Approaching the intrinsic band gap in suspended high-mobility graphene nanoribbons

We report electrical transport measurements on a suspended ultra-low-disorder graphene nanoribbon (GNR) with nearly atomically smooth edges that reveal a high mobility exceeding 3000 cm${}^2$ V${}^{-1}$ s${}^{-1}$ and an intrinsic band gap. The experimentally derived band gap is in quantitative agreement with the results of our electronic structure calculations on chiral GNRs with comparable width taking into account the electron-electron interactions, indicating that the origin of the band gap in nonarmchair GNRs is partially due to the magnetic zigzag edges.

Figure 1

Resistance versus gate voltage for (a) sample A (lower-disorder) and (b) sample B, measured at various temperatures. The solid lines are the model fitting. The two samples belong to a single GNR with uniform width ($W$ ∼ 20 nm) and thickness ($d$ ∼ 1.4 nm), and both have the same length $L$ ∼ 600 nm. Insets: schematic illustration of a GNR-FET consisting of a suspended GNR (right) and the contact electrodes and an AFM image of a GNR suspended by Au electrodes (left).

Figure 2

Mobility as a function of temperature for samples A and B. The solid squares and solid circles are the mobility extracted from the model fitting in Fig. 1; the hollow squares are the field-effect mobility. The dashed lines are a guide to the eye.

Figure 3

(a) Temperature dependence of the minimum conductance for samples A, B, and C. (b) Temperature dependence of the residual carrier density extracted from the model fitting in Fig. 1 for samples A, B, and C. The solid lines are fits to the simple activated behavior.

Figure 4

(a) Conductance versus gate voltage measured at various temperatures for sample A. (b) I-V characteristics measured at different gate voltages and at $T=4$. 3 K for sample A.

Figure 5

(a) Unrolled projection of a $(n,m)$-CNT of minimum circumference (|$\stackrel{}{OB}$|). The chiral angle $\theta$ is determined by the translational vector $\stackrel{}{OA}=\left(n,m\right)=(3,2)=3\overrightarrow{a_1}+2\overrightarrow{a_2}$. (b) Cross-section of a (3,2)-GNR with ∼20 nm width. The periodic unit cell used in the calculation is shown shaded in green. The zoom-in regions show the spatial distribution of spin-up (cyan) and spin-down (red) magnetization. The magnitude of the magnetization is given by the radius size, with the largest radius corresponding to spin magnetization 0.13 ${\mu }_B$.

Figure 6

(a) Electronic band structure and (b) density of states of a (3,2)-GNR; results in the absence ($U=0$ eV) and presence ($U=6.4$ eV) of electron-electron correlation are shown in red and blue, respectively. (c) Calculated band gaps (black) and maximum spin magnetization (red) for GNRs of $(n,m)$-type (6,0), (7,1), (5,1), (4,2), (3,2), and (3,3), corresponding to chiral angles $\theta$ in ascending order.