{imp},0}+n_{\text{K}}\right)/{\xi }^2\right]}^{1/2}$ and ${\sigma }_{\text{min}}=\text{Ce}{\left[\left(n_{\text{imp},0}+n_{\text{K}}\right){\xi }^2\right]}^{-1/2}$ with $C$ and $n_{\text{imp},0}$ determined from the fit to $1/\mu$ vs $n_{\text{K}}$ at $V_{\text{g}}=30\text{V}$ in Fig. 2a, and $\xi =32\text{nm}$.Reuse & Permissions