Electron Transport in Disordered Graphene Nanoribbons

We report an electron transport study of lithographically fabricated graphene nanoribbons (GNRs) of various widths and lengths. At the charge neutrality point, a length-independent transport gap forms whose size is inversely proportional to the GNR width. In this gap, electrons are localized, and charge transport exhibits a transition between thermally activated behavior at higher temperatures and variable range hopping at lower temperatures. By varying the geometric capacitance, we find that charging effects constitute a significant portion of the activation energy.

Figure 1

(a) $dI/dV$ of a GNR with $W=36\mathrm{nm}$ and $L=500\mathrm{nm}$, plotted as a function of $V_g$. Dashed lines highlight measurement of $\Delta V_g$. Right inset shows an atomic force microscope image of the device. Left inset shows a close-up of $dI/dV$ within the gap regime plotted as a function of $V_g-V_D$, where $V_D=21\mathrm{V}$ is the gate voltage for the charge neutrality point. (b) $T$ dependence of the minimum conductance of the same GNR in (a). The dashed and dotted lines are a fit to simple activated behavior and variable range hopping with $\gamma =1/2$, respectively. An arrow highlights the position of $T^{*}$. Inset shows $dI/dV(V_g)$ at several temperatures.

Figure 2

GNR transport energy scales: ${\Delta }_m$ (solid), $E_a$ (crosshatched), and $k_B{T}^{*}$ (open) plotted as a function of GNR width. Circles, triangles, squares, and stars correspond to ribbons of $L=0.5$, 1, 1.5, and $2\mu \mathrm{m}$, respectively. The dashed lines are the fits described in the text.

Figure 3

(a) Differential conductance as a function of $V_g$ and $V_b$ measured in a GNR with $L=1\mu \mathrm{m}$ and $W=31\mathrm{nm}$.(b) Current as a function of $V_b$ with $V_g$ fixed in the off-resonant condition marked by the dotted line in (a). $\Delta V_b$ is highlighted by the vertical dashed lines. (c) $\Delta V_b$ as a function of $W$. Symbols follow the convention set in Fig. 2. (d) The critical electric field ${\mathcal{E}}_{\mathrm{cr}}$ versus $W$ converted from the data set in (c).

Figure 4

Temperature dependence of the conductance minimum for dual gated (circles) and back gated (triangles) GNRs with the similar $W$ and $L$. The dashed lines are Arrhenius fits in the high temperature regime. The inset shows SEM images of back gated (left) and dual gated (right) devices. Scale bar represents 500 nm.