Magnetotransport Properties of Graphene Nanoribbons with Zigzag Edges

The determination of the electronic structure by edge geometry is unique to graphene. In theory, an evanescent nonchiral edge state is predicted at the zigzag edges of graphene. Up to now, the approach used to study zigzag-edged graphene has mostly been limited to scanning tunneling microscopy. The transport properties have not been revealed. Recent advances in hydrogen plasma-assisted “top-down” fabrication of zigzag-edged graphene nanoribbons (Z-GNRs) have allowed us to investigate edge-related transport properties. In this Letter, we report the magnetotransport properties of Z-GNRs down to $\sim 70\mathrm{nm}$ wide on an $h\text{−}\mathrm{BN}$ substrate. In the quantum Hall effect regime, a prominent conductance peak is observed at Landau $\nu =0$, which is absent in GNRs with nonzigzag edges. The conductance peak persists under perpendicular magnetic fields and low temperatures. At a zero magnetic field, a nonlocal voltage signal, evidenced by edge conduction, is detected. These prominent transport features are closely related to the observable density of states at the hydrogen-etched zigzag edge of graphene probed by scanning tunneling spectroscopy, which qualitatively matches the theoretically predicted electronic structure for zigzag-edged graphene. Our study gives important insights for the design of new edge-related electronic devices.

Figure 1

STM images of the hydrogen-plasma etched graphene on $6H\text{−}\mathrm{SiC}(0001)$ and atomic force microscopy (AFM) images of Z-GNRs on $h\text{−}\mathrm{BN}$ before and after hydrogen-plasma etching. (a) STM overview ($V_s=-1.0\mathrm{V}$,$I=100\mathrm{pA}$,$T=4.9\mathrm{K}$) of the etched graphene, showing an intact hexagonal pit. (b) Englarged STM image ($V_s=-500\mathrm{mV}$, $I=300\mathrm{pA}$, $T=4.9\mathrm{K}$) of the dotted area in (a). The black superimposed graphene lattice shows that the etched edge is predominantly in a zigzag orientation. Inset shows the FFT image of the top-layer graphene near the edge, where bulk graphene lattice and the $(\sqrt{3}\times \sqrt{3})R30°$ superstructure are highlighted by yellow and green hexagons, respectively. (c) AFM image of circular dot patterns in MLG on $h\text{−}\mathrm{BN}$ created by EBL and oxygen-plasma etching. The scale bar is 500 nm. (d) AFM image of hydrogen-plasma etched hexagonal hole arrays in graphene on $h\text{−}\mathrm{BN}$. The scale bar is 500 nm.

Figure 2

Magnetotransport of the Z-GNR device. (a) Schematic diagram of a Z-GNR device with two terminals. A typical $\mathrm{Z}\text{−}\mathrm{GNR}/h\text{−}\mathrm{BN}$ device with width $\sim 68\mathrm{nm}$ shown as inset AFM (scale bar is 300 nm). (b) Landau fan diagram $\mathrm{G}(V_g,B)$. (c) The typical transfer curves at several $B$ from a ($\sim 3\mathrm{k}\mathrm{\Omega }$ contact resistance was subtracted). (d) The AFM image of a control sample#tp20. The scale bar is 300 nm. (e) Landau fan diagram of sample#tp20 $\mathrm{G}(V_g,B)$. Color scale is the same as Fig. 2.

Figure 3

Temperature dependence behavior of $G_{\text{peak}}$, $G_{\min 1}$, and $G_{\min 2}$. (a),(b) The typical transfer curves for #t116 and #tp20 at several temperatures $B=9\mathrm{T}$. (c) $T$ dependence of $G_{\text{peak}}$, $G_{\min 1}$, and $G_{\min 2}$. The straight lines are linear fits to the data at the high-temperature activation range. (d) Activation energy estimated by $T$ dependence of $G_{\min 1}$, $G_{\min 2}$, and $G_{\min \_tp20}$ as a function of applied magnetic field $B$. The blue dashed line is fitted to $B$. The red dotted line and black dot-dashed line are fitted to $\sqrt{B}$.

Figure 4

Nonlocal measurement ($1,3//2,4$) of Z-GNR. (a) AFM image of the typical $\mathrm{Z}\text{−}\mathrm{GNR}/h\text{−}\mathrm{BN}$ device ($l\sim 280\mathrm{nm}$, $w\sim 65\mathrm{nm}$) and the nonlocal measurement geometry; scale bar is 250 nm. (b) Nonlocal resistance (red curves) and longitudinal resistance (blue curve) measured in Z-GNR device.

Figure 5

Edge states at hydrogen-etched edge of graphene. (a) Atomically resolved STM topography ($V_s=-500\mathrm{mV}$, $I=100\mathrm{pA}$, $T=4.9\mathrm{K}$) shows the edge of the hydrogen-plasma etched graphene on $6H\text{−}\mathrm{SiC}(0001)$ substrate. (b) The atomic lattice model of the top-layer graphene shown in (a) (the gray ones and the white ones are carbon and hydrogen atoms) (c) $dI/dV$ spectra measured along the green line in (a). (d) Solid triangles show the zigzag-edge-state amplitude extracted from (c) by Lorentz fitting, as a function of the distance from the zigzag edge, and red curve is the exponential decay fitting of the experimental data. (e) $dI/dV$ spectra measured along the graphene edge, as the purple line shown in (a). (f) Solid squares show the zigzag-edge-state amplitude extracted from (e) by Lorentz fitting, indicating the amplitudes are uniform alone the edge. The spectra in (c) and (e) were measured with tip stabilized at $V_s=-500\mathrm{mV}$ and $I=100\mathrm{pA}$.