Atomic and Electronic Structures of Divacancy in Graphene Nanoribbons(offprint)

This article appeared in a journal published by Elsevier.The attached copy is furnished to the author for internal non-commercial research and education use,including for instruction at the authors institutionand sharing with colleagues.Other uses,including reproduction and distribution,or selling or licensing copies,or posting to personal,institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle(e.g.in Word or Tex form)to their personal website orinstitutional repository.Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:/copyrightAtomic and electronic structures of divacancy in graphene nanoribbonsJun Zhao a ,1,Hui Zeng a ,n ,1,Jianwei Wei ba College of Physical Science and Technology,Yangtze University,Jingzhou,Hubei 434023,ChinabSchool of Mathematics and Physics,Chongqing University of Technology,Chongqing 400054,Chinaa r t i c l e i n f oArticle history:Received 2May 2011Received in revised form 6October 2011Accepted 17October 2011Available online 20October 2011Keywords:Graphene Point defectsElectronic transport First principlea b s t r a c tFirst principles calculations have been performed to investigate the electronic structures and transport properties of defective graphene nanoribbons (GNRs)in the presence of pentagon–octagon–pentagon (5–8–5)defects.Electronic band structure results reveal that 5–8–5defects in the defective zigzag graphene nanoribbon (ZGNR)is unfavorable for electronic transport.However,such defects in the defective armchair graphene nanoribbon (AGNR)give rise to smaller band gap than that in the pristine AGNR,and eventually results in semiconductor to metal-like transition.The distinct roles of 5–8–5defects in two kinds of edged-GNR are attributed to the different coupling between p n and p subbands influenced by the defects.Our findings indicate the possibility of a new route to improve the electronic transport properties of graphene nanoribbons via tailoring the atomic structures by ion irradiation.&2011Elsevier B.V.All rights reserved.1.IntroductionThe unique electronic and transport properties make the graphene material a subject of great interest for electronic device applications [1,2].The novel properties of graphene originate from the linear energy dispersion at the two nonequivalent Dirac points,called K and K 0valleys,where the conductance band conically contacting the valence band [2].In particular,the quasi-one-dimensional graphene nanoribbons (GNRs)are the important components of these graphene nanostructures.A powerful method to open an energy gap in lithographically patterned graphene ribbon structures has been demonstrated,leading to the confinement of charge carriers in the GNRs for the realization of room-temperature nanoscale electro-nics [3].The formation of graphene edges has a crucial impact on the electronic properties of narrow GNRs,namely,the armchair edge and the zigzag edge according to the atomic arrangement pattern of their edges [4].Meanwhile,various bended GNRs based on these two kinds of edges are shown to control the valley polarization of the tunneling currents [5].More recently,Wu et al.pointed out that local strains in graphene can be used to generate a valley filter for the valleytronics device [6].Many GNRs-based nanodevices have been successfully fabricated,such as field effect transistors [7],gas molecule sensor [8],spintronic device [9],quantum dots [10],and so on.Most impor-tantly,the advantage for the potential use of GNRs-based nanodevice is that they can be utilized by using mature lithography and etching routes.Previous experiments have demonstrated that irradiating carbon nanostructures with electron or ion beams can conven-tionally introduce vacancy defects in carbon-based nanomaterials [11].Several controllable defects,such as Stone–Wales (SW)defect [12],adatoms [13],vacancies [14,15],substitution [16]and disorder [17],have been evidenced in GNRs.More recently,Ugeda et al.have experimentally shown that vacancies can effectively modify the electronic properties of this graphene-like system by using low temperature scanning tunneling microscopy (LT-STM)[18].Simulations have predicted that the most likely defects to be formed under Ar þirradiation are vacancies,and furthermore,the divacancy appearing in about 30–40%of the influences [19,20].Extensive experimental [11,21]and theoretical efforts [22,23]have been devoted to the understanding of the reconstruction of vacancy defects and its influence on the electro-nic transport properties of GNRs.In particular,divacancy consisting of two pentagons side by side with an octagon (5–8–5)is the most stable defects in carbon nanotubes because of its lowest transfor-mation energy [24].Previous theoretical prediction of divacancy defects in GNRs has shown that three pentagons and three heptagons (5–5–5–7–7–7)become more stable than the 5–8–5defects [25].However,this does not preclude the presence of the 5–8–5defects in the graphene nanoribbon via morphological modifications induced by irradiation techniques [11].Specifically,previous study has predicted that the hole-like defect in the carbon nanotubes is favorable for electron transport in spite of its larger transformation energy compared with the situation in the carbon nanotube that consisting of smaller size vacancy [26].Therefore,a systematic investigation on the influence of vacancy defect is crucial for the development of functionalized graphene-nanoelec-tronic device.Contents lists available at SciVerse ScienceDirectjournal homepage:/locate/physbPhysica B0921-4526/$-see front matter &2011Elsevier B.V.All rights reserved.doi:10.1016/j.physb.2011.10.028nCorresponding author.Tel./fax:þ867168060942.E-mail address:zenghui@ (H.Zeng).1These authors contributed equally to the work.Physica B 407(2012)204–208In this communication,we conduct the investigation on the influence of5–8–5defects on the geometry and electronic transport properties in both armchair and zigzag GNRs.Following the defini-tion of GNR given by the previous work[27],we simulate the armchair-edged GNR named11-AGNRs,where11is the number of dimers across the ribbon’s width.Correspondingly,the6-zigzag graphene nanoribbon(ZGNR)is chosen for comparison because it has approximately the same width and length as the11-AGNR.The super cell contains6unit cells(156atoms)in the pristine AGNR configuration and12unit cells(168atoms)in the pristine ZGNR configuration during the geometry optimization.The electronic structure and transport properties of the defective and the pristine GNRs are shown for comparison.The most striking result is that the 5–8–5defect in the armchair nanoribbons is favorable for electronic transport compared with the case in the pristine AGNR.2.MethodWe perform the atomic geometry optimization by using the density functional theory utilized in the SIESTA code[28,29].The interaction between valence electrons and the atomic core is calculated by standard norm-conserving Troullier–Martins pseu-dopotential[30].The Brillouin zone was sampled by6Â2Â1 k-point mesh based on the Monkhorst–Pack scheme[31].We adopt the numerical double-z plus polarization(DZP)basis set,and plane cutoff energy is chosen as200Ry.The generalized gradient approx-imation(GGA)was used to calculate exchange correction term[32]. All nanostructure geometries were converged until forces acting on all atoms do not exceed0.01eV/˚A,and the calculations are per-formed at electronic temperature T¼300K.To evaluate the transport properties of the defective nanor-ibbons,we take the two-probe geometry system into account [33].It is constructed in such a way that the central region containing an optimized supercell with the5–8–5defects,whichis surrounded by two leads made of two unit supercells on each side.In the quantum transport simulation,the central region is connected to two semi-infinite electrodes which are accounted for through a left(L)and right(R)self-energy,denoted by S L and S R.The transmission coefficient T(E)as a function of the electron energy E is calculated in the framework of the Laudauer formula:TðEÞ¼4Tr½ImðS L G r S R G aÞ ð1Þwhere G rðG aÞrepresents retard(advanced)Green’s function.It is calculated from the definition:G rC¼½ES CÀH CÀS r LÀS r R ¼ðG a CÞyð2Þwhere H C and S C represent the Kohn–Sham single-electron Hamiltonian and overlap matrix.Furthermore,the conductance of the system is evaluated at the Fermi level of the device such that GðEÞ¼G0TðEÞ,with G0¼ð2e2Þ=h denoting the quantum conductance.3.Results and discussionsThe optimized structures of defective GNRs are shown in Fig.1. The5–8–5defects in the AGNR are directed along the horizontal direction,and no distinct length change is observed along this direction.Moreover,the presence of5–8–5defects makes the GNRs remarkably shrink towards the center of the octagon,and corre-spondingly the four hexagons that connected with the octagon have been twisted a certain angle,thereby the width of the GNR around the defects is significantly decreased.The C–C length is approxi-mately reduced to4.00˚A compared with the pristine C–C bond length with2unit cells that has the length of about4.97˚A.It is found that the length of the newly formed C–C bond substantially stretches to1.61˚A,and the other C–C bonds that form the octagon also stretch to share the tension induced by the two missing atoms. Similarly,the defective ZGNR length along the width direction is increased due to the spatial stretch that is induced by the two pentagons.The newly formed C–C bond length is1.59˚A in this configuration,which is comparable with the situation in the defective AGNR.Thus,four H atoms located nearest to the5–8–5 defects stretch out and the C–C–C angle is increased to1241.The lengths of the C–C bonds that formed the octagon are increased to some extent.Moreover,the horizontal length of the defective ZGNR has not experienced significant change in spite of the local shrink towards the center in the octagon.Overall,the presence of the5–8–5 defects on the atomic reconstructions of the GNRs is(a)the pentagon induced stretch along the5–8–5defects direction;(b)the shrink towards the octagon that perpendicular to the5–8–5defects direc-tion.The difference in atomic reconstruction results between the ZGNR and AGNR originates from the GNR in the length direction sharing the tension as well as the direction in which periodic boundary condition is applied.The spin-polarized electronic band structures of the defective GNRs are depicted in Fig.2,with the corresponding pristine results shown for comparison.It can be seen that opposite spin-polarization bands of the pristine AGNR are completely degen-erate.The highest occupied band A and the lowest unoccupied band A0move away from the Fermi level at the G-point,opening a 0.63eV symmetric band gap,thereby the band structure of the pristine AGNR manifests semiconductor properties.In the case of the defective AGNR,however,the5–8–5defect creates a defect state labeled g that appears slightly above the Fermi level.This g-state hybridizes with the A,A0-bands to evolve into theC, Fig.1.Reconstructed atomic structures of(a)armchair-and(b)zigzag-edged graphene nanoribbons in the presence of5–8–5defects.The darker(gray online) colored atoms and lighter(white online)colored atoms represent carbon and hydrogen atoms.The lengths of C–C bond(highlighted by yellow color)and angles (highlighted by blue arc)are denoted by red numbers;the unit of bond length and degree is˚A and degree,respectively.(For interpretation of the references to color in thisfigure legend,the reader is referred to the web version of this article.)J.Zhao et al./Physica B407(2012)204–208205C 0-bands that anticross at the Fermi level close to the G -point,as shown in Fig.2(b).It is found that the Fermi level of this configura-tion is downward shifted and its highest occupied C-band crosses the Fermi level,leading to semiconductor to metal-like transition.Correspondingly,the dispersion between its highest occupied C-band and the lowest unoccupied C 0-band at the G -point is substantially narrowed.As expected,the electronic bands of the defective configuration that far from the Fermi level experience less change.For the band structure of the pristine ZGNR,it is found that the opposite spin-polarized bands are fully non-degenerate and symmetric with respect to the Fermi level.The non-degenerate bands of opposite spin arise from zone-folded effect as a result of comparatively large unit cells during atomic optimization.The band structures manifest metallic characteristics as there is one band crosses the Fermi level in each of the spin bands.The presence of the divacancy in the ZGNR induces the movement of the bands with respect to the Fermi level,that is,the A,A 0-bands associated with a -spin evolve into the C,C 0-bands and the B,B 0-bands associated with b -spin evolve into the D,D 0-bands.In particular,the D 0-band does not cross the Fermi level as it is lifted with respect to the Fermi level,and correspondingly the D-spin crosses the Fermi level.Similar to the case in carbon nanotubes with divacancy defects,the 5–8–5defects here give rise to a defect state above the Fermi level withsmall dispersion that flattens near the p -point.Overall,the a -spin states near the Fermi level have not experienced much change,and the electronic property mainly depends on the modified bands in b -spin polarized states.It is noted that the two valleys K and K 0are separated for ZGNR,in contrast to the mixed valleys for AGNR.The intervalley scattering processes measured in terms of scanning tunneling microscopy (STM)imply that the substantial reduction in the Fermi velocity arises from the defects [34].Therefore,the vacancy defects in the irradiated graphene,in turn,provide the footprint for experimental characterization.The charge density of all configurations is shown in Fig.3.In the AGNR cases,both the pristine and the defective AGNR present a rather homogeneous charge density distribution,and the divacancy induces imperceptible charge distribution change.The states of opposite spin orientation are degenerate in all bands in the AGNR cases.On the contrary,in the pristine ZGNR the electronic states of carbon atoms on the edge is mainly governed by a -spin (positive value)whereas the electronic state of carbon atoms that is first nearest the edge is governed by b -spin (negative value).Moreover,the spin-polarized charge density is mirror symmetric with respect to the midplane between two edges [27].These results are in accordance with its band structure splitting.When the 5–8–5defects are introduced in the ZGNR,the localized electron states associated with a -spin near the two pentagons have been observed,with the magnitude of charge density comparable with the situation in the carbon atoms on the edge.To understand the distinct differences in transport properties between the AGNR and the ZGNR,we should notice that GNRs do not always present a well-defined parity associated to mirror reflection with respect to their axis.As a result,a perfect odd-index AGNR retains a single mirror symmetry plane,thereby its eigen-states present a well-defined parity with respect to this symmetry plane;while ZGNRs have completely different transport character-istics depending on the different coupling between p n and p subbands [35,36].Specifically,the spin-polarization densities in the AGNR are completely degenerate.In contrast with the situation in AGNR,the electronic spin densities in the ZGNR depicted in Fig.3demonstrates that they are strictly symmetric with respect to the s -axis,as shown in Fig.1.No distinct change is observed in the density distribution on the edge.The formation of the 5–8–5defect in the ZGNR gives rise to larger spin charge density,especially for thesixFig.2.Electronic band structures of the (a)pristine AGNR,(b)defective AGNR with divacancy defects,(c)pristine ZGNR and (d)defective ZGNR with divacancy defects.The solid red (dotted blue)line denotes the a -spin (b -spin)polarized bands.The defect state is labeled by g ,and the dotted black line indicates the Fermi level.(For interpretation of the references to color in this figure legend,the reader is referred to the web version of thisarticle.)Fig.3.Spin-polarized charge density of the AGNRs (top panel)and ZGNRs (bottom panel)with no defect (left column)and the 5–8–5defects (right column).The opposite spin states is completely degenerate in the AGNR cases,while the spatial distribution is the charge difference between a -spin and b -spin (r a ðr Þ-r b ðr Þ)in the ZGNR cases.J.Zhao et al./Physica B 407(2012)204–208206atoms as components of two symmetric pentagons,which indicates that the electrons are localized around this area.The reduction of electron transport is due to the fact that comparable electrons are localized,as evidenced by Fig.3.It is worth to mention that the shape of nanoribbons can lead to extraordinary resonant tunneling trans-port [5].Besides,the mechanism of impurity scattering in different shapes of nanoribbons is shown to have differences [37].Here,our report is focused on the electronic transport proper-ties of the two sets,that is,armchair and zigzag edge of GNRs,are shown in Fig.4.The conductance gap for the pristine AGNR is 0.16eV,with two symmetric plateaus extending to 70.9eV with respect to the Fermi level.Unexpectedly,the conductance gap of the AGNR consisting of 5–8–5defects is decreased to 0.08eV,which is slightly smaller than that in the pristine AGNR.We attribute this to the presence of the C band crossing the Fermi level as well as the localized g band that close to the Fermi level.In the divacancy configuration,the first plateaus around the Fermi level resemble the pristine nanostructure.Hence,the conductance under larger electron energy is decreased when compared with the case of the pristine,which is a consequence of the 5–8–5defects giving rise to significant electron backscattering.It is noticed that the transmission dip located at À1.56eV is also related to strong electron backscattering.Considering indistinctive charge distribu-tion as the presence of 5–8–5defects induce (see Fig.3),it is reasonable to conclude that the width reduction of atomic geometry in the defective AGNR gives rise to extraordinary electronic states.As is well known,the transport is mainly dependent on the electronic transmission near the Fermi level,thus the reduced conductance gap reveals that the presence of the 5–8–5defects is favorable for electronic transport.ZGNRs can exhibit peculiar electronic properties due to their wave functions sharply localized along the GNRs edges at low energies.As for the pristine ZGNR,its conductance is symmetric with respect to the Fermi level and the edge state lead to the conductance peak in the vicinity of Fermi level.The first plateau extends to 71.3eV,which is in consistence with previous report [38].In contrast to the AGNR nanostructure that consisting of divacancy defects,where the presence of the 5–8–5defects can improve its electron transport,the 5–8–5defects in the ZGNR substantially decreases the conductance in the vicinity of Fermi level.Furthermore,the divacancy has significant impact on the first plateau around the Fermi level,as evidenced by theconductance dip located at À1.4eV.As can be seen here clearly that the presence of 5–8–5defects in the ZGNR is unfavorable for electronic transport.4.ConclusionIn this work,we have investigated the influence of 5–8–5defects on the electronic and transport properties in both the zigzag and the armchair graphene nanoribbons by using density functional theory combined with non-equilibrium Green’s func-tion.It is predicted that the presence of 5–8–5defect in ZGNR is unfavorable for electron transport,while such defects can significantly improve the electron transports in the AGNR.The distinct roles of 5–8–5defects in these two kinds of edged-GNR leads to different transport properties,which are attributed to the different coupling between p n and p subbands that are influenced by the defects.The defects and shapes of the GNR could have beneficial effects and ion beams can be used to tailor the nanostructure to tune the electronic transport of GNR for designing novel nanodevice.AcknowledgmentWe gratefully acknowledge Dr.M.A.Kuroda 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