Defect symmetry influence on electronic transport of zigzag nanoribbons
 Hui Zeng^{1, 2}Email author,
 JeanPierre Leburton^{2, 3, 4},
 Yang Xu^{5} and
 Jianwei Wei^{6}
DOI: 10.1186/1556276X6254
© Zeng et al; licensee Springer. 2011
Received: 19 August 2010
Accepted: 24 March 2011
Published: 24 March 2011
Abstract
The electronic transport of zigzagedged graphene nanoribbon (ZGNR) with local StoneWales (SW) defects is systematically investigated by first principles calculations. While both symmetric and asymmetric SW defects give rise to complete electron backscattering region, the welldefined parity of the wave functions in symmetric SW defects configuration is preserved. Its signs are changed for the highestoccupied electronic states, leading to the absence of the first conducting plateau. The wave function of asymmetric SW configuration is very similar to that of the pristine GNR, except for the defective regions. Unexpectedly, calculations predict that the asymmetric SW defects are more favorable to electronic transport than the symmetric defects configuration. These distinct transport behaviors are caused by the different couplings between the conducting subbands influenced by wave function alterations around the charge neutrality point.
Introduction
As a truly twodimensional nanostructure, graphene has attracted considerable interest, mainly because of its peculiar electronic and transport properties described by a massless Dirac equation [1, 2]. As such, it is regarded as one of the most promising materials since its discovery [3–5] because charge carriers exhibit giant intrinsic mobility and long meanfree path at room temperature [6, 7], suggesting broad range of applications in nanoelectronics [8–11]. Several experimental [4, 8, 12, 13] and theoretical [2, 14, 15] studies are presently devoted to the electronic, transport, and optical properties [16] of graphene. By opening an energy gap between valence and conduction bands, narrow graphene nanoribbons (GNR) are predicted to have a major impact on transport properties [17, 18]. Most importantly, GNRbased nanodevices are expected to behave as molecular devices with electronic properties similar to those of carbon nanotubes (CNTs) [19, 20], as for instance, Biel et al. [21] reported a route to overcome current limitations of graphenebased devices through the fabrication of chemically doped GNR with boron impurities.
The investigation of transport properties of GNRs by various experimental methods such as vacancies generation [22], topological defects [23], adsorption [24], doping [25], chemical functionalization [26–28], and molecular junctions [29] have been reported. Meanwhile, defective GNR with chemically reconstructed edge profiles also have been experimentally evidenced [30] and have recently received much attention [31, 32]. In particular, StoneWales (SW) defects, as one type of topological defects, are created by 90° rotation of any CC bond in the hexagonal network [33], as shown by Hashimoto et al. [34]. More recently, Meyer et al. [35] have investigated the formation and annealing of SW defects in graphene membranes and found that the existence of SW defects is energetically more favorable than in CNTs or fullerenes. Therefore, the influences of SW defects on electronic transport of GNRs is crucial for the understanding of the physical properties of this novel material and for its potential applications in nanoelectronics.
In this brief communication, we investigate the influence of SW defects on the electronic transport of zigzagedged graphene nanoribbons (ZGNRs). It is found that the electronic structures and transport properties of ZGNRs with SW defects can very distinctively depend on the symmetry of SW defects. The transformation energies obtained for symmetric SW defects and asymmetric SW defects are 5.95 and 3.34eV, respectively, and both kinds of defects give rise to quasibound impurity states. Our transport calculations predict different conductance behavior between symmetric and asymmetric SW defects; asymmetric SW defects are more favorable for electronic transport, while the conductance is substantially decreased in the symmetric defects configuration. These distinct transport behaviors result from the different coupling between the conducting subbands influenced by the wave function symmetry around the charge neutrality point (CNP).
Model and methods
The optimization calculations are done by using the density functional theory utilized in the framework of SIESTA code [36, 37]. We adopt the standard normconserving ToullierMartins [38] pseudopotentials orbital to calculate the ionelectron interaction. The numerical doubleζ polarized is used for basis set and the plane cutoff energy is chosen as 200 Ry. The generalized gradient approximation [39] proposed by Perdew and Burke and Ernzerhof was employed to calculate exchange correction term. All nanostructure geometries were converged until no forces acting on all atoms exceeded 0.01eV/Å.
In this study, we consider symmetric and asymmetric SW defects contained in 6ZGNRs, where 6 denotes the number of zigzag chains (dimers) across the ribbon width [18]. Taking into account screening effects between electrodes and central molecules, we use 10unit cell's length as scattering regions, and 2 units as electrodes to perform transport calculation. The electron temperature in the calculation is set to be 300 K.
Results and discussions
In Figure 1, we show the geometry of defective ZGNR after relaxation. After introducing symmetric SW defects, the GNR shrinks along the width axis, by 0.526 Å, and correspondingly, the nearest four H atoms move toward the central region by 0.21 Å. As a result, the bond angles of the edge near the SW defects are reduced from 120 to 116°, as shown in Figure 1c, d. In contrast to the shrinking along the width axis, the SW defects stretch from 4.88 to 5.38 Å along the length axis direction. No distinct change for the HC bond length at the edge is observed. Thus, the effect of symmetric SW defects on the geometry modification is limited to the defective area, with mirror reflection around their axis. However, the presence of asymmetric SW defects to the geometry modification is far more complex. They twist the whole structure by shifting the left side upward, while the right side is downward shifted. Hence, the mirror symmetry is broken because of the asymmetric SW. The transformation energies for symmetric and asymmetric SW defects are 5.95 and 3.34eV, respectively. These results imply that the asymmetric SW defects are energetically more favorable than the symmetric SW defects.
Conclusion
In summary, we investigate the influence of local structural defects on the electronic transport of ZGNR using first principles calculations. The transformation energies reveal that the asymmetric SW defects is energetically more favorable than the symmetric SW defects. Both defects give rise to complete electron backscattering region that depends on the spatial symmetry of the defects. Our transport calculations predict that the asymmetric SW defects are more favorable for electronic transport in contrast to the substantially decreased in the symmetric defects configuration. We attribute these distinct transport behaviors to the different coupling between the conducting subbands influenced by the wave function modification around the CNP.
Abbreviations
 CNP:

charge neutrality point
 GNR:

graphene nanoribbons
 HOES:

highestoccupied electronic states
 LUES:

lowestunoccupied electronic states
 SW:

StoneWales
 ZGNR:

zigzagedged graphene nanoribbon.
Declarations
Acknowledgements
The authors gratefully thank Prof. K.L. Yao and Dr. M. A. Kuroda for their technical assistance with performing ab initio transport properties and the relax calculation in the Mac OS X Turing cluster. This study is financially supported by the Scientific Research Foundation of Yangtze University (Grant No.801080010111) and the Chongqing University of Technology (Grant No.2008EDJ01), and the Natural Science Foundation of China under Grant No.11047176.
Authors’ Affiliations
References
 Geim AK, Novoselov KS: The rise of graphene. Nat Mater 2007, 6: 183–191. 10.1038/nmat1849View ArticleGoogle Scholar
 Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK: The electronic properties of graphene. Rev Mod Phys 2009, 81: 109–162. 10.1103/RevModPhys.81.109View ArticleGoogle Scholar
 Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA: Electric field effect in atomically thin carbon films. Science 2004, 306: 666–669. 10.1126/science.1102896View ArticleGoogle Scholar
 Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, Dubonos SV, Firsov AA: Twodimensional gas of massless Dirac fermions in graphene. Nature 2005, 438: 197–200. 10.1038/nature04233View ArticleGoogle Scholar
 Zhang YB, Tan YW, Stormer HL, Kim P: Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005, 438: 201–204. 10.1038/nature04235View ArticleGoogle Scholar
 Berger C, Song Z, Li X. Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov AN, Conrad EH, First PN, de Heer WA: Electronic confinement and coherence in patterned epitaxial graphene. Science 2006, 312: 1191–1196. 10.1126/science.1125925View ArticleGoogle Scholar
 Orlita M, Faugeras C, Plochocka P, Neugebauer P, Martinez G, Maude DK, Barra AL, Sprinkle M, Berger C, de Heer WA, Potemskil M: Approaching the dirac point in highmobility multilayer epitaxial graphene. Phys Rev Lett 2008, 101: 267601. 10.1103/PhysRevLett.101.267601View ArticleGoogle Scholar
 Bunch JS, van der Zande AM, Verbridge SS, Frank IW, Tanenbaum DM, Parpia JM, Craighead HG, McEuen PL: Electromechanical resonators from graphene sheets. Science 2007, 315: 490–493. 10.1126/science.1136836View ArticleGoogle Scholar
 Yan QM, Huang B, Yu J, Zheng FW, Zang J, Wu J, Gu BL, Liu F, Duan WH: Intrinsic currentvoltage characteristics of graphene nanoribbon transistors and effect of edge doping. Nano Lett 2007, 7: 1469–1473. 10.1021/nl070133jView ArticleGoogle Scholar
 Martins TB, Miwa RH, da Silva AJR, Fazzio A: Electronic and transport properties of Borondoped graphene nanoribbons. Phys Rev Lett 2007, 98: 196803. 10.1103/PhysRevLett.98.196803View ArticleGoogle Scholar
 Fiori G, Iannaccone G: Simulation of graphene nanoribbon fieldeffect transistors. IEEE Electron Dev Lett 2007, 28: 760–762. 10.1109/LED.2007.901680View ArticleGoogle Scholar
 Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK: Twodimensional atomic crystals. Proc Natl Acad Sci USA 2005, 102: 10451–10453. 10.1073/pnas.0502848102View ArticleGoogle Scholar
 Lee C, Wei X, Kysar JW, Hone J: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008, 321: 385–388. 10.1126/science.1157996View ArticleGoogle Scholar
 Fujita M, Wakabayashi K, Nakada K, Kusakabe K: Peculiar localized state at zigzag graphite edge. J Phys Soc Jpn 1996, 65: 1920–1923. 10.1143/JPSJ.65.1920View ArticleGoogle Scholar
 Miyamoto Y, Nakada K, Fujita M: Firstprinciples study of edge states of Hterminated graphitic ribbons. Phys Rev B 1999, 59: 9858–9861. 10.1103/PhysRevB.59.9858View ArticleGoogle Scholar
 Dresselhaus MS, Jorio A, Hofmann M, Dresselhaus G, Saito R: Perspectives on carbon nanotubes and graphene Raman spectroscopy. Nano Lett 2010, 10: 751–758. 10.1021/nl904286rView ArticleGoogle Scholar
 Nakada K, Fujita M, Dresselhaus G, Dresselhaus MS: Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys Rev B 1996, 54: 17954–17961. 10.1103/PhysRevB.54.17954View ArticleGoogle Scholar
 Son YW, Cohen ML, Louie SG: Energy gaps in graphene nanoribbons. Phys Rev Lett 2006, 97: 216803. 10.1103/PhysRevLett.97.216803View ArticleGoogle Scholar
 Avouris Ph: Molecular electronics with carbon nanotubes. Acc Chem Res 2002, 35: 1026–1034. 10.1021/ar010152eView ArticleGoogle Scholar
 Weitz RT, Zschieschang U, Eenberger F, Klauk H, Burghard M, Kern K: Highperformance carbon nanotube field effect transistors with a selfassembled monolayer gate dielectric. Nano Lett 2007, 7: 22–27. 10.1021/nl061534mView ArticleGoogle Scholar
 Biel B, Triozon F, Blase X, Roche S: Chemicallyinduced mobility gaps in graphene nanoribbons. Nano Lett 2009, 9: 2725–2729. 10.1021/nl901226sView ArticleGoogle Scholar
 Carlsson JM, Scheffer M: Structural, electronic, and chemical properties of nanoporous carbon. Phys Rev Lett 2006, 96: 046806. 10.1103/PhysRevLett.96.046806View ArticleGoogle Scholar
 Cortijo A, Vozmediano MAH: Effects of topological defects and local curvature on the electronic properties of planar graphene. Nucl Phys B 2007, 763: 293–308. 10.1016/j.nuclphysb.2006.10.031View ArticleGoogle Scholar
 Choi SM, Jhi SH: Selfassembled metal atom chains on graphene nanoribbons. Phys Rev Lett 2008, 101: 266105. 10.1103/PhysRevLett.101.266105View ArticleGoogle Scholar
 Biel B, Blase X, Triozon F, Roche S: Anomalous doping effects on charge transport in graphene nanoribbons. Phys Rev Lett 2009, 102: 096803. 10.1103/PhysRevLett.102.096803View ArticleGoogle Scholar
 Cantele G, Lee YS, Ninno D, Marzari N: Spin channels in functionalized graphene nanoribbons. Nano Lett 2009, 9: 3425–3429. 10.1021/nl901557xView ArticleGoogle Scholar
 LópezBezanilla A, Triozon F, Roche S: Chemical functionalization effects on armchair graphene nanoribbon transport. Nano Lett 2009, 9: 2537–2541.View ArticleGoogle Scholar
 CervantesSodi F, Csányi G, Piscanec S, Ferrari AC: Edgefunctionalized and substitutionally doped graphene nanoribbons: Electronic and spin properties. Phys Rev B 2008, 77: 165427. 10.1103/PhysRevB.77.165427View ArticleGoogle Scholar
 Wang B, Wang J, Guo H: Ab initio calculation of transverse spin current in graphene nanostructures. Phys Rev B 2009, 79: 165417. 10.1103/PhysRevB.79.165417View ArticleGoogle Scholar
 Koskinen P, Malola S, Häkkinen H: Evidence for graphene edges beyond zigzag and armchair. Phys Rev B 2009, 80: 073401. 10.1103/PhysRevB.80.073401View ArticleGoogle Scholar
 Wassmann T, Seitsonen AP, Saitta AM, Lazzeri M, Mauri F: Structure, stability, edge states, and aromaticity of graphene ribbons. Phys Rev Lett 2008, 1011: 096402. 10.1103/PhysRevLett.101.096402View ArticleGoogle Scholar
 Dubois SMM, LopezBezanilla A, Cresti A, Triozon F, Biel B, Charlier JC, Roche S: Quantum transport in graphene nanoribbons: Effects of edge reconstruction and chemical reactivity. ACS Nano 2010, 4: 1971–1976. 10.1021/nn100028qView ArticleGoogle Scholar
 Stone AJ, Wales DJ: Theoretical studies of icosahedral C60 and some related structures. Chem Phys Lett 1986, 128: 501–503. 10.1016/00092614(86)806613View ArticleGoogle Scholar
 Hashimoto A, Suenaga K, Gloter A, Urita K, Iijima S: Direct evidence for atomic defects in graphene layers. Nature 2004, 430: 870–873. 10.1038/nature02817View ArticleGoogle Scholar
 Meyer JC, Kisielowski C, Erni R, Rossell MD, Crommie MF, Zettl A: Direct imaging of lattice atoms and topological defects in graphene membranes. Nano Lett 2008, 8: 3582–3586. 10.1021/nl801386mView ArticleGoogle Scholar
 Ordejón P, Artacho E, Soler JM: Selfconsistent orderN densityfunctional calculations for very large systems. Phys Rev B 1996, 53: R10441R10444.View ArticleGoogle Scholar
 Soler JM, Artcho E, Gale JD, Garía A, Junquera J, Ordejón P, SánchezPortal D: The SIESTA method for ab initio orderN materials simulation. J Phys Condensed Matter 2002, 14: 2745–2779. 10.1088/09538984/14/11/302View ArticleGoogle Scholar
 Toullier N, Martins JL: Efficient pseudopotentials for planewave calculations. Phys Rev B 1993, 43: 1993–2006. 10.1103/PhysRevB.43.1993View ArticleGoogle Scholar
 Perdew JP, Burke K, Ernzerhof M: Generalized gradient approximation made simple. Phys Rev Lett 1996, 77: 3865–3868. 10.1103/PhysRevLett.77.3865View ArticleGoogle Scholar
 Taylor J, Guo H, Wang J: Ab initio modeling of quantum transport properties of molecular electronic devices. Phys Rev B 2001, 63: 245407. 10.1103/PhysRevB.63.245407View ArticleGoogle Scholar
 Brandbyge M, Mozos JL, Ordejón P, Taylor J, Stokbro K: Densityfunctional method for nonequilibrium electron transport. Phys Rev B 2002, 65: 165401. 10.1103/PhysRevB.65.165401View ArticleGoogle Scholar
 Datta S: Transmission function, Smatrix and Green's functions. In Electronic Transport in Mesoscopic Systems. New York: Cambridge University Press; 1995:117–163.View ArticleGoogle Scholar
 Li Z, Qian H, Wu J, Gu BL, Duan W: Role of symmetry in the transport properties of graphene nanoribbons under bias. Phys Rev Lett 2008, 100: 206802. 10.1103/PhysRevLett.100.206802View ArticleGoogle Scholar
 Areshkin DA, Gunlycke D, White CT: Ballistic transport in graphene nanostrips in the presence of disorder: Importance of edge effects. Nano Lett 2007, 7: 204–210. 10.1021/nl062132hView ArticleGoogle Scholar
 Oeiras P, AraújoMoreira FM, da Silva FM: Defectmediated halfmetal behavior in zigzag graphene nanoribbons. Phys Rev B 2009, 80: 073405. 10.1103/PhysRevB.80.073405View ArticleGoogle Scholar
 Wei JW, Hu HF, Zeng H, Wang ZY, Wang L, Peng P: Effects of nitrogen in StoneWales defect on the electronic transport of carbon nanotube. Appl Phys Lett 2007, 91: 092121. 10.1063/1.2778544View ArticleGoogle Scholar
 Ren Y, Chen KQ: Effects of symmetry and StoneWales defect on spindependent electronic transport in zigzag graphene nanoribbons. J Appl Phys 2010, 107: 044514. 10.1063/1.3309775View ArticleGoogle Scholar
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