Letter pubs.acs.org/NanoLett
Edge-Dependent Transport Properties in Graphene Hidenori Goto,*,†,‡ Eri Uesugi,† Ritsuko Eguchi,† Akihiko Fujiwara,§ and Yoshihiro Kubozono†,‡ †
Research Laboratory for Surface Science and ‡Research Center of New Functional Materials for Energy Production, Storage, and Transport, Okayama University, Okayama 700-8530, Japan § Japan Synchrotron Radiation Research Institute, Spring-8, Hyogo 679-5198, Japan S Supporting Information *
ABSTRACT: Graphene has two kinds of edges which have different electronic properties. A singular electronic state emerges at zigzag edges, while it disappears at armchair edges. We study the edge-dependent transport properties in few-layer graphene by applying a side gate voltage to the edge with an ionic liquid. The devices indicating a conductance peak at the charge neutrality point have zigzag edges, confirmed by microRaman spectroscopy mapping. The hopping transport between zigzag edges increases the conductance. KEYWORDS: Graphene, edge, Raman spectroscopy, ionic liquid gate, transport property, flat band
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importance for graphene-edge applications as well as fundamental physics, chemistry, and nanoscience achievable only at the boundary of a Dirac fermion system. So far, the edge transport in graphene has been studied theoretically by using graphene nanoribbons (GNRs) because GNRs have a large fraction of edges, and the electronic property significantly depends on whether the ribbon has the zigzag or armchair edge; GNRs with armchair edges are metallic or semiconducting depending on the width of ribbon, while GNRs with zigzag edges are metallic owing to the flat band.4 GNRs with mixed edges exhibit one-dimensional localization.15,21,22 But the experimental results for edgedependent transport in GNR have not yet been conclusive23−25 because the quantum confinement effect due to rough edges masks the edge-dependent phenomena; the energy gap opens and the system becomes an insulator despite the edge chirality. To overcome this difficulty, it should be noted that the edge state appears not only in zigzag GNRs but also at zigzag edge in semi-infinite graphene.4 Here, we study edge transport by applying a side gate voltage Vsg to the bulk graphene to eliminate the quantum confinement effect. In this case, the total conductance consists of bulk and edge conductance, Gtotal = Gbulk + Gedge(Vsg), only the latter of which depends on the side gate voltage. Thus, the component of conductance that depends on Vsg reflects the electronic states localized at the edge. Some reports have discussed the side-gated transport properties of graphene,25−28 but the properties of the edge state have not been reported. In order to identify the edge state localized in a few atoms from the edge, the side gate electrode must be attached within atomic distance of the edge. For this
eculiar properties at edges (or at surfaces in threedimensional materials) resulting from the lack of inversion symmetry have attracted much interest in the past few years. For example, a topological insulator is metallic only at its edges.1,2 Spin splitting due to the giant Rashba effect at surfaces is another phenomenon caused by the breaking of inversion symmetry.3 Graphene, a single atomic layer of graphite, also has interesting properties at its edges. Since carbon atoms are arranged in a honeycomb lattice, graphene has two kinds of boundaries, called armchair and zigzag edges. These two edges have different electronic band structures; the armchair edge has no carriers at the charge neutrality point (Dirac point) like bulk graphene, while the zigzag edge has a singular density of states localized at the edge. This edge state originates from a flat band, which was theoretically predicted4 in 1996 before graphene was isolated in 2004.5 The different edge characteristics have been observed by scanning tunneling microscopy/spectroscopy (STM/STS),6 and recently by transmission electron microscopy (TEM),7 and micro-Raman spectroscopy.8−10 However, it remains unclear how the edge state affects carrier transport. It is believed that the edge state does not contribute to the electronic transport because the group velocity in the flat band is zero.11,12 But this is the case for a flat band formed by a perfect zigzag edge. Since the actual edge consists of mixture of armchair and zigzag edges,9,13,14 the local charge density at zigzag edges may contribute to the conductance due to the hopping transport.15 Meanwhile, theory shows that a mixed edge produces a dispersive edge state,16 indicating that electrons can propagate along a mixed edge. From these fundamental viewpoints, it is meaningful to clarify the edgedependent transport properties in graphene. Moreover, the singular density of states causes strong electron correlation, leading to striking phenomena such as spin polarization4,17,18 and superconductivity.19,20 Thus, the elucidation of the transport properties related to a zigzag edge is of great © 2013 American Chemical Society
Received: December 5, 2012 Revised: January 31, 2013 Published: February 14, 2013 1126
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10−6 Torr with a cryogenic microprobe system (Riko International Ltd. i-series). To improve the S/N ratio, we deduced the conductance from the slope of the I−V curve. The drain voltage was typically swept between ±10 mV. The back gate voltage Vbg was applied through a highly doped Si substrate and the side gate voltage Vsg was applied with gel of ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate (bmim[PF6]).31 Although it appears that the ionic liquid shorts the source and drain contacts in Figure 1f, the ionic liquid does not contribute to the conductance. Actual conductance between two contacts via the ionic liquid was measured to be below experimental error of 10−8 S. Raman spectra were measured with a JASCO NRS-3100 using a linearly polarized laser with a wavelength of 488 nm and a power of 2.7 mW. Under these conditions no degradation of the device was observed. The blue line in Figure 2a shows Vbg dependence of conductance measured after the oxygen plasma etching. The
purpose, we used an ionic liquid gate in which the gate voltage was applied across an electric double layer (EDL) less than 1 nm in thickness.29,30 The ionic liquid also serves as a flexible gate because the liquid can penetrate into the nanosized complex structure. In this way, we can contact the selfassembled and closely spaced gate electrode along all the edge, which is unattainable with a conventional solid gate using electron-beam lithography. Graphene-edge field effect transistors (FETs) were prepared as follows. Graphene was prepared on 300 nm thick SiO2/ doped Si substrates by micromechanical cleavage of bulk graphite (Figure 1a). Electrodes were fabricated with photo-
Figure 1. (a−e) Fabrication process of graphene-edge FET. (f) Schematic view of device structure and configuration of measurement terminals. (g) Optical microscope image of prepared device.
Figure 2. (a) Schematic side view and transfer characteristics of a graphene-edge FET with an ionic-liquid side gate. Back gate and side gate voltage (Vbg and Vsg) dependences of conductance are plotted with blue and red symbols, respectively. (b) Schematic side view and transfer characteristics of graphene FET with an ionic-liquid top gate. Back gate and top gate voltage (Vbg and Vtg) dependences of conductivity are plotted with blue and red symbols, respectively. Both devices in (a) and (b) consist of bilayer graphene. The interface between graphene and the ionic liquid is indicated by the red line. The current flows in the direction perpendicular to the paper, and the source and drain electrodes are excluded for clarity.
lithography and vacuum deposition of metal (Cr 5 nm/Au 50 nm) and insulating layer (LiF 30 nm) (Figure 1b). The insulating layer was prepared to passivate the electrodes. The device was coated with photoresist (Tokyo-Oka TSMR8900, ∼1 μm in thickness) (Figure 1c) and a part of the photoresist on graphene is removed by photolithography (Figure 1d). The uncovered region of graphene was etched by oxygen plasma (Figure 1e). A power of oxygen plasma was 300 W, and the vertical etching rates for photoresist and graphene were 8.7 and 1.3 nm/min, respectively. To avoid damage to the graphene under the photoresist, etching time was carefully chosen. As a result, no significant change in mobility was observed after the etching. A schematic view and an optical microscope image of the device are shown in Figure 1f,g. The transport measurement was performed by use of a semiconductor parametric analyzer (Agilent B1500A). The transport properties at room temperature were measured in an Ar atmosphere with a probe system (HiSOL, Inc. HMP-400), and the temperature dependence of them was measured in a vacuum below 1.0 ×
photoresist coating led to hole-doping in the graphene as shown by the positive shift of the charge neutrality point. But we confirmed that the edge conduction was not affected by the doped holes as described later. After this measurement, the ionic liquid was poured on the device and Vsg was applied. The EDL capacitance per area of this liquid was measured with Agilent B1500A and evaluated to be 9.6 μF/cm2.31 This value corresponds to an EDL 0.6 nm thick, assuming the relative permittivity of the ionic liquid ε = 7.29 Thereby only the electronic state within EDL thickness d from the edge is modulated. Since d is much smaller than the mean free path in 1127
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state. Furthermore, the singular density of states at the zigzag edge is theoretically expected to appear around the charge neutrality point.4,16 This agrees with the location of the experimental conductance peak, suggesting that the conductance peak originates from the zigzag edge. Such a conductance anomaly was not always observed but was found in 9 out of a total of 25 prepared devices (Table 1). To examine whether or not the conductance peak relates to the edge chirality, we characterized the edge of this device (referred to as device A) with Raman spectroscopy. Raman spectroscopy is a powerful and sensitive tool to determine the edge chirality of single-layer graphene,8,9,13,14 bilayer graphene,10 and graphite.33 Regardless of the number of layers, the intensity of the D band is strong at armchair edges and zero at zigzag edges. This is because only the armchair edges can cause the intervalley scattering of the electrons or holes, which is necessary in the Raman double resonance mechanism for the emergence of the D band.8−10 After removing the ionic liquid and the photoresist from the device, Raman spectra were measured. The polarization of the incident light is parallel to the edge, leading to the most distinctively different D band intensities between the two edge chiralities.9 (see Table S1 in the Supporting Information) Figure 3b shows the Raman spectra measured at the graphene edge taken at places indicated by I and II in Figure 3c,d. The D and G bands at 1370 and 1588 cm−1 are noticeable. Raman maps were taken by scanning the device with a step of 0.5 μm and a spatial mapping resolution of about 1.0 μm. The integrated intensity map of the G peak shows the location of the graphene layer (Figure 3c). The boundaries between graphene, electrodes, and substrate are indicated by dashed lines. The integrated intensity map of the D peak (Figure 3d) characterizes the structural defects and the edge chirality. A strong D peak is found only at the graphene edge. In Figure 3d, we find a weak D peak in the central region of the edge, suggesting the presence of a zigzag edge. The result did not depend on the polarization of the laser light (see Figure S2 in the Supporting Information). For comparison, we also measured the Raman map of device B, which shows no conductance peak at the charge neutrality point (Figure 4a). The G and D peak maps are shown in Figure 4b,c, respectively. In this case, a strong D peak is found all along the edge. This does not mean the edge is purely armchair chirality, but it is clear that device A has a higher fraction of zigzag edge than device B. We confirmed that the devices with a high fraction of zigzag edge show a conductance peak, indicating that a conductance peak at the neutrality point is related to the presence of the zigzag edge. Note that a conductance peak does not originate from impurities at the edge, which should increase D peak intensity.34 It is most likely that the singular density of states at the zigzag edge increases the conductance. To understand the correlation between the conductance peak and the Raman D peak, we classified the measured devices into four categories (with or without a conductance peak and
bulk graphene (10−100 nm), we can control the edge channel transport without interacting with diffusive transport in the modulated region. Vsg dependence of conductance with the ionic liquid is plotted on the same panel as Figure 2a with a red line and enclosed by a dashed circle for clarity. Note that the Vsg dependence of the conductance is smaller than the Vbg dependence. This behavior is completely different from that in graphene FET whose whole surface is covered with an ionic liquid (Figure 2b). In this case, the ionic liquid gate can modulate the conductance more effectively than the solid gate due to the large EDL capacitance. The different ionic-liquid gate voltage (Vsg, Vtg) dependence between Figure 2 panel a and panel b means that the ionic liquid does not penetrate into the boundaries between graphene/photoresist and graphene/ substrate in the graphene-edge FET. Figure 3a shows an enlarged view of the red line of Figure 2a. Red arrows indicate sweep direction and the sweep rate of Vsg
Figure 3. (a) Vsg dependence of conductance of device A. Device A consists of bilayer graphene. A conductance peak is found in this device. (b) Raman spectra taken at places indicated by I and II in (c) and (d). D and G bands were observed at 1370 and 1588 cm−1, respectively. (c) Integrated intensity map of G peak taken from 1560 to 1654 cm−1 (G band mapping). (d) Integrated intensity map of D peak taken from 1331 to 1427 cm−1 (D-band mapping). The scale bar is 1 μm.
was 6.0 mV/s. The Vsg was swept in the range of ±1 V within the electrochemical window32 to avoid the chemical reaction between the ionic liquid and the graphene edge. As mentioned above, the doped holes from the photoresist do not affect edge transport, because the charge neutrality point shown by the broad conductance minimum is located at Vsg ∼ 0 V. The actual conductance exhibits an additional peak at the charge neutrality point, its magnitude indicated by ΔG. Since the ionic liquid does not contact the graphene except at its edge, this conductance peak suggests the presence of a distinct edge
Table 1. Number of Devices Which Show a Conductance Peak or Not, and Which Show a Strong Raman D Peak or Not
transport measurement Raman spectroscopy
strong D peak 2
conductance peak
no conductance peak
9
16
weak D peak 4
not measured 3 1128
strong D peak 8
weak D peak 1
not measured 7
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from the hopping transport between zigzag edges, it diminishes with decreasing temperature, because the hopping due to thermal excitation is suppressed. On the other hand, if the conductance peak is related to the band transport along the edge channel, it should be more clearly observed at low temperatures, because impurity and phonon scattering which prevents the band transport is suppressed. Using a device which shows a conductance peak, we study how the conductance peak changes with decreasing temperature. In Figure 5a, con-
Figure 4. (a) Vsg dependence of conductance of device B. Device B consists of 10-layer graphene. (b,c) Integrated intensity map of G and D peak taken under the same condition as Figure 3c,d, respectively. The scale bar is 1 μm. Figure 5. (a) Temperature dependence of conductance curves from 290 to 230 K. This device consists of single-layer graphene. (b) Magnified view of the region enclosed by the dashed line in (a). The curves are offset for clarity. The scale of conductance, 0.01 mS, is indicated. The part indicated by the arrow shows the conductance peak.
with a strong or weak D peak) in Table 1. Here, the inflection of a conductance curve around Vsg = 0 was defined as a conductance peak as seen in Figure 3a. On the other hand, a smooth minimum of a conductance curve is regarded as no conductance peak as seen in Figure 4a. As concerns a Raman D peak, the integrated intensity, which was recorded in units of counts per second (cps), was divided by the number of graphene layers for a systematical comparison of all the measured devices. If the intensity map has values exceeding 100 cps along all the edge, this device was classified as a strong D peak. The other device was defined as a weak D peak. A weak Raman D peak was observed in 4 out of 6 devices that showed a conductance peak. On the other hand, a strong D peak along the edge was observed in 8 out of 9 devices that showed no conductance peak. Thus, we find the strong correlations between a conductance peak and a weak D peak and between no conductance peak and a strong D peak. The presence of the exceptional two devices that showed a conductance peak and a strong D peak may be due to unintentional impurities absorbed at the edge. Nevertheless, the meaningful correlation between the conductance peak and weak D peak, i.e., the presence of zigzag edge is proved from this statistical analysis. Figure S3 in the Supporting Information is shown to convince the reproducibility of the correlation between conductance curves and Raman maps in the other devices. Here, we discuss the edge chirality and the transport mechanism. Okada et al. showed that an armchair edge is energetically more stable than a zigzag edge.35 However, the actual edge is far from thermodynamic equilibrium, with STM36 and TEM7 respectively showing that 24 and 38% of edges were zigzag. Raman spectroscopy also shows that a perfect armchair or zigzag edge is not realized even though cleaved graphene’s edges meet at the crystallographic angles, that is, multiples of 30° that correspond to the angle of intersection between armchair and zigzag edges.9,13,14 From these results, we infer that the edge of our device included both zigzag and armchair forms. According to theoretical studies in GNRs, carrier transport in mixed edges is possible due to the one-dimensional hopping15 or the dispersive edge state.16 These transport mechanisms can be distinguished by temperature dependence of the conductance peak. If the conductance peak originates
ductance curves measured at 290, 270, 250, and 230 K are compared. Vsg is swept from the negative to positive value, and the sweep rate is 5.8 mV/s. The dependence of the conductance on Vsg was reduced with decreasing temperature, because the movement of anions and cations in the ionic liquid became slower at low temperatures. The conductance eventually showed no Vsg dependence below 210 K, the freezing point of the ionic liquid. In Figure 5b, the curves are magnified around Vsg = 0 V, and the each curve is offset by −0.05 mS for clarity. As seen from Figure 5b, the conductance peak observed at 290 and 270 K shown by the arrow is clearly suppressed at 230 K. This result supports the hopping transport mechanism. Furthermore, the magnitude of the observed conductance peak ΔG (Figure 2a) is 10−6−10−5 S, which is much smaller than the channel conductance 2e2/h ∼ 8 × 10−5 S expected for a one transport channel. This also shows that our edge transport has a hopping character rather than that in a perfect single edge channel. Thus, we infer that the prepared edge is a mixture of zigzag and armchair edges and that a high fraction and the large segments of zigzag edge result in the conductance peak at the charge neutrality point. Each segment of zigzag edges is at least larger than the electron wavelength (estimated to be 1.3 nm), because the zigzag edge does not contribute to the Raman D peak when the specular reflection of electrons in the zigzag edge is possible.9 To summarize, it seems reasonable that hopping conduction between the singular density of states at zigzag edges increases the conductance. In conclusion, we have studied edge transport in graphene by means of an EDL side gate. Using this simple technique, we first succeeded in clarifying edge-dependent carrier transport. Although the edge does not have perfect chirality, the carrier density localized at the zigzag edge can contribute to the carrier transport at the charge neutrality point. It is fundamentally 1129
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intriguing problem how the conductance peak changes with preparing the ideal zigzag edge.14,37,38 Our method will be developed to study low-dimensional transport properties, because graphene is an ideal two-dimensional material and its edge conductance has one-dimensional characteristics. Furthermore, since the graphene edge is chemically highly reactive,34 the fabrication of functional devices by chemical decoration is expected. Thus, our EDL side gate technique is a first step toward graphene-edge devices, both for fundamental research and practical applications.
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ASSOCIATED CONTENT
S Supporting Information *
Method identifying graphene edge, polarization dependence of Raman mapping, reproducibility of experiment, and the orientation dependence of conductance peak. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
H.G. and E.U. contributed equally to the preparation of graphene devices and to the transport and Raman spectroscopy measurement. R.E., A.F., and Y.K. provided valuable discussions and suggestions for the overall project and discussed the experimental data. H.G. was responsible for the overall project direction, planning and integration. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by Grants-in-Aids (22244045, 24654105, and 23684028) from MEXT, Japan, by the LEMSUPER project (JST-EU Superconductor Project) and ACT-C project in the Japan Science and Technology Agency (JST) and as a Special Project of Okayama University/MEXT. We are grateful to T. Kambe for comments and suggestions and to M. Mifune for Raman spectroscopy.
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REFERENCES
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