Graphene nanoribbons with smooth edges behaveas quantum wiresXinran Wang1,2†, Yijian Ouyang3, Liying Jiao1, Hailiang Wang1, Liming Xie1, Justin Wu1,

Jing Guo3 and Hongjie Dai1*

Graphene nanoribbons with perfect edges are predicted toexhibit interesting electronic and spintronic properties1–4,notably quantum-confined bandgaps and magnetic edgestates. However, so far, graphene nanoribbons produced bylithography have had rough edges, as well as low-temperaturetransport characteristics dominated by defects (mainly variablerange hopping between localized states in a transport gap nearthe Dirac point5–9). Here, we report that one- and two-layernanoribbon quantum dots made by unzipping carbon nano-tubes10 exhibit well-defined quantum transport phenomena,including Coulomb blockade, the Kondo effect, clear excitedstates up to ∼20 meV, and inelastic co-tunnelling. Togetherwith the signatures of intrinsic quantum-confined bandgapsand high conductivities, our data indicate that the nanoribbonsbehave as clean quantum wires at low temperatures, and arenot dominated by defects.

In this study, we focused on graphene nanoribbons with widthw ≈ 10–20 nm (Fig. 1) and with expected bandgaps of Eg ≈1 (eV)/w (nm) ≈ 50–100 meV (ref. 2). Recent transmission electronmicroscopy (TEM, Fig. 1c), aberration-corrected TEM(Supplementary Fig. S1, ref. 11) and scanning tunnelling microscopy(STM) measurements12 revealed that an appreciable fraction of nano-ribbons in our samples exhibited smooth edges with little roughness,although some exhibited edge roughness on the order of �1 nm.About 70% of nanoribbons in our samples are non-AB-stackedbilayer ribbons (Supplementary Fig. S1), with �10% being single-layer ribbons11. The electrical properties of a large number of thenanoribbons exhibited variability, and a fraction of nanoribbonswith short lengths (,100 nm) showed high conductance up to�7e2/h (Supplementary Fig. S5) and ‘clean’ quantum transportcharacteristics at low temperatures. Figure 2a plots the room-tempera-ture conductance–back-gate voltage G–Vgs characteristics of ahigh-quality nanoribbon device (‘GNR1’) with a ribbon width ofw ≈ 14 nm and channel length of L ≈ 86 nm (Fig. 2a, lower inset).The nanoribbon showed a topographic height of �1.0 nm afterelectrical annealing to remove physisorbed species13, correspondingto either a single-layer or bilayer nanoribbon10,13. The device exhibiteda high p-channel conductance of G . 4e2/h at room temperature(Fig. 2a). The resistance mainly came from quantum resistance atthe contact of the graphene nanoribbon, and we estimated ourcontact transparency to be �70% near the ‘on’ state. The conductivitys¼GL/w ≈ 0.97 mS and the calculated peak field-effect mobilitym¼ (dG/dVgs)(L2/Cg) ≈ 1,600 cm2 V21 s21 (where the gate capaci-tance Cg¼ 0.41 aF was calculated using three-dimensional electro-static simulation14) were much higher than those of previouslyreported nanoribbons (s≈ 0.1–0.3 mS, m≤ 700 cm2 V21 s21) with

similar widths and numbers of layers (≤2)10,15–17. Note that forshort channel devices, the so called ‘ballistic mobility’ and parasiticresistance could make the extracted mobility value lower than themobility due to scattering18.

The p-channel conductance of the nanoribbon increased as itwas cooled from 290 K to 50 K (Fig. 2a, upper inset20). At low temp-eratures (,�60 K), conductance at the Dirac point exhibited adrastic (�100-fold) dip in a narrow gate range (DVgs ≈ 2 V)without any resonance-like sharp peaks due to localized stateswithin the dip5 (Fig. 2b, Supplementary Fig. S6), suggesting anintrinsic bandgap of the nanoribbon1,2 rather than the defect-induced transport gap (see Supplementary Information for ourcontrol experiments on lithographic ribbons)5–9. Considering theasymmetrical Schottky barriers for electrons and holes at thepalladium contacts, we used the non-equilibrium Green’s function(NEGF) approach to fit the experimental minimum conductanceas a function of temperature to extract Eg ≈ 72+18 meV for thisw ≈ 14 nm ribbon (Supplementary Fig. S2, see SupplementaryInformation for details).

At a base temperature of 2 K, the p-channel conductance ofGNR1 was above 3e2/h (Fig. 2b, inset). The conductivity was upto �20 times higher than previous nanoribbons with similarwidths at low temperatures5–9,16. Near the bandgap, the nanoribbonbehaved as a single quantum dot confined between the leads, andcharge transport was through single electron charging21. Weobserved two prominent large diamonds (size, �60–70 meV) nearzero Vgs, presumably corresponding to the bandgap region

22, butthe origin of two large centre diamonds was unclear. A singlelarge central diamond (with the size of Eg plus charging energy)corresponding to the bandgap separating the electron and holebranches was expected, as in the case of semiconducting carbonnanotubes22. We note, however, that the appearance of twocentral diamonds varied in different cool downs. In another cooldown of the same ribbon, a single large diamond was observed(Supplementary Fig. S3). Also, gate-switching events (Fig. 2c,Supplementary Fig. S3) appeared common for nanoribbon devicesdue to the sudden change in the charge environment of the nano-ribbons. These observations suggested that less intrinsic factorscould be involved, possibly involving mobile adsorbates or chargeimpurities on or near the nanoribbons. Such effects have beensuggested to induce mid-gap states in graphene nanoribbons23,which could cause deviation from the single central diamondexpected for the bandgap region.

On both sides of the bandgap region, regular Coulomb-blockadediamonds associated with charging through a single graphenenanoribbon quantum dot (suggested by closed periodic diamonds,

1Department of Chemistry, Stanford University, Stanford, California 94305, USA, 2National Laboratory of Microstructures, School of Electronic Science andEngineering, Nanjing University, Nanjing 210093, China, 3Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida,32611, USA; †Present address: Department of Material Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

*e-mail: hdai@stanford.edu

LETTERSPUBLISHED ONLINE: 28 AUGUST 2011 | DOI: 10.1038/NNANO.2011.138

NATURE NANOTECHNOLOGY | VOL 6 | SEPTEMBER 2011 | www.nature.com/naturenanotechnology 563

© 2011 Macmillan Publishers Limited. All rights reserved.

mailto:hdai@stanford.eduhttp://www.nature.com/doifinder/10.1038/nnano.2011.138www.nature.com/naturenanotechnology

20 nm

a

100 nmGNR

h = 1.7 nmw ≈ 27 nm

CNTd = 6.9 nm

c

w ≈ 17 nm

200 nm

b

GNRw ≈ 14 nm

CNT

Figure 1 | High-quality unzipping-derived graphene nanoribbons. a, AFM image of a typical high-quality as-made graphene nanoribbon (GNR, w ≈ 27 nm)next to a carbon nanotube (CNT) on the substrate. The obvious difference in height can be used to distinguish them. The nanoribbons are typically

�0.3–0.6 nm higher than those made from exfoliated graphene with the same number of layers as a result of the PmPV coatings introduced in thesynthesis10,13. h, height; w, width; d, diameter. It appears from the trace of the nanoribbon and nanotube that they have approximately equal widths. This is

because (1) the trace is more parallel to the orientation of the nanotube and (2) the AFM tip-size effect15 depends on the height of the structure, with the

higher nanotube therefore causing more widening due to the conical shape of the AFM tip. b, AFM image of GNR1 (w ≈ 14 nm; discussed in the main text)before device fabrication. We carefully carried out AFM after device fabrication to ensure that only the nanoribbon was connected by the leads.

c, TEM image of a w ≈ 17 nm graphene nanoribbon with subnanometre edge roughness.

d

e

Vgs (V)

Vds (mV)−5

0.2

0.3

0.4

0 5 10

Vgs (V)

V ds

(mV

)V d

s (m

V)

cT = 2K

40

20

0

−20

−40

−3 −2 −1 0 1 2 3Vgs (V)

1.5

1.0

0.5

0.0

V ds

(mV

)

20

−20

−20

0

20

40

1.0

0.5

0.0−40

1.0

0.5

0.0

−3 −2 −1 0 1

Vgs (V)−3 −2 −1 0 1

1.6 1.8 2.0 2.2 2.4 2.6 2.8

0.4

0.2

0.0

0

G (e

2 /h)

G (e

2 /h)

b

−20

−40 400.01

0.1

24

4

124

2

0 2010−10Vgs (V)

Vgs (V)

2 K290 K250 K200 K150 K100 K60 K

4

0

G (e

2 /h)

G (e

2 /h)

123456

No. of holes

321Δε10 = 3.6

Δε20 = 16.2

No. of electronsa4

3

2

1

0−40 −20 0 20

100 200T (K)

3.6

3.9

G (e

2 /h)

40Vgs (V)

L ~ 86 nmw ~ 14 nmG

(e2 /

h)

100 nm

Figure 2 | Electron transport of GNR1 (L ≈ 86 nm). a, Room-temperature low-bias (Vds¼ 1 mV) G–Vgs characteristics of GNR1. Lower inset: AFM image ofthe device. Upper inset: G versus T at Vgs¼VDirac235 V in the hole channel. The metallic behaviour, also observed in high-quality carbon-nanotube devices20,suggests that the palladium contact is ohmic to the valence band, and the lower resistances at lower temperatures are due to reduced scattering by thermal

depopulation of acoustic phonons. b, Low-bias (Vds¼ 1 mV) G–Vgs characteristics of GNR1 under various temperatures down to 60 K. Inset: zero-bias G–Vgscharacteristics at 2 K. c, Colour scale differential conductance versus Vds and Vgs near the bandgap, showing single electron charging behaviour. A gate

switching was present near Vgs ≈ 1.5 V (indicated by the arrow). d, Differential conductance in the electron branch near the bandgap, showing regularCoulomb diamonds with excited states. The number of electrons in the quantum dot is marked for each diamond. The excited-state energies D1n0 (for

the nth excited state relative to the ground state in meV) are also marked. e, Top panel: differential conductance in the hole branch near the bandgap. The

number of holes in the quantum dot is marked for each diamond. Bottom panel: zero Vds line cut from the top panel, showing the peak pairing and enhanced

conductance in the odd-numbered diamond valleys, a signature of the Kondo effect. Spin configurations are also marked for each valley. Inset: constant

Vgs line cut in the middle of the third hole diamond in the top panel. The conductance is enhanced at zero bias, as expected for the Kondo effect28.

LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2011.138

NATURE NANOTECHNOLOGY | VOL 6 | SEPTEMBER 2011 | www.nature.com/naturenanotechnology564

© 2011 Macmillan Publishers Limited. All rights reserved.

http://www.nature.com/doifinder/10.1038/nnano.2011.138www.nature.com/naturenanotechnology

in clear contrast to dots in series or parallel in previous nanoribbons6,7)were observed, with the number of holes and electrons in the dot beingassignable (Fig. 2d,e). We noticed slight asymmetry for Coulomb dia-monds in the electron and hole branches, probably due to asymmetrictunnel barrier owing to the high-work-function palladium contact.The size of the diamonds along the bias voltage Vds axis in the electronbranch (n-channel) was Eadd ≈ 28 meV (Fig. 2d), consistent with thecharging energy Ec¼ e2/C ≈ 24.7 meV, where C¼Cgþ CsþCd ≈6.48 aF is the total capacitance of the quantum dot22,24 (Cs and Cd aresource and drain capacitances, respectively, and gate capacitanceCg¼ e/DVgs¼ 0.43 aF based on the size of the diamonds DVgs ≈0.37 V along Vg, very close to that from the 3D electrostatic simulation).

We observed several discrete lines parallel to the edges ofCoulomb diamonds (Fig. 2d), which were attributed to transportthrough discrete excited states in the nanoribbon quantum dot25,26

due to quantization along the length of the nanoribbons22,27. Thefirst two measured energy levels outside diamond 1 could beassigned as the first and second excited states, D121¼ 3.6 meVand D131¼ 16.2 meV, respectively, where D1n1¼ 1(k‖(n)) 21(k‖(1)) is the single-particle level above the ground state. In lightof the uncertainties in the nanoribbon structures (number oflayers and edge structures), we used a simple model based on quan-tization of tight-binding Hamiltonians in the width and transportdirections with particle-in-a-box boundary conditions to qualitat-ively understand the excited-states energy (see SupplementaryInformation for details). As shown in Supplementary Table S1,the calculated Eg and D1n1 for single- and several non-AB-stackedbilayer nanoribbons were qualitatively in agreement (within afactor of �3) with experiments. Quantitative comparison,however, was not possible due to the lack of detailedstructural information.

In the hole branch, the Kondo effect28,32 was observed at 2 K asenhanced conductance at zero bias inside the odd-hole-numberCoulomb diamonds (Fig. 2e, see the Kondo ridge or zero-bias

horizontal lines in the 2D conductance plot). The differentialconductance at zero bias showed the pairing of peaks, with non-zero intravalley conductance (Fig. 2e). The Kondo resonanceswere attributed to exchange interaction between a localized electronspin in the quantum dot and the delocalized electron spins in themetal leads. In the odd-number diamonds, the unpaired spin canform a spin singlet with electrons in the leads to give high conduc-tance28. We can roughly estimate the Kondo temperature TK fromthe bias at which the Kondo resonance is suppressed in theKondo ridges34. From the G versus Vds plot in the inset to Fig. 2e,this energy scale is on the order of 1 meV (the width of theKondo resonance peak near zero bias is �2 mV), correspondingto TK ≈ 10 K, which is about an order of magnitude highercompared with carbon-nanotube quantum dots34,35. Recently, TKwas found to be as high as �30–90 K in defective graphene, attri-buted to strong coupling of Dirac electrons to magnetic defects36.

Several other interesting transport phenomena were also presentin GNR1. In Fig. 2e, finite (non-zero) conductance regions can beobserved inside several even-hole-number diamonds beyond hori-zontal lines intersecting the excited state lines at the edge of theCoulomb diamonds. These were attributed to inelastic co-tunnellingof carriers through an excited state when the addition energyexceeded the single-particle level spacing26. In the p-channel awayfrom the bandgap (Vgs ≈ 230 V), phase-coherent transport andlow contact barriers leading to Fabry–Perot-like interference wereobserved19 (Supplementary Fig. S4). At �50 K, we observed con-ductance plateaux spaced by �e2/h in GNR1 and other ribbons(Supplementary Fig. S10 and Supplementary Information),likely due to sub-bands in graphene nanoribbons, as suggestedpreviously38,39.

Well-defined quantum transport features were also observed inlonger graphene nanoribbons (L . �100 nm), although lessfrequently, suggesting a higher likelihood of defects and perturbingenvironmental effects in longer nanoribbons. Figure 3 shows results

f

−40

1.0 1.2 1.4 1.6Vgs (V)

1.8 2.0 2.2

11.52 11.525.76

Δε42=20.64

Δε32=10.56

Δε32=12.96

Δε31=16.32

Δε21=5.76

Δε31=16.32

Δε20=9.12

Δε21=5.76

Δε21=5.76

Δε32=11.52

Δε31=16.8

Δε32=9.6

Δε42=19.68

Δε20=9.12

Δε30=20.16

Δε20 = 9.12

40

0

V ds

(mV

)

c

No. of electronsNo. of holes7 6 5 4 3 2 1 1 2 3 4 5

T = 3.3 K 0.6

0.4

0.2

0.0

60

40

20

0

−20

−40

−601 2 3

V ds

(mV

)

Vgs (V)

ba d e1

40 30

0

−30

Δε10 = 2.52

1

6 5 4 3 2 1

0

Δε10 = 3.6Δε20 = 10.08

Δε30 = 19.44

Δε30 = 19.8

1.8 1.9 2.0

35

30

25

1 2 3 4Number of holes

E add

(meV

)

5 6 7

0.1 L ~ 140 nmw ~ 17 nm

100 nm

0.01

0.001

V ds

(mV

)

Vgs (V)−40 −20 0 20 40

Vgs(V)

G (e

2 /h)

290 K250 K200 K150 K100 K50 K

−0.25

3020100

−10−20−30

−0.2 −0.15Vgs (V)

V ds

(mV

)

−0.1

1 0

Δε30Δε20

Δε10

Figure 3 | Electron transport of a high-quality quantum dot in GNR2 (L ≈ 140 nm). a, Low-bias (Vds¼ 1 mV) G–Vgs characteristics under varioustemperatures down to 50 K. Inset: AFM image of the device. b, Experimentally measured single electron addition energy Eadd as a function of number of

holes in the quantum dot, with an even–odd pattern. A small gate-switching event occurred in diamond 6, and Eadd(6) was measured after correcting the

switching. Single-particle level spacings could be extracted. For example, D110¼ Eadd(2)2Eadd(1), D121¼ Eadd(4)2Eadd(3). c, Differential conductance as afunction of Vgs and Vds at 3.3 K near the bandgap. The number of electrons and holes in the quantum dot are marked. d, High-resolution differential

conductance scan across diamond 0 and 1, clearly showing excited states. The excited states are marked and assigned to the corresponding single-particle

level spacings. e, Simulated differential conductance of the same area as in d at T¼ 5 K. See Supplementary Information for details. f, Differentialconductance scan for six Coulomb diamonds on the hole branch. The number of holes and ground-state configuration for each diamond are illustrated.

All the excited states are marked and assigned to the corresponding energy level spacings. See Supplementary Fig. S9 for the raw data without dashed lines

drawn here to guide the eye.

NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2011.138 LETTERS

NATURE NANOTECHNOLOGY | VOL 6 | SEPTEMBER 2011 | www.nature.com/naturenanotechnology 565

© 2011 Macmillan Publishers Limited. All rights reserved.

http://www.nature.com/doifinder/10.1038/nnano.2011.138www.nature.com/naturenanotechnology

for a nanoribbon device (GNR2) with a longer L ≈ 140 nm channel(w ≈ 17 nm; Fig. 3a, inset), exhibiting G ≈ 4e2/h in the p-channeland peak field-effect mobility m≈ 3,200 cm2 V21 s21 at roomtemperature. Variable temperature measurements again confirmeda single sharp dip in conductance near the bandgap (Fig. 3a) andEg ≈ 60+17 meV was estimated (Supplementary Fig. S2). At T ≈3.3 K, the conductance was suppressed near the bandgap, andregular Coulomb diamonds in both hole and electron brancheswere observed, separated by two relatively large diamonds similarto GNR1 (Fig. 3c). In the hole branch, we observed up to sevenregular diamonds, with the sizes of the diamonds or single electronaddition energy Eadd following an even–odd pattern

22 (Fig. 3b). Theeven numbers of diamonds were larger than the corresponding odddiamonds because of the extra single-particle level spacings, whichcould be readily extracted (Supplementary Table S2). In carbonnanotubes, electronic states are fourfold degenerate because ofspin and valley degeneracy, and fourfold shell filling has beenobserved33,37. In nanoribbons, however, valley degeneracy is lifted

due to the different boundary conditions1,2, resulting in twofoldspin degenerate states. The extracted energy-level spacings(Supplementary Table S2, Fig. 3f ) agreed qualitatively with ourtheoretical calculations based on twofold degenerate states ingraphene nanoribbons.

We observed a wealth of well-defined excited states up to�20 meV in nearly all the Coulomb diamonds (Fig. 3d,f ), andassigned them to the single-particle energy-level spacings basedon the ground-state configuration of the quantum dot and ourcalculations (see Supplementary Information). Using the samemodelling approach as for GNR1, we found that the D1n1 wereagain of the same order of magnitude as the experimentallyobserved excited-states spectra, as were the sizes of the even–odddiamonds (Supplementary Table S2). We also carried out numericalsimulation of Coulomb diamonds and excited states to quantitat-ively match our experiments (Fig. 3e, see SupplementaryInformation). The origins of some excited states are unclear andrequire further investigation, such as the three lines terminatedon diamond 0 with energies �8 meV, 18 meV and 213 meV,respectively (Fig. 3d, Supplementary Fig. S9). These stateshave much higher energy than D121 and are possibly a result ofinteraction effects22.

Figure 4 presents transport data for a third graphene nanoribbondevice (GNR3: w ≈ 14 nm, L ≈ 60 nm, Fig. 4a inset), which alsoexhibits a high p-channel conductance and a sharp dip near theDirac point at low temperatures, with an estimated Eg ≈ 49+15 meV (Supplementary Fig. S2). At 4.2 K, the differential conduc-tance plot near the Dirac point showed a single large diamondcorresponding to the bandgap, albeit with a gate switching eventat Vgs ≈ 8 V (Fig. 4b).

Our control experiments found that lithographically patternedgraphene nanoribbons30 generally showed lower conductance anddefect dominant transport characteristics at low temperatures (seeSupplementary Information and Supplementary Fig. S6), similarto previous reports5–9. A fraction of nanoribbon devices fromunzipped nanotubes did not show well-defined quantum transportsignatures, especially for long nanoribbons (SupplementaryInformation and Supplementary Figs S7, S8). These nanoribbonsalso exhibited lower conductance and mobility, probably due to alower ribbon quality.

Taken together, our results show that the quantum transportfeatures of graphene nanoribbons are highly reflective of ribbonquality. We note that a recent paper reported improved quality ofgraphene nanoribbons derived from heavily oxidized nanotubesby annealing31. However, signatures of a transport gap were stillpresent in those nanoribbons. The room-temperature on-stateconductivities of GNR1 and GNR2 shown here are �700 and�800 times higher than a typical device reported in ref. 31. Ourgraphene nanoribbons differ from carbon nanotubes, with a fractionof the ribbons exhibiting conductance levels exceeding 4e2/h, aswell as twofold electron shell filling, and from previous lithographicnanoribbons without overwhelming effects of the transport gap.High-quality graphene nanoribbons may have potential as newtypes of quantum wires for exploring new physics (such as magneticedge states2,3) and device concepts (such as spin qubits4) not poss-ible in seamless nanotubes.

MethodsGraphene nanoribbon making. High-quality nanoribbons were synthesizedfrom multiwalled carbon nanotubes according to the method in ref. 10.Briefly, multiwalled carbon nanotubes (Aldrich 406074-500MG, producedby the arc discharge method: diameter, 4–15 nm; number of walls, 5–20)were calcined at 500 8C for 2 h. The calcined nanotubes (15 mg) and 7.5 mgpoly(m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene) (PmPV) werethen dissolved in 10 ml 1,2-dichloroethane and sonicated for 1 h. The solutionwas ultracentrifuged at 40,000 r.p.m. for 2 h and the supernatant collected forexperiments. Most nanoribbons in the final products were 1–2 layers thick10,11.

a

1

2

4

2

4

6

L ~ 60 nmw ~ 14 nm

4

6

0.1

60b

0

20

40

−40

−20

V ds (

mV

)G

(e2 /

h)

109876Vgs (V)

40200−20−40Vgs (V)

−60

1.0

0.5

0.0

290 K250 K200 K150 K100 K50 K

100 nm

Figure 4 | Electron transport of GNR3 (L ≈ 60 nm). a, Low-bias (Vds¼1 mV) G–Vgs characteristics under various temperatures down to 50 K.

Inset shows the AFM image of the device. b, Differential conductance as a

function of Vgs and Vds near the bandgap, showing single electron charging

behaviour. The central diamond (with size �55 meV as marked by the solidblue lines) corresponds to the bandgap of the nanoribbon. There was a gate

switching event near Vgs ≈ 8 V marked by the arrow.

LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2011.138

NATURE NANOTECHNOLOGY | VOL 6 | SEPTEMBER 2011 | www.nature.com/naturenanotechnology566

© 2011 Macmillan Publishers Limited. All rights reserved.

http://www.nature.com/doifinder/10.1038/nnano.2011.138www.nature.com/naturenanotechnology

Graphene nanoribbon device fabrication. The high-quality nanoribbon solutionwas spun on 300 nm SiO2/p

þþ silicon substrate with pre-patterned metal markers,and AFM was used to locate individual 1–2-layer nanoribbons. Although somenanotubes were also deposited on the substrate, they were quite easy to recognizedue to their much larger apparent height (.� 4 nm) than the nanoribbons(,�1.8 nm) under AFM (Fig. 1a,b). Extra care was taken to avoid contactingnanotubes during the device fabrication process, which was confirmed again bycarrying out AFM on the finished devices. Electron-beam lithography was used topattern the source/drain, followed by evaporation of 20 nm palladium and metallift-off to form metal leads. The devices were finally annealed in argon at 200 8C for�15 min to improve the contacts.

Low-temperature measurement setup. The graphene nanoribbon devices weremounted in a variable-temperature insert for low-temperature measurements.The G–Vgs characteristics of the nanoribbon devices were measured during cooldowns using a standard semiconductor analyser (Agilent 4156C) with a low biasof Vds¼ 1 mV. Below �50 K, we switched the measurement setup to a standardlock-in setup. We used two separate programmable d.c. sources (Keithley 237) forVds and Vgs and measured the differential conductance using a lock-in amplifier(Stanford Research Systems SR830).

TEM analysis. TEM samples were made on porous silicon grids (SPI Supplies,US200-P15Q UltraSM 15 nm porous TEM windows), and TEM was performedusing an FEI Tecnai G2 F20 X-TWIN with an operating voltage of 200 kV.

Received 9 June 2011; accepted 18 July 2011;published online 28 August 2011

References1. Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Edge state in

graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev.B 54, 17954–17961 (1996).

2. Son, Y-W., Cohen, M. L. & Louie, S. G. Energy gaps in graphene nanoribbons.Phys. Rev. Lett. 97, 216803 (2006).

3. Son, Y-W., Cohen, M. L. & Louie, S. G. Half-metallic graphene nanoribbons.Nature 444, 347–349 (2006).

4. Trauzettel, B. et al. Spin qubits in graphene quantum dots. Nature Phys. 3,192–196 (2007).

5. Han, M. Y., Brant, J. C. & Kim, P. Electron transport in disordered graphenenanoribbons. Phys. Rev. Lett. 104, 056801 (2010).

6. Todd, K., Chou, H-T., Amasha, S. & Goldhaber-Gordon, D. Quantum dotbehavior in graphene nanostrictions. Nano Lett. 9, 416–421 (2009).

7. Gallagher, P., Todd, K. & Goldhaber-Gordon, D. Disorder-induced gap behaviorin graphene nanoribbons. Phys. Rev. B 81, 115409 (2010).

8. Stampfer, C. et al. Energy gaps in etched graphene nanoribbons. Phys. Rev. Lett.102, 056403 (2009).

9. Molitor, F. et al. Transport gap in side-gated graphene constrictions. Phys. Rev. B79, 075426 (2009).

10. Jiao, L. et al. Facile synthesis of high-quality graphene nanoribbons. NatureNanotech. 5, 321–325 (2010).

11. Xie, L. et al. Graphene nanoribbons from unzipped carbon nanotubes: atomicstructures, Raman spectroscopy and electrical properties. J. Am. Chem. Soc.113, 10394–10397 (2011).

12. Tao, C. et al. Spatially resolving spin-split edge states of chiral graphenenanoribbons. Preprint at http://arXiv.org/abs/1101.1141 (2011).

13. Wang, X. et al. N-doping of graphene through electrothermal reactions withammonia. Science 324, 768–771 (2009).

14. Wang, X. et al. Room-temperature all-semiconducting sub-10-nm graphenenanoribbon field-effect transistors. Phys. Rev. Lett. 100, 206803 (2008).

15. Li, X., Wang, X., Zhang, L., Lee, S. & Dai, H. Chemically derived, ultrasmoothgraphene nanoribbon semidonductors. Science 319, 1229–1232 (2008).

16. Chen, Z., Lin, Y-M., Rooks, M. J. & Avouris, P. Graphene nano-ribbonelectronics. Physica E 40, 228–232 (2007).

17. Lin, Y-M. & Avouris, P. Strong suppression of electrical noise in bi-layergraphene nanodevices. Nano Lett. 8, 2119–2125 (2008).

18. Wang, J. & Lundstrom, M. Ballistic transport in high electron mobilitytransistors. IEEE Trans. Electron. Dev. 50, 1604–1609 (2003).

19. Liang, W. et al. Fabry–Perot interference in a nanotube electron waveguide.Nature 411, 665–669 (2001).

20. Javey, A. et al. Ballistic carbon nanotube field-effect transistors. Nature 424,654–657 (2004).

21. Kouwenhoven, L. P. et al. in Mesoscopic Electron Transport NATO AdvancedStudy Institutes, Ser. E, Vol. 345 (eds Sohn, L. L. et al.) 105–214 (Kluwer, 1997).

22. Jarillo-Herrero, P. et al. Electron–hole symmetry in a semiconducting carbonnanotube quantum dot. Nature 429, 389–392 (2004).

23. Wehling, T. O., Katsnelson, M. I. & Lichtenstein, A. I. Impurities on graphene:midgap states and migration barriers. Phys. Rev. B 80, 085428 (2009).

24. Kong, J. et al. Chemical profiling of single nanotubes: intramolecular p–n–pjunctions and on-tube single-electron transistors. Appl. Phys. Lett. 80,73–75 (2002).

25. Kouwenhoven, L. P. et al. Excitation spectra of circular, few-electron quantumdots. Science 278, 1788–1792 (1997).

26. De Franceschi, S. et al. Electron cotunneling in a semiconductor quantum dot.Phys. Rev. Lett. 86, 878–881 (2001).

27. Bockrath, M. et al. Single-electron transport in ropes of carbon nanotubes.Science 275, 1922–1925 (1997).

28. Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor.Nature 391, 156–159 (1998).

29. Biercuk, M. J. et al. Electrical transport in single-wall carbon nanotubes.Top. Appl. Phys. 111, 455–493 (2008).

30. Wang, X. & Dai, H. Etching and narrowing graphene from the edges.Nature Chem. 2, 661–665 (2010).

31. Shimizu, T. et al. Large intrinsic energy bandgaps in annealed nanotube derivedgraphene nanoribbons. Nature Nanotech. 6, 45–50 (2011).

32. Tan, C. L. et al. Observations of two-fold shell filling and Kondo effect ina graphene nano-ribbon quantum dot device. Preprint at http://arXiv.org/abs/0910.5777 (2009).

33. Liang, W., Bockrath, M. & Park, H. Shell filling and exchange coupling inmetallic single-walled carbon nanotubes. Phys. Rev. Lett. 88, 126801 (2002).

34. Nygard, J., Cobden, D. H. & Lindelof, P. E. Kondo physics in carbon nanotubes.Nature 408, 342–346 (2000).

35. Buitelaar, M. R. et al. Multiwall carbon nanotube as quantum dots. Phys. Rev.Lett. 88, 156801 (2002).

36. Chen, J-H. et al. Tunable Kondo effect in graphene with defects. Nature Phys.http://dx.doi.org/10.1038/nphys1962 (2011).

37. Moriyama, S. et al. Four-electron shell structures and an interactingtwo-electron system in carbon-nanotube quantum dots. Phys. Rev. Lett. 94,186806 (2005).

38. Lin, Y-M., et al. Electrical observation of subband formation in graphenenanoribbons. Phys. Rev. B 78, 161409(R) (2008).

39. Liang, X. et al. Formation of bandgap and subbands in graphene nanomesheswith sub-10 nm ribbon width fabricated via nanoimprint lithography. NanoLett. 10, 2454–2460 (2010).

AcknowledgementsThe authors thank D. Goldhaber-Gordon for helpful discussions. The work at Stanford wassupported in part by the Office of Naval Research (ONR), the ONR Graphene MURI,MARCO MSD Focus Center and Intel. Aberration corrected transmission electronmicroscopy was performed at the NCEM at Lawrence Berkeley Lab, which was supportedby the US Department of Energy (contract no. DE-AC02-05CH11231). The work atUniversity of Florida was supported in part by the National Science Foundation (NSF)and the ONR.

Author contributionsX.W. and H.D. conceived and designed the experiments. X.W. and J.W. fabricated thedevices, performed the experiments and analysed the data. Y.O. and J.G. performedsimulations. L.J. provided graphene nanoribbon samples. H.W. and L.X. performed TEMcharacterizations. X.W., Y.O., J.G. and H.D. co-wrote the paper. All authors discussedthe results and commented on the manuscript.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper at www.nature.com/naturenanotechnology. Reprints andpermission information is available online at http://www.nature.com/reprints. Correspondenceand requests for materials should be addressed to H.D.

NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2011.138 LETTERS

NATURE NANOTECHNOLOGY | VOL 6 | SEPTEMBER 2011 | www.nature.com/naturenanotechnology 567

© 2011 Macmillan Publishers Limited. All rights reserved.