Figure 1

(Color online) Schematic representation of the graphene nanoribbon setup used in the simulations.Reuse & Permissions

Figure 2

(Color online) (a) and (b) Energy dependence of the average linear conductance of graphene nanoribbons with varying edge roughness. All nanoribbons have the same length $\left(L=45\text{nm}\right)$ and similar widths ($W=4.4\text{nm}$ for armchair and $W=4.7\text{nm}$ for zigzag). (c) Typical etching profiles used in (a) and (b) (only segments of the nanoribbon atomic structure are shown). Left: armchair and right: zigzag.Reuse & Permissions

Figure 3

(Color online) Average conductance of (a) metallic armchair $\left(W=4.3\text{nm}\right)$ and (b) zigzag $\left(W=4.6\text{nm}\right)$ nanoribbons as a function of the Fermi energy for three different widths when moderate roughness is present (zero temperature). The dashed lines indicate the conductance gap estimated by the change in the slope of the curves (see insets). A total of ten realizations of the edge roughness types 3 for armchair and 4 for zigzag were used for each curve presented.Reuse & Permissions

Figure 4

(Color online) (a) Transport gap dependence on the nanoribbon width. The dashed and dashed-dotted lines are fittings to the data as explained in the main text. (b) On/off linear conductance ratio as a function of ribbon length. The solid lines are guides for the eyes and the dashed lines indicate fittings to exponential curves. Each data point corresponds to an average over 50 realizations of edge roughness. Inset: localization length as a function of ribbon width (circles are for armchair and squares are for zigzag). Solid (empty) symbols represent $E_F=0$ $\left(E_F=0.2t\right)$. Lines are fittings of the functional form $\xi =A{W}^{\alpha }$ (see main text).Reuse & Permissions

Figure 5

(Color online) The effect of combined edge and bulk disorders on the average conductance of short graphene nanoribbons. (a) Armchair and (b) zigzag orientations (both with the same width $W=8.3\text{nm}$ and length $L=22\text{nm}$). The edge disorder corresponds to the case 2 of Fig. 2c; the bulk disorder has parameters $n_{\text{imp}}=0.04$, $K_0=0.5$, and $\xi =2a_0$. Inset: average linear conductance of armchair nanoribbons with bulk disorder and perfect edges at zero temperature ($L=22\text{nm}$, $W=4.4\text{nm}$ and five realizations per curve). The dashed lines correspond to correlation lengths $\xi /a_0=10$, 3, and 1 from top to bottom ($n_{\text{imp}}=0.02$ and $K_0=1$ in all three cases).Reuse & Permissions

Figure 6

(Color online) Suppression of conductance quantization steps due to weak edge disorder. (a) Armchair and (b) zigzag orientations. A total of 100 realizations were used in each case. Solid (dashed) lines indicate zero (room) temperature in the contacts. Inset: average conductance versus energy for a metallic armchair nanoribbon with $L=22\text{nm}$, no bulk disorder, $p_1=0.05$ (ten realizations), and increasing widths $W=4.4$, 9.1, and 18.5 nm; solid (dashed) lines represent zero (room) temperature, while dotted lines describe the perfect edge case at zero temperature.Reuse & Permissions

Figure 7

(Color online) Relative suppression of the nth conductance step as a function of (a) and (c) nanoribbon length and (b) and (d) defect concentration for metallic armchair $\left(W=4.4\text{nm}\right)$ and zigzag $\left(W=5.2\text{nm}\right)$ orientations. Each data set corresponds to an average over 100 realizations. The index $n$ indicates the order of the conductance step and the solid lines are guides for the eyes. The dotted lines are explained in the main text.Reuse & Permissions