Exceptional,ballistic,transport,in,epitaxial, graphene,nanoribbons,

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1 Exceptional,ballistic,transport,in,epitaxial, graphene,nanoribbons,, Jens%Baringhaus 1% Christoph%Tegenkamp 1,%Frederik Edler 1, Ming%Ruan 2,%Edward%Conrad 2,% Claire%Berger 2,3,%Walt%A.%de%Heer 2 *% 1 Institut für Festkörperphysik, Leibniz Universität, Hannover, Appelstrasse 2, 30167Hannover,Germany 2 SchoolofPhysics,GeorgiaInstituteofTechnology,GA30332K0430Atlanta,USA 3 CNRSKInstitutNéel,38042Cedex6,Grenoble,France *correspondingauthor Graphene3based, high3performance, nanoelectronics, motivates, most, graphene, research., However, conventionally, produced, graphene, nanostructures, and, ribbons, in, particular, are,highly, resistive, and, therefore, ineffective.,we,have,produced,arrays,of,thousands,of,~40,nm,wide,graphene, nanoribbons, grown, on, thermally, annealed, steps, etched, in, single, crystal, silicon, carbide., Their, resistances, are, consistently, close, to, the, resistance, quantum,, essentially, temperature, independent, and, depend,only, slightly, on, ribbon, length, consistent, with, ballistic, transport., Resistivities, are, up, to,50, times, smaller, than, copper,, and, more, than, 1000, times, smaller, than, lithographically, patterned, graphene, ribbons, at, room, temperature., A, non3 linear, resistance, increase, observed, for, ribbons, longer, than, 15, µm,, suggests, room,temperature,phase,coherent,transport.,ballistic,transport,is,confirmed, in, cryogenic, transport, measurements, on, electrostatically, gated, graphene, ribbons., Our, unprecedented, observations, are, consistent, with, polarized, transport, in, an, edge, state., Our, ribbons, are, ideal, for, nanographene, device, interconnects,and,may,be,applied,in,non3conventional,electronics., The concept of digital graphene nanoelectronics 1,2 was based on a decade of priorcarbonnanotubeselectronicsresearch.defectfreemetalliccarbonnanotubes are ballistic conductors with micron scale mean free paths 3,4. Similarly graphene ribbons were also expected to be ballisticconductors andideal interconnects in nanographene circuits 1. However narrow lithographically patterned graphene ribbons were found to have low mobilities and transport gaps on the order of 1eV/W (W is the nanoribbon width in nm) 5. It was subsequently found that their edges are disordered causing strong localization of the charge carriers, and large mobilitygaps 6K8.Thelowmobilitiesinthesedisorderednanoribbonsprecludetheir usesinhighkperformancenanoelectronics. In order to overcome the disorder caused by nanolithographic processes, a structuredgrowthprocesswasdeveloped 9.InthismethodgrapheneribbonsselfK

2 assemble on steps that are etched into electronicskgrade singlekcrystal silicon carbide wafers. Heating the steps that are etched into the (0001) surface of hexagonal SiC to temperatures greater than 1100 C causes graphene ribbons to form on the sidewalls of the steps 9K13. This selective growth results from the significantly slower growth rates on the (0001) face compared with other silicon carbidecrystalfaces 9K13. Intheheatingprocess,thenominallyverticalsidewallsannealandrecrystallize toformwellkdefinedsiccrystalfacets,whichhaveaslopeofabout25 withrespect to the horizontal 11K13. Figure. 1a schematically shows the structure of sidewall graphene layer that is consistent with observations and established properties of epitaxial graphene grown on sidewalls. Accordingly we assume that the bottom edgeiscovalentlybondedtothesubstrate 14.Thetopedgeofthesidewallgraphene seamlesslyconnectstothesemiconductingbufferlayer 15K17 onthetopsurface,as shown in Ref. 14. Consequently the two edges are dissimilar which may affect the transportproperties.theexactmorphologyofthegrapheneribbonishowevernot essentialforourpurposeshere,whereweconcentrateonthetransportproperties of the ribbons. We show below that the transport properties are not critically sensitive to the crystallographic orientation of the step, or to the width of the grapheneribbons.extendedarraysofthesesidewallribbons,withwidthsranging from20to100nmhavebeenproducedusingthismethod(fig.1b). AngleKresolvedphotoemissionspectroscopy(ARPES)studyofgrapheneonparallel arraysofthesesidewallribbonsshowsthatthebandstructurecorrespondstothat ofagraphenemonolayer 18 (Fig.1c).Thesemeasurementsshowthatthesidewall grapheneribbonsaremetallicandslightlyndoped:thediracpointisabout~100 mev below the Fermi level. ARPES measurements of the horizontal surfaces does not show a significant graphene signalindicating that the graphene is confined to the sidewalls. The fact that a wellkdefined Dirac cone is observed in ARPES shows that the ribbons are wellkaligned and that the sidewall slope is uniform (28 consistent with the (2K207) facet) for the approximately 1000 ribbons that contributetothearpessignal.(theabsenceofquantumconfinementinducedfine structurehasbeenexplained 13 ). Note that recent ARPES studies 13 have also shown that the curved graphene that coversthetopedgeisfoundtobesemiconductingwithabandgaplargerthan0.5ev, possibly due to curvature effects 13. In those studies graphene was deliberately overgrowntocoverthetopofthesidewalls 10. Scanning tunneling spectroscopy measurements confirm that the graphene on the sidewalls is metallic and that the horizontal surfaces (i.e. the SiC substrate, covered with a buffer layer 15K17 ) are semiconducting (Fig.1d). MicroKRaman measurements show a single Lorentzian 2D peak, consistent with monolayer graphene and a relatively intense D peak that is due to finite size effects in the narrow ribbon 19 (Fig. 1e). Ribbon widths are measured using electrostatic force microscopy(efm)conductivekatomicforcemicroscopy(ckafm),fig.2,andspatially

3 resolved STS methods. A deconvolution procedure that reliably adjusts for tip radiuseffects 20. Wenextdiscussthetransportpropertiesoftheribbons.Anarrayof20nmdeep parallel trenches was etched along the [1100] direction, that favors zigzag edges (Fig. 1a). After graphitization, graphene decorates the 28 sloped sidewalls to produce40nmwideribbons.theresistancesofthegrapheneribbonsaremeasured usingafourprobescanningtunnelingmicroscope(stm).inthesemeasurements,a ribbon from the array is selected and four STM probes are placed on ribbon as showninthescanningelectronmicroscopy(sem)image(fig.3a).acurrenti12is passedthroughouterprobesandthepotentialdifferencev34betweenthetwoinner probes (separated by a distance L) is measure. The four point resistance of the ribbon segment is R4pt(L)=V34/I12. The fourkpoint measurement (for diffusive conductors) is insensitive to the contact resistances. A histogram of the conductancesg=r K1 of40ribbonswithl 1K5µmtemperatures30 T 300(Fig,3b lowerinset)showsaremarkablepeakag0=r0 K1 (R0=h/e 2 =25.8kΩ). TheribbonresistancesdependlinearlyonL(Fig.3b): R(L)= ΔR+R L= R0(α+L/L0) (1) wherer istheresistanceperunitlength,l0=r0/r,andδr=αr0isanoffset.for these 5 ribbons, measured at room temperature, <α> = 0.98±0.02 andl0 ranges from4µmto58µm.thisresultisstrikingsinceordinarilyoneexpectsthatr(l)=ρ L/WwhereWistheribbonwidthandρ=R W=R0W/L0isthesheetresistancein Ω per square. However the offset resistance that dominates the resistance is indicative of ballistic transport. The dispersion in L0 correlates with the sample annealingconditions(seeexperimentalmethods). Forthetwooptimizedribbonsmeasuredatroomtemperature(Fig.3bupperinset) α= 1.04 and 0.98; L0 = 560 µm and 900 µm; and ρ=1.2 and 1.8 Ω per square. In contrast,thesheetresistanceofneutralgrapheneρ~6kωpersquare;fora0.3nm coppersheetisρ=56ωpersquare.moreover,forlithographicallyproducedribbons ofcomparablewidth 21 ρ>20kω persquareandisstronglytemperaturedependent. The resistance of the nanoribbons exhibits an exceptionally weak temperature dependence(fig.3d)increasingbylessthat2%from30kto300k,whichimplies that electronkphonon coupling is small. Note that there is some similarity with ballisticcarbonnanotubes 4,butforthenΔR=R0/4;L0<1µm(atroomtemperature), andtheresistanceincreasesbyafactorof10from50kto300kduetothelarge electronkphononcoupling. The offset resistance ΔR~h/e 2 is important. The conductance G of a onek dimensionalconductorwithnoccupiedsubbandscaningeneralbewritteninterms ofthelandauerequation(see,forexample 22 ):

4 G=(e 2 /h)σgntn (2) Where 0 TN 1 is the transmission coefficient of the N th onekdimensional subbandwithdegeneracygnandthesummationisoverthesubbandsthatthefermi levelcrosses(eg.fig.1f).inthetightbindingapproximation,thebandstructureofa chiralgrapheneribbon(i.e.anonkarmchairribbon)[wakabayshi]issimilartothat of zigzag ribbons (Fig. 1f ). In particular, like zigzag ribbons, chiral ribbons have edgestates(n=0,fig.1f)withadegeneracygn=0=2denotebyn=0 ±,(forthetwospin directions)forg N 1=4,(duetospinandvalleydegeneracies). IfonlyonenonKdegeneratesubband,sayN=0 +,contributestothetransportthen G=(e 2 /h)t0so that R=(h/e 2 )T0 K1. If the conductor has elastic scattering centers, withanaveragespacingofl0,thatperfectlyrandomizethedirectionofthecarriers so that scattering occurs with equal probability in the forward and backward direction, then the transmission probability can be expressed by T0=(1+L/L0) K1 (Ref. 22 )(ActuallyL0measuresthelengthrequiredsothatT0=1/2,notnecessarily the average distance between scattering centers; backscattering from a specific scatterermaybemuchsmallerthan½ 22.)Ineithercase: R(L)=(h/e 2 )(1+L/L0). (3) which is what we measure within a few percent. Hence our experiments suggest thattransportinballisticandinvolvesonlyasinglenonkdegeneratechannel. Ifidealinvasiveprobes 22 4 areused,r(l)willbemeasuredbothin2andin4 pointmeasurements.anidealinvasiveprobeactsasascatteringcenterwitht=1/2 that randomizes the carrier direction, so that half of the charge carriers are back scatteredattheprobes.thispropertyultimatelyaccountsforδrinballisticribbons. We observed the scattering property of probes as follows (see Fig. 3c). We contacted a ribbon with two probes and found(as usual) the twokpoint resistance R12=R0. When a third probe contacted the ribbon (Fig. 3c), and R12 essentially doubled(itreturnedtoitsoriginalvaluewhentheprobeiswithdrawn).whenthe fourthprobewasintroduced,r12essentiallytripled.theexperimentwasperformed atroomtemperatureontworibbonswithsixseparatetipapproachesoneach.the experiment(whichhasnoclassicalexplanation)isimmediatelyexplainedinterms ofthelandauerequation.forsinglechannelr=h/e 2 (assumingl0>>l)scatteringat thepassiveprobesreducesthetransmissionsothatr12=(h/e 2 )TPP K1 =2h/e 2 (inthe ideal case when TPP=1/2). When a second passive probe is added, then multiple scatteringbackandforthbetweentheprobesmustbeconsidered 22 sothatr12=(2 TPP K1 K1) h/ e 2 = 3 h/ e 2 in the ideal case (see Fig. 3c). Experimentally we find on averagethattpp=0.59forasinglepassiveprobeandtpp=0.56for2passiveprobes showing that the probes are close to ideal. Most importantly, this experiment

5 stronglyconfirmsthatthetransportisballisticandinvolvesonlyasingleconducting channel(seealsobelow). We nextdiscussthenonklinearlyobservedinthelongribbons(fig.3binset).for L>15 µm: R R0( exp(L/L*)) where L*=5.6 µm. For L<5 µm, R 30Ω/µm (ρ 1Ω/square). The striking (exponential) increase is reminiscent of Anderson localization, however, the resistance prefactor, is anomalous. The nonk linearity is intriguing because it suggests phase coherence, which that is not expectedatroomtemperatureattheµmlengthscale.neverthelesstheabsenceof temperature dependence of the resistance (in stark contrast with nanotubes 4 ) is consistentwithcoherenttransport.clearlymoreworkisrequiredforverification. It is clear that the transport in graphene sidewall ribbons is well explained in terms of a single conducting channel with a mean free path L0 that extends up to tensofmicrons(seefig.3b).togainfurtherinsightwerewriteeq.asfollows G/G0=(1+L/L0+) K1 + (1+L/L0K) K1 + Σ Ν 1gNTN (4) therebyseparatingoutthen=0 + andn=0 K contributions.atlowtemperature,when EF Emin1 thent N 1=0sothatonlythefirsttwotermcontribute(Fig.1f).When EF Emin1 the third term contributes and steps may be expected when EF=Emin1. In factconductancestepsδg 0.5µShavebeenobservedatT=33KbyLinetal 21 in lithographicallypatterned,1.7µmlong,30nmwideribbonssuppliedwithagate.in their case, from Eq. 4 we deduce that L0=2 nm and L N 1=4 nm (T0=1.1 x10 K3 ; TN 1=2.5x10 K3 ).Thesesmallvaluesareduetothestronglocalizationcausedbyedge disorder 6,7.Inourcase,L0ismorethanafactorof10 5 larger. TotestEq.4weproducedseveralsidewallribbonsamples,suppliedwithatop gatesothatthechargedensitycanbevaried.figure4showstheresultsforaw=39 nm L= 1.6 µm graphene sidewall ribbon. The ribbon was seamlessly connected to ~1µmwidegraphenesidewallpadstoproduceanHshapedgeometry(Fig.4e).Two metalcontactswereprovidedoneachofthetwopads(onthetopandbottomofthe verticals of the H) facilitating 4 point measurements as indicated. A 20 nm thick alumina film covered with gold formed the gate (Fig.4e). The resistance of the grapheneribbonwasmeasuredasafunctionofgatevoltagevgandtemperaturet. This graphene ribbon was formed on a natural step connecting the sidewall graphene contact pads. Spurious conducting paths between the graphene contact padswereetchedbyreactiveionetchingaftermasking.thechargedensityinduced on the ribbon by the top gate voltage Vg is n(vg)=kvgx cm K2 that was calibratedusingasimilarlyproducehallbar. TheconductanceG(Vg,T)(Fig.4a)showsseveralimportantfeatures.Forpositive Vg at T=4K the conductance increases from 0.95 G0 to 1.4 G0, for negative Vg it increases from 0.95 G0 to 1.15 G0. In contrast to Lin et al 21 the response is asymmetric with respect to Vg. A minimum is found near Vg=0(as expected when

6 EF=0). Weak stepklike features are observed in G(Vg) for positive Vg (Fig. 4a). In particularaplateauatg=1.2g0isseenforvg=1.v.forreference,fora39nmzigzag ribbon,stepsmaybeexpectedwhenefcoincideswithsubbandminimaenmin,i.e.at E±1=±90; E±2± 150; E±2±210 mev etc.thisoccurswhenvg= ± 0.6; ±1.7; ±3.2 V. ConsequentlythestepatVg=1VmaybeduetotheN=1subband.ConsequentlyT N 1~ 3x10 K2. Assuming that TN=(1+L/LN) K1 we find that LN 50 nm, which is comparabletotheribbonwidthandafactorof10greaterthanlinetal.reported Thereisnoindicationofstronglocalizationhoweverscatteringissignificantatthe ribbonedgesforthesestates.ontheotherhand,foref=0(i.e.vg=0)att=0onlythe N=0 states contribute. We find that T0=0.91(see below) corresponding to L0= 17 µm(consistentwiththemeasurementsinfig.3).thisisafactorof340greaterthan LN 1subbands.ThisanalysisshowsthattheN=0subbandisindeedexceptional.It should be noted that when L= 5 µm, TN 1 =(1+L/L N 1) K1 10 K3 so that their contribution to the conductance is minimal. That is, for sufficiently long ribbons, onlythen=0subbandcontributestothetransport. Note that G(Vg,T) can be approximated by G(Vg,T) =G(Vg,T=4K)+GN=0(T). Since weestablishedthatn=0 + subbandhasno(significant)temperaturedependence(fig. 3d),weconcludethatGN=0(T)islikelyduetoN=0 K subband.byfittingwefindthat fort 100K,G(Vg=0,T)=GN=0++GN=0K(T) 0.91G TG0;GN=0K(T)appearsto saturateatg=0.3g0atroomtemperature,implyingthattn=0k=0.33(l0k=0.5µm)at roomtemperatureand0.07at4k(l0k=0.1µm).hencewetentativelyconcludethat the N=0 K subband has a relatively large mean free path (compared with the N 1 subbands)butitappearstobesubjecttolocalizationeffects(incontrasttothen=0 + andthe N 1subbands). Reproducible conductance fluctuations (ΔG(Vg,T=4K)~ 0.03 G0) are observed (Fig. 4a,inset).Theiramplitudesareontheorderoftheconductancedip(ΔG(B,T=4K)~ ~0.05G0)astypicalforweaklocalization(Fig.4b).SincetheyarepresentforVg=0, anditsamplitudeisofthesameorderasgn=0k(t=4k)wetentativelyascribethemto then=0 K subband. The conductance G(Vb,T) (Fig. 4c) has a zero bias voltage (Vb) dip. G(Vb) increases with increasing Vb and saturates at G 1.2 G0 For Vb 50 mv, G(Vb,T) is independentoft.wepreviouslydeterminedthatthen=0 K subbandisresponsible fortemperaturedependenceoftheconductance.sincethetemperaturedependence diminishesathighbiasimpliesthattheconductancedipisapropertyofthen=0 K subband aswell. The streaked appearance of G(Vg,Vb) corresponds to Vg/Vb=1.47, showingthat,likevg,vbalsoaffectsef(asexpected). The asymmetry of the G(Vg) (Fig. 4a) is intriguing and may be explained as follows. Since the unkgatedleadstothegrapheneribbonareslightlyndoped (as observedinarpes,fig.1c)thenwhenthegatepkdopestheribbon(i.e.fornegative Vg) a pn junction forms at the ribbonktoklead contact. The spatial extent of the pn junctioniscomparabletothedielectricthickness(20nm) 23 whichisshorterthan

7 themeanfreepathl N 1,(seeabove).Consequently,transportpastthejunctionfor these channels is suppressed (see 23,24 ) however it is not suppressed for the N=0 channel 22,23, essentially because of its metallic character (rather than Klein tunneling asinthe2dcase 22,23 ). Summarizing, the data presented here demonstrate that transport in long graphenesidewallribbonsisdominatedbyasingleconductingchannelwithamean free path that can exceed tens of microns. The channel conducts at EF=0, which impliesthattheribbonsaremetallic.itisknownthatonlythesubbandassociated with the edge state provides transport at EF=0 in narrow graphene ribbons. Consequently,thesubbandwithaconductanceof1G0isanedgestate.Wefindthat the contributions due to other subbands are much smaller, consistent with mean free paths on the order of the ribbon width. Therefore transport involving those channels is diffusive on the micron scale.thepropertiesobservedherehavenot been seen in lithographically produced graphene ribbons, that are found to be subject to strong localization effects at low temperatures causing significant mobilitygaps. The ballistic transport properties observed here may be explained in terms of the topological properties of the edge state (which exists for all ribbons except armchairribbons 25K27 ).Referringtothegenericbandstructurediagram(Fig.1f)we note that for EF E1min only the N=0 subband contributes to the transport. We furthernotethatinthisenergywindow,efinterceptsthissubbandonlytwice,once forpositivekatk + andoncefornegativekatk K (correspondingtothetwovalleys) The group velocity v0(k + )=de0(k + )/dk <0 and v0(k K )=de0(k K )/dk =Kv0(K + )>0. Consequently,elasticallybackscatteringrequiresamomentumchangeΔp= (K + KK K )= Δktobeimpartedtothecarriers.Howeverthisrequiresdisorderontheatomic scale. If the ribbon edges are wellkformed then scattering will be inhibited. Hence, transport in the N=0 subband is protected 25K27. Note that the argument does not applyforn 0(cfFig.1f). Thispropertyofgrapheneribbonswithgeneralchiraledgeshasbeenpredicted bywakabayashietal. 25,26 whodemonstratedverylongmeanfreepathsintransport simulations of ribbons with wellkformed edges (zigzag or chiral), even in the presence of relatively large impurity concentrations. They showed that the perfectlyconductingchannel propertywasdirectlyrelatedtotheimbalanceinthe forwardandbackwardmovingstatesineachvalley(thatpersistsoutsidetheenergy window EF E1,Fig.1f).Whiteetal. 27 alsopredictedballisticconductioninthe presenceofimpuritiesfromsimulations.(however,weobservetransportinasingle nonkdegenerate channel: g0=1 while the above theories predict for the edge state thatg0=2duetothespindegeneracywhichisnotaccountedfortheoretically.)note thatif this interpretation is correct then it follows that for long graphene sidewall ribbons,electronictransportisvalleypolarized,wherepositivecurrentsarecarried inthek K valleyandnegativecurrentsarecarriedinthek + valley(cf.fig.1d).

8 It is clear that the experimental result agree in considerable detail with the properties expected for a protected edge state. In fact, the high temperature annealingisexpectedtoproduceribbonswillwellkformededgesthatarecovalently bondedtothesiliconcarbide,asexperimentallyshowninbynorimatsuetal. 14 who furtherprovideevidencethatcovalentlybondededgesarepreferablyzigzag. Thedataconclusivelyshowthattheconductanceofthemetallicsubbandise 2 /h andnot2e 2 /h.wenotedabovethatthetwoedgesaremostprobablydistinctwhich isexpectedtoaffectthetransportintheedgestate.anotherpossibleexplanationis thatthetransportisspinpolarized,whichisinagreementwithseveralpredictions ofspinpolarizationinedgestates 28,29.Moreover,experimentscurrentlyunderway strongly support that the transport is spin polarized and these results will be published later. In any case, room temperature ballistic transport has been demonstrated on an unprecedented length scale. Furthermore, transport involves onlyasingleballisticchannel,whichinabsenceofamagneticfield,isnotexpected. Finally, the reversible effect of a passive probe (which is an indisputable ballistic conductor property) had not been demonstrated before. Hence we have demonstrated that robust ballistic nanoribbons are easily and reliably made on a largescale. Dissipationless transport is obviously of considerable importance for future graphene nanoelectronics, in particular considering that the graphene at the top edge of the sidewall is semiconducting as recently demonstrated 13. This combination suggests a transistor where two ballistic graphene ribbons are connectedbyasemiconductinggraphenestrip.afieldeffecttransistorisformedby applyingagateoverthesemiconductor.ontheotherhandifthetransportisindeed spin and valley polarized, asit well may bethecase,then this may lead to novel spintronic 30 andvalleytronic 31 devices 28,29,31.Moreover,iftheseribbonsareinfact quantum mechanically phase coherent on the micron scale at room temperature, thenthiswillleadtotheintriguingpossibilityofroomtemperaturephasecoherent devices. Experimental,methods, Grapheneribbonswereproducedbythermallyannealing 10 eithernaturaloretched stepsonthe(0001)faceofelectronicsgradesic 9,11,12.Etched20nmdeeptrenches, aligned along the[1100] direction,(which is favorable for the formation of zigzag edges, Fig. 1a) and annealed at 1600 C for 15 min. as described in Ref. 20, This methodwasusedthesamplesinfigs.1band4.samplesinfig.3werefirstheated to1150 Candsubsequentlyto1300 Cinan410 K5 mbaratmosphere,afterwhich theywereheatedinuhvfor15minat1100 C(green,Fig.3b)or1150 C(allothers). Thenaturalstepsampleswerepreparedonchipsthatwereprovidedwithtwo200 nmdeeptrenchedthatwereseparatedby1µmwithanaturalstepthatconnected thetwoandannealedassamplesinfig.4 20.

9 AFMandCKAFMwereusedtomeasuretheribbonwidths(see 20 )andtomeasure theultimatesidewallslopes.sem,afm,efmandckafmwereusedforfig.2.arpes (Fig. 1 d) wasusedforgraphene bandstructure measurements, to determine the number of graphene layers and to measure the sidewall slopes 13. Micro Raman spectroscopy(fig.1e)verifiesquality 20. AnOmicronNanoprobesystem(inHannover),fortemperaturesfrom30Kto300K (usingtungstentips)wasusedforthemultiprobemeasurementsinfig.3.theset pointforsts(fig.1d)was2v/0.1na.probeswerepositionedusingabuiltkinsem (Fig. 3a). The resistance between neighboring ribbons was >500 kω. A Janis variabletemperaturecryostatsystem(fortemperaturesfrom4kto300k)witha9 T magnet was used for the measurements(in Atlanta) reported in Fig. 4. Samples weremeasuredusingstandardtransporttechniques 20. Acknowledgements, CT thanks the German Research Foundation Priority Program 1459 Graphene for financial support. CB, EC, and WdH thank Rui Dong, Zelei Guo, John Hankinson, Jeremy Hicks, Yike Hu, Zhigang Jiang, Markus Kindermann, Jan Kunc, AnKPing Li, MeridithNevius,JamesPalmer,AntonSiderovandPaulGoldbartforassistanceand comments. CB, EC, and WdH thank the AFOSR, NSF, W.M. Keck foundation for financialsupport: JB and FE performed the transport experiments relating to Figs. 3 and 1d. CT performed and conducted the transport experiments, discussed the data and commented on the paper. MR performed all experiments except those relating to Fig.3and1d.ECperformedARPESexperiments.CBandWdHdesignedtheproject, performedtheatlantabasedexperimentsandwrotethepaper.

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12 FigureCaptions Figure1 Structure and characterization of epitaxial graphene sidewall nanoribbons. (a) Schematic diagram of a graphene ribbon on an annealed and facetted sidewall, showing the seamless connection to the covalently bonded semiconducting buffer layeronthetopterraceandthecovalentbondedgrapheneedgeatthebottomedge (see 14 ). (b) AFM image of an array sidewall graphene covered with 20 nm deep trenches(insetshows3dview,verticaldimensionismagnified,roundingisdueto tip effects). (c) ARPES of the sidewall ribbons showing the Dirac point is slightly belowef(i.e.slightlyndoped)(d)stsatt=30k.theabsenceofagapintheribbon indicates that it is metallic; the large gap in the buffer layer indicates that it is insulating.(e)ramanspectraofsidewallribbons(aftersubtractionofsicspectrum). The D, G, 2D peaks (wellkfitted with single Lorenzians as shown) are at , , and cm K1, and the peak widths are 28.3, 19.8 and 39.6cm K1, respectively,consistentwithmonolayergrapheneonthe(0001)siface.(f)generic tightbindingbandstructureofnonkarmchairgrapheneribbon(zigzagorchiral)with lattice constant a. N labels the onekdimensional subbands. Within a window EF Emin1only the N=0 subband (corresponding to the edge state) contributes to transport. In absence of atomic disorder, backscattering (involving the transition indicated in red) is suppressed: transport in this state is protected. When EF Emin1, the N 1 channels contribute to transport. Backscattering for those channelswithinasinglevalleyisallowed(indicatedinblue). Figure2 Sidewallgrapheneribbonona3.3nmstepon6HKSiCimagedusingvariousmethods. (a) AFM, showing upper (light) and lower (dark) terraces. (b) Scanning electron microscopy (SEM, 30 kev) showing a clear contrast between the graphene and substrate.(c)efm,thatshowscontrastduetotheworkfunctiondifferencebetween the substrate and the graphene ribbon.(d) CKAFM that measures the resistance of the ribbon and relies on an electrically continuous path, providing the highest contrast.accuratewidthdeterminationsrequireadeconvolutionofthetipradiusas explainedindetailinref. 20. Figure3 Multiprobe inksitu transport measurements of 40 nm wide graphene sidewall ribbons.(a)semimageshowing4probespositionedonasidewallribbon,withtwo outerprobessupplyingacurrentithroughtheribbon,andtwoinnerprobesforthe potential measurement.(b) FourKpoint(R4pt) and twokpoint(r2pt) resistances as a function of probe spacing L (for ribbon production conditions, see Experimental Methods). Linear fits that extrapolate to R0 within a few percent for L=0. Slopes correspond to R = 6.2, 1.6, 0.92, 0.44 (K.25) kω/µm from top to bottom corresponding to L0=. 4.2, 28, 16, 58, (K100) µm respectively, (inset) Two point

13 resistances of 2 ribbons measured at room temperature showing essentially identical nonklinear increases for L>15 µm; for small L, R =46 and 28 Ω/µm (corresponding to 1.8 and 1.1 Ω/square), and L0= 560 and 900 µm. (c) Effect of passive probes touching graphene ribbons. A single passive probe essentially doubles the twokpointresistance;twopassiveprobestriplesit,showingthatthe passiveprobesactasscatteringcenters.theshadedareaandopencirclesindicate theoretical limits for an ideal invasive probe (T=1/2) and a nonkinvasive probe (T=0). (Lower inset) Histogram of fourkpoint resistances of unselected ribbons showing a pronounced peak at h/e 2. (d) FourKpoint resistance as a function of temperature(l=5µm)showinglessthat10%changefrom30kto300k. Figure4. Transportingraphenegatedsidewallribbon.(a)ConductanceversusVgforT=4,7, 12, 20, 35, 55 K (bottom to top). Minimum conductance at Vg=0 corresponds to Dirac point (where only N=0 statecontributes;g~1g0 ). Conductance increases slightly for Vg>0 with a 0.2 G0 step at Vg=1V that may correspond to the N=1 subband, indicating T1~0.05. (b) Magnetoresistance (T=4, 7, 12, 20, 35, 55, 80, 120K,bottomtotop)showingΔG=0.05G0conductancedipatB=0.(c)Conductance versusvb,t=4,7,12,20,35,55k(bottomtotop);notetheδg~0.2g0dipatvb=0. (d) Conductance versus Vb and Vg measured at T=4K, showing streaks corresponding to Vb/Vg=1.47. (e) Optical image of sidewall ribbon supplied with leadsandgate.nominalwidthofgatedribbonis39nm;nominallengthis1.6µm. White dashed lines indicate location of the graphene leads, white line indicates graphene ribbon. Green region locates the gate structure. Dark areas are the gold contacts.

14 E&EF(eV)" "µm" -0.2 (b)" -1.5 (a)" 5" " 2D" D" Figure"1" 0" Bias""voltage"(V)" 1" 0" 0.2 ΔE N" &1" &2" &3" 0"" &1" -3.0 (d)" &1" 0.1 3" 2" 1" 0" 1" 0" k(å&1)" 1" Energy" SiC"substrate"" (buffer"layer)" 3" Intensity"(a.u.)" di/dv"(na/v)" 4" -0.1 (c)" G" Sidewall" graphene" " (e)" 2000" 2500" Raman"shi>"(cm&1)" 3000" &1" K- (f)" 0" k"(2π/a)" K+ 1"

15 SEM" AFM" EFM" SEM" C&AFM" 400nm" Figure"2"

16 Resistance (h/e 2 )" (c)" (a)" T=1/2 d L T=0 V I V I V I Number of passive probes" R 4pp (h/e 2 ) R 4pp (h/e 2 ) Conductance ( e 0 2 /h) Inner probe spacing L(µm) R 2pp (h/e 2 ) Frequency L (µm) Temperature (K) (b)" (d)" Figure"3"

17 G(e 2 /h) (a) V g (V) G(e 2 /h) di/dv (e 2 /h) (b) B (T) (c) V b (mv) V b (V) (d) -2-1 V g (V) (e) V b I - I + V - V + V g Figure 4