We report on (magneto)-transport experiments in chemically derived narrow
graphene nanoribbons under high magnetic fields (up to 60 Tesla). Evidences of
field-dependent electronic confinement features are given, and allow estimating
the possible ribbon edge symmetry. Besides, the measured large positive
magnetoconductance indicates a strong suppression of backscattering induced by
the magnetic field. Such scenario is supported by quantum simulations which
consider different types of underlying disorders (smooth edge disorder and long
range Coulomb scatters).Comment: 4 pages, 4 figure

Cresti, Alessandro

Dai, Hongjie

Escoffier, Walter

Goiran, Michel

Li, Xiaolin

Poumirol, Jean-Marie

Raquet, Bertrand

Roche, Stephan

Wang, Xinran

Physical Review B

English

arXiv

Cresti, A.

Roche, S.

Wang, X.R.

Li, X.L.

Dai, H.J.

HAL Descartes

Edge magnetotransport fingerprints in disordered graphene nanoribbons

4 páginas, 4 figuras.-- PACS number(s): 72.80.Vp, 73.22.Pr, 75.47.-m.-- et al.We report on (magneto)transport experiments in chemically derived narrow graphene nanoribbons under high magnetic fields (up to 60 T). Evidences of field-dependent electronic confinement are given and allow estimating the possible ribbon edge symmetry. A large positive magnetoconductance indicates a strong suppression of backscattering induced by the magnetic field. Such scenario is supported by tight-binding calculations which consider different types of underlying disorders (smooth edge disorder and long-range Coulomb scatterers).Part of this work was supported by EuroMagNET, Contract
No. 228043. S.R. acknowledges the ANR/P3N2009
(Project No. ANR-09-NANO-016-01).Peer reviewe

Digital.CSIC

Edge magnetotransport fingerprints in disordered graphene nanoribbonsJean-Marie Poumirol,1 Alessandro Cresti,2,* Stephan Roche,3,4 Walter Escoffier,1 Michel Goiran,1 Xinran Wang,5Xiaolin Li,5 Hongjie Dai,5 and Bertrand Raquet11Laboratoire National des Champs Magnétiques Intenses, INSA UPS CNRS, UPR 3228,Université de Toulouse, 143 avenue de Rangueil, 31400 Toulouse, France2LETI, MINATEC, CEA, F38054 Grenoble, France3INAC, SP2M, Lsim, CEA, 17 avenue des Martyrs, Grenoble, France4CIN2, CSIC-ICN, Campus UAB, E-08193 Barcelona, Spain5Department of Chemistry and Laboratory of Advanced Materials, Stanford University, Stanford, California 94305, USAReceived 13 July 2010; published 30 July 2010We report on magnetotransport experiments in chemically derived narrow graphene nanoribbons underhigh magnetic fields up to 60 T. Evidences of field-dependent electronic confinement are given and allowestimating the possible ribbon edge symmetry. A large positive magnetoconductance indicates a strong sup-pression of backscattering induced by the magnetic field. Such scenario is supported by tight-binding calcula-tions which consider different types of underlying disorders smooth edge disorder and long-range Coulombscatterers.DOI: 10.1103/PhysRevB.82.041413 PACS numbers: 72.80.Vp, 73.22.Pr, 75.47.mThe control of the current flow in graphene nanoribbonsGNRs constitutes a fascinating challenge for the future ofcarbon-based electronic devices. The description of low-energy excitations as massless Dirac fermions in grapheneresulting in large mobility at room temperature1, togetherwith the possibility for band-gap engineering2 suggest astrategy to outperform silicon devices.3,4 However, the lateralsize reduction goes along with a problematic decay of thecharge mobility.4,5 Low-temperature transport measurementson lithographically patterned GNRs unveil an ubiquitousenergy gap, irrespective of the edges symmetry,2 exceedingthe confinement gap6,7 and driven by disorder-inducedcharging effects.8,9 Nonperfect edges are also expected toproduce a significant scattering source. Consequences on theelectronic transport have been theoretically anticipated withthe formation of a mobility gap, even in the presence of anultrasmooth edge roughness.10 Sources of disorder such asbulk vacancies,11 charges in the oxide,7,9 or structuraldeformations12 are also believed to alter the conductance,although the dominant scattering source remains debated. Inthat perspective, experimental works on narrow GNRs re-main sorely lacking.This Rapid Communication presents evidences of theone-dimensional 1D transport character in a 11-nm-wideGNR and the possibility of tuning backscattering effects bymeans of an external magnetic field. Tight-binding calcula-tions allow some assignment of the gate-dependent conduc-tance modulations to the underlying van Hove singularities,and hence some estimation of the likely ribbon edge symme-try. The application of perpendicular high magnetic field fur-ther induces a marked enhancement of the conductance inlarge contrast to the magnetofingerprints of grapheneflakes.13 Close to the charge neutrality point CNP, the mea-sured positive magnetoconductance MC is attributed to theformation of the first Landau state, responsible for the clos-ing of the energy gap and of a marked reduction in back-scattering processes. Conductance simulations support thescenario of an interplay between the magnetic bands forma-tion and a disorder-induced interband scattering suppression.Both edge disorder and long-range Coulomb scatterers yieldsimilar conclusions.Experiments are carried out on the first generation ofchemically derived GNRs with smooth edges14 deposited onSi /SiO2500 nm wafer and connected to Pd electrodes dis-tanced by 270 nm. Two ranges of ribbon widths are ad-dressed: 11–30 nm and 70–100 nm. In the following, wefocus on the narrow ribbons which exhibit evidence of mag-netic edge currents at the root of the observed positive MC.An extended analysis of the 11-nm-wide GNR is presented.Results on the 30-nm-wide GNR are qualitatively similar.Measurements on larger GNR, here 90 nm, are briefly dis-cussed to emphasize the effect of the electronic confinementon the MC.Figure 1 inset shows the gate voltage-dependent con-ductance of the 11-nm-wide GNR under 50 mV bias voltageVb, and at various temperatures from 169 K down to 20K. The V-shape curves are typical for a semiconductingribbon.8 Interestingly, a detailed analysis of the GVg curvesat 80 K and below unveils reproducible modulations super-imposed to the overall increase in the conductance versus theelectrostatic doping. These structures become more pro-nounced at lower bias voltages Fig. 1 main frame, red/grayand blue/dark gray curves obtained at 50 mV and 1 mV,respectively. We assign such conductance profile to thepresence of van Hove singularities vHs, responsible for theenhancement of the backscattering in the diffusive regime.To validate such scenario, extensive tight-binding band-structures calculations are performed on a set of ribbonssymmetries with varying widths.15 Calculations include zig-zag GNR zGNR and armchair GNR aGNR of three typesN=3m, 3m+1, and 3m+2, N being the number of dimerlines. The N values are chosen to explore the full range of theribbon sample width dispersion here 111 nm, as evalu-ated by careful atomic force microscopy AFM analysis.Figure 1 also shows the density of states Vg dotted-dashed curve for the armchair configuration of type 3m withPHYSICAL REVIEW B 82, 041413R 2010RAPID COMMUNICATIONS1098-0121/2010/824/0414134 ©2010 The American Physical Society041413-1N=90 corresponding to a nominal width of 10.947 nm whichturns out to be the most likely ribbon geometry deducedfrom the theoretical analysis.15 Indeed, without any free pa-rameters, an agreement is observed between pronouncedmodulations of the conductance local minima or drasticslope changes present on the two GVg curves and the the-oretical sequence of the vHs. Such correspondence is notachieved at all for zGNR and other 3m+1 and 3m+2 typesof aGNR.15 Note that other N values, multiple of 3, from 87to 93, in the range of the width uncertainty, also lead to asatisfactory agreement. The energies of the correspondingbands undergo a maximum shift on the order of 6%, whichcannot be discriminated on the GVg curves. We concludethat the conductance exhibits 1D subbands fingerprints con-sistent with an armchair arrangement and 3m dimer linesaround 903 along the GNR width.The application of a transverse magnetic field on the 11-nm-wide GNR drastically increases its conductance by morethan 50% at 80 K and by more than one decade at 20K Fig.2, left panel. The gain of transmission is further modulatedby the electrostatic doping in a complex but very reproduc-ible manner. The MC remains of large amplitude, even whenseveral subbands are involved in conduction. Conversely, fora 90-nm-wide GNR Fig. 2a, black dashed curve and gen-erally speaking for graphene flakes,16 only the very low mag-netic field MC is slightly positive and results from a weaklocalization regime. At larger field, the conductance of largewidth GNR is strongly reduced, following the two-fluidmodel at the CNP in a diffusive regime17 and further exhibitsa steplike decrease in the quantum regime, unveiling thegraphene Landau levels LLs.18,19 In the following, we bringevidence that the large positive MC and its energy depen-dence obtained for the narrow GNR result from a subtle in-terplay between the specific magnetic band structures and thefield-induced reduction in disorder-driven backscattering.The tight-binding band-structure calculations reveal thatthe 1D subbands of the GNR tend to the graphene LL as themagnetic field increases, since the magnetic confinementgradually overcomes the electronic one.15 At the CNP, theonset of the zero-energy LL induces a closing of the energyband gap of the GNR. In Fig. 2b the simulated magneticfield dependence of the energy gaps for the three types ofaGNR is reported. Assuming a flat band model at the CNP,the ribbon energy gaps EgB will modulate the thermallyactivated regime, in which the MC is expressed as GBexp− EgB2kT+T . Here, kT accounts the kinetic-energy win-dow of charge carriers defined by eVb /2. As seen in Fig.2a, a reasonable agreement between experiments and theactivation model is obtained, using the field dependence ofthe 90 aGNR tight-binding gap with kT212 meV,which is consistent with the 50 mV experimental Vb. Weconclude that if the sequence of the vHs for an aGNR of type3m appears as the most likely fingerprint of the GVg modu-lations at zero field, the agreement is further reinforced bythe large positive MC.To explore the magnetoconductance whatever the electro-static doping, tight-binding transport simulations are per-formed using the Green’s functions formalism and Landauer-Büttiker method.20 In contrast to a Boltzmann transporttreatment,21 this approach includes all quantum interferenceseffects which are relevant for the range of parameters con-sidered here impurity density, mean free path, and ribbonlength. Three different types of disorders are considered:FIG. 1. Color online Conductance versus Vg at 80 K measuredon the narrow GNR width 11 nm and for two Vb, 50 mV, and 1mV respectively, red/gray and blue/dark gray curves. The densityof states of a 90 aGNR is superimposed dashed curve. Top inset:GVg at various temperatures for a wider gate voltage range. Bot-tom inset: AFM image of the GNR device.FIG. 2. Color online a Left panel: magnetoconductance at 80K for the narrow ribbon for various Vg top; and at 80, 50, and 20K for Vg=0 curves with symbols: measurements; solid lines: simu-lated data. The MC for a 90-nm-wide GNR is also shown, varyingfrom 0.6G0 to 0.4G0 dashed curve. b Right panel: computedfield-dependent energy gaps for three different types of aGNR. In-set: schematic of the GNR device.POUMIROL et al. PHYSICAL REVIEW B 82, 041413R 2010RAPID COMMUNICATIONS041413-2the Anderson disorder with on-site energies varying at ran-dom in the range −w /2,w /2 and w=2 eV; the edgeroughness with a 5% of removed carbon atoms on the sixouter chains at each edge; and randomly dispersed impuritiesdescribed by a long-range Gaussian potential with a density1.151016 m−2 spatial range =1 nm, strength in therange −u /2,u /2 with u=2 eV. These disorders are wellrepresentative of the possible scattering sources consideredin the literature.10–12 In particular, edge roughness seems un-avoidable in nanoribbons, even when chemically derived;4whereas impurities with long-range potential mimic screenedcharged ions trapped in the oxide. Finally Anderson disorderqualitatively reproduces impurities on the surface of theGNR. Ripples on the ribbon surface represent another pos-sible source of long-range disorder, but with a much weakerimpact than charged impurities in the oxide.22 The impact iseven less significant in our sample, whose width is narrowerthan the typical ripples wavelength 15 nm. Therefore,we do not include this type of disorder in our analysis. In thefollowing, transport calculations are performed at finite tem-perature T=80 K and for Vb=50 mV. A contact resistanceof 10 k	 is also included.4Figure 3 shows the computed magnetoconductance at sev-eral gate voltages, for each type of disorder. First, it is clearthat the use of the Anderson disorder is inappropriate to de-scribe the experimental MC. The conductance is indeedweakly sensitive to the magnetic field only effective at lowVg−5 V, and this behavior hardly changes with other dis-order strengths not shown here. In contrast, a huge positiveMC is observed at low Vg where only a single conductivechannel is active for the case of edge roughness. When twoor three channels are available for conduction Vg−15 V, the MC displays, however, a more fluctuating trend,but becomes again positive at higher gate voltages. This par-tially reproduces the general trend of the measured MC, sug-gesting that edge roughness can partly account for disordereffects but does not fully dominate the scattering processes.Finally, Gaussian disorder qualitatively reproduces the ex-perimental trend for all Vg: the conductance increases withgate voltage and the MC is positive at almost any magneticfield and Vg values. In any case, the computed conductanceremains larger than the experimental one. We demonstratethat reinforcing the disorder its density or strength bringsthe system into a strongly localized quantum regime with nowell-defined positive MC.15 Nevertheless, a more quantita-tive agreement between simulated and measured conduc-tances might be achieved by considering a Gaussian disordersuperimposed to an ultrasmooth edges roughness.15The magnetoconductance obtained for Gaussian impuri-ties or edge disorder can be further rationalized by visual-izing the magnetic edge states that develop in the high mag-netic field limit, as already discussed in the context ofquantum wires.23 Due to the broken time-reversal symmetry,edge channels on the upper edge are created and conveycurrent in opposite direction than the channels at the loweredge. If disorder is not strong enough, the spatial separationbetween the channels induced by the high magnetic fieldprovokes a strong suppression of backscattering. Figure 4images the spectral current distribution at the energy E=200 meV for several magnetic fields. At zero magneticfield Fig. 4a, the current flow is weak as well as relatedconductance. Increasing B magnifies the current densityalong the ribbon Figs. 4b and 4c, but the presence ofscatterers limits the total current flow between source anddrain. Figure 4d illustrates the partial backscattering alongthe lower edge where electrons can only move from right toleft and partial transmission to the right contact along theupper edge yellow arrows, when the current flow reaches alocalized state. This effect is further reduced with the forma-tion of fully developed magnetic edges at higher field Fig.4e which further enhances the positive MC.One notes that for the Anderson disorder, the homoge-neous short-range scattering potential makes strongly diffi-cult a spatial separation between the chiral channels, thusprohibiting the predominance of magnetic edge channels. In0 20 40 60012345B (T)G(G0×10−1 )Vg=−5 VVg=−15 VVg=−25 VVg=−35 VVg=−45 V0 20 40 60B (T)0 20 40 60B (T)0 200 40000.20.40.60.8E (meV)B=0B=60 T(a) (c)(b)αβFIG. 3. Color online Magnetoconductancefor the 90 aGNR at different Vg with a Ander-son disorder, b edge roughness, and c Gauss-ian impurities. Inset of c:  and  transmissionfactors denote the contributions of the first chan-nel and the higher bands at zero field and 60 T.EDGE MAGNETOTRANSPORT FINGERPRINTS IN… PHYSICAL REVIEW B 82, 041413R 2010RAPID COMMUNICATIONS041413-3contrast, the mechanism is efficient on the first conductivechannel when bulk disorder is absent edge roughness orweak and long-range scattering potential prevails. In thiscase, intraband scattering within the first energy band ispartially suppressed and the conductance increases as themagnetic channels are pushed to the edges. A detailed analy-sis disentangles the contribution of the first channel from thehigher subbands represented by the  and  factors,respectively15. For a Gaussian disorder,  Fig. 3c,inset, so the first channel dominates transport and its mag-netic field dependence. The long-range nature of the Gauss-ian potential markedly reduces the interband scattering andpreserves the positive MC of the first channel well beyondthe second vHs, as observed experimentally. The higherchannels are less active and do not show any marked positiveMC. This is explained by the spatial enlargement of the mag-netic edge states, which then come into contact more easily,due to the narrow width of the ribbon. Conversely, the short-range nature of edge disorder favors enhanced interbandscattering and mixing between channels, as evident from Fig.3b, where the positive MC is reduced when the second andthird subbands start to be involved at Vg−15 V.In large magnetic field, charge-transport properties inchemically derived graphene nanoribbons can be tuned bythe formation of magnetic edge states. The resulting positivemagnetoconductance obtained experimentally has been fur-ther satisfactorily reproduced by tight-binding simulations,pinpointing the likely contribution of both charged impuritiesand smooth edge roughness.Part of this work was supported by EuroMagNET, Con-tract No. 228043. S.R. acknowledges the ANR/P3N2009Project No. ANR-09-NANO-016-01. H.D. acknowledgesfunding from Office of Naval Research ONR and Intel.*Current address: IMEP-LAHC, Minatec, Grenoble, France.1 A. K. Geim and K. Novoselov, Nature Mater. 6, 183 2007.2 M. Y. Han, B. Özyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett.98, 206805 2007.3 G. Liang et al., IEEE Trans. Electron Devices 54, 677 2007.4 X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, and H. Dai, Phys.Rev. Lett. 100, 206803 2008.5 Y.-M. Lin, V. Perebeinos, Z. Chen, and P. Avouris, Phys. Rev. B78, 161409R 2008.6 Y.-W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 97,216803 2006.7 C. Stampfer, J. Güttinger, S. Hellmüller, F. Molitor, K. Ensslin,and T. Ihn, Phys. Rev. Lett. 102, 056403 2009.8 M. Y. Han, J. C. Brant, and Ph. Kim, Phys. Rev. Lett. 104,056801 2010.9 P. Gallagher, K. Todd, and D. Goldhaber-Gordon, Phys. Rev. B81, 115409 2010.10 D. A. Areshkin, D. Gunlycke, and C. T. White, Nano Lett. 7, 2042007; M. Evaldsson, I. V. Zozoulenko, H. Xu, and T. Heinzel,Phys. Rev. B 78, 161407R 2008; T. C. Li and S.-P. Lu, ibid.77, 085408 2008; E. R. Mucciolo, A. H. Castro Neto, and C.H. Lewenkopf, Phys. Rev. B 79, 075407 2009; D. Querlioz etal., Appl. Phys. Lett. 92, 042108 2008; A. Cresti et al., NanoRes. 1, 361 2008; P. Zhao et al., ibid. 1, 395 2008.11 S. Ihnatsenka and G. Kirczenow, Phys. Rev. B 80,201407R2009.12 M. I. Katsnelson and A. K. Geim, Philos. Trans. R. Soc. A 366,195 2008.13 K. Novoselov et al., Nat. Phys. 2, 177 2006; X. Wu, X. Li, Z.Song, C. Berger, and W. A. de Heer, Phys. Rev. Lett. 98,136801 2007.14 X. Li et al., Science 319, 1229 2008.15 See supplementary material at http://link.aps.org/supplemental/10.1103/PhysRevB.82.041413 for details of the conductancesimulations and supplementary experimental data.16 F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K.Savchenko, Phys. Rev. Lett. 100, 056802 2008.17 S. Cho and M. S. Fuhrer, Phys. Rev. B 77, 081402R 2008.18 V. P. Gusynin and S. G. Sharapov, Phys. Rev. B 71, 1251242005.19 T. S. Li et al., Philos. Mag. 89, 697 2009.20 A. Cresti et al., Eur. J. Phys. B 53, 537 2006.21 S. Adam et al., Proc. Natl. Acad. Sci. U.S.A. 104, 18392 2007.22 A. Deshpande, W. Bao, F. Miao, C. N. Lau, and B. J. LeRoy,Phys. Rev. B 79, 205411 2009; Y. Zhang et al., Nat. Phys. 5,722 2009; J. H. Chen et al., Solid State Commun. 149, 10802009.23 A. Cresti, G. Grosso, and G. P. Parravicini, Phys. Rev. B 77,115408 2008.FIG. 4. Color online Spectral current distribution at the energy E=200 meV for a 90 aGNR in the presence of Gaussian disorder onlyat a B=0, b B=10 T, c B=30 T, d B=50 T, and e B=60 T. Charge flows from left to right.POUMIROL et al. PHYSICAL REVIEW B 82, 041413R 2010RAPID COMMUNICATIONS041413-4

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