Physics Letters A 376 (2012) 3277–3280

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Physics Letters A

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Tailoring atomic structure to control the electronic transport in zigzaggraphene nanoribbon

Hui Zeng a,1, Jun Zhao a,∗,1, Jianwei Wei b, Xianliang Zeng a, Yang Xu c

a College of Physical Science and Technology, Yangtze University, Jingzhou, Hubei 434023, Chinab College of Optoelectronic Information, Chongqing University of Technology, Chongqing 400054, Chinac Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, Zhejiang 310027, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 August 2012Received in revised form 14 September2012Accepted 19 September 2012Available online 25 September 2012Communicated by R. Wu

Keywords:Graphene nanoribbonElectron transportTailoring nanostructureDensity functional theory

We have performed ab initio density functional theory calculation to study the electronic transportproperties of the tailored zigzag-edged graphene nanoribbon (ZGNR) with particular electronic transportchannels. Our results demonstrated that tailoring the atomic structure had significantly influencedthe electronic transport of the defective nanostructures, and could lead to the metal-semiconductingtransition when sufficient atoms are tailored. The asymmetric I–V characteristics as a result of symmetrybreaking have been exhibited, which indicates the route to utilize GNR as a basic component for novelnanoelectronics.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Graphene, which consists of a single atomic plane of carbonatoms [1], emerges as rising star in the field of theoretical physicsand materials science. It has attracted tremendous amounts oftheoretical and experimental investigations due to its novel elec-tronic structure and transport properties [2,3], such as ballistictransport [4] and quantum Hall effects [5]. The novel propertiesof graphene originate from the linear energy dispersion at thetwo nonequivalent Dirac points, where the conductance band con-ically contacts the valence band [6]. In particular, the quasi-one-dimensional graphene nanoribbons (GNRs) are regarded as the keycomponents of these nanostructures, which are composed of verynarrow atomic strips [7]. The approach of engineering the energygap in lithographically patterned graphene nanoribbon structureshas been demonstrated in experiments [8]. This route opens anew prospective for the minimization of electronic device by us-ing GNRs since the atomic structure then can be easily tailored viaconventional lithographic techniques.

It is well known that the electronic structure of GNRs di-rectly depends on their width and the shapes of the edges (arm-chair or zigzag) [9]. The crucial issue referred to the realization

* Corresponding author. Tel.: +86 716 8060942; fax: +86 716 8060942.E-mail address: zhaojun@yangtzeu.edu.cn (J. Zhao).

1 These authors contributed equally to the work.

0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.physleta.2012.09.025

of graphene-based nanodevice in future is effectively modulatingthe electronic transport by tailoring the atomic structure. Recently,Jin et al. have reported an approach to obtain stable freestand-ing carbon chains connected with two graphene flakes by utiliz-ing energetic electron irradiation inside a transmission electronmicroscope (TEM) [10]. This technology has provided a powerfulroute to fabricate both a pure carbon constriction of the thinnestGNRs and a channel contacted by carbon atoms as leads. Mean-while, Chuvilin et al. have shown similar results, mainly includingone channel and two channels connecting with two carbon atomicleads [11]. More importantly, quantum dots related transport phe-nomenon haven been demonstrated in specifically tailored GNRsand the energy gaps can be tuned by local potential experimen-tally, which is of crucial importance to the application of GNRs infuture [12,13].

In this Letter, we study the electronic and transport proper-ties of tailored GNRs with zigzag edge by using density functionaltheory (DFT) calculation. It is found that the electronic transportproperties of the pre-designed GNRs are substantially governed bythe symmetry of the atomic nanostructure. Our calculated resultshave shown that the possibility to design the GNR-based devicecomponents provided that tailoring the geometry of nanostructurein high precision is experimentally accessible, especially for theetched pattern. It is considered that the modification of the trans-port properties in terms of energetic beam irradiation to designthe building block makes GNR as promising candidate for novelnanoscale devices.

3278 H. Zeng et al. / Physics Letters A 376 (2012) 3277–3280

2. Model

Following the previous work, the length of ZGNR width is clas-sified by the number (N) of the zigzag chains [14]. We have per-formed the simulation on the electronic transport properties of8-ZGNR consisting of 12 unit cells for the pristine configuration.Motivated by the recent experimental characterization, we havebuilt four defective structural configurations, including the pristine,two symmetric configurations with different number of atoms, andthe asymmetric configuration formed by removing more atoms, asshown in Fig. 1. The tailored contact between the two halves of allthe nanostructures taken into account was saturated by hydrogen.The C–H bond length in all of the configurations is approximately1.1 Å. Initiatively, as much as 10 hexagonal rings have been tailoredfor the multichannel configuration by removing 16 carbon atoms,and its geometric design is similar to the summarized schematicsketch for measurement in Ref. [12]. The symmetric 2-channel con-figuration is formed by using one carbon hexagon to connect theperfect GNR on both sides, as a result of tailoring two more carbonatoms in its atomic geometry. Based on the symmetric 2-channelconfiguration, we have constructed the asymmetric nanostructureby means of shaping the edge to form the reconstructed atomic ar-rangement. We adopt the framework of ab initio density functionaltheory [15] utilized in the SIESTA code [16] to relax the atomicnanostructure and calculate the electronic structures. The standardnorm-conserving Troullier–Martins pseudopotential is employed tocalculate the ion–electron interaction [17]. The exchange correctionterm is calculated within the form proposed by Perdew and Burkeand Ernzerhof in the generalized gradient approximation [18]. Weadopt numerical double-ζ basis set with polarization and the planecutoff energy is chosen as 200 Ry. The relax process ensures theforce acting is less than 0.01 eV/Å, and the calculations are carriedout at electronic temperature T = 300 K. The transport propertiesare performed by the nonequilibrium Green’s function method [19,20]. Detailed knowledge about the nonequilibrium Green’s func-tion method is available in Ref. [21]. The electronic and trans-port properties of various configurations have been calculated incomparison with the pristine results to evaluate the influencesof the tailoring atomic nanostructure on the electric transportof GNRs.

3. Results and discussions

The electronic band structures of spin-polarized density ofstates (DOS) are shown in Fig. 2. In the pristine nanostructure, twoextremely high peaks originated from the edge state of GNR arefound to be located near the charge neutrality point (CNP). Theyare distributed below the CNP for α-spin state and β-spin state, re-spectively. It can be attributed to the fact that two spin states shiftin the opposite direction with respect to the CNP. Hence, the sharppeak induced by the β-spin state is larger than that of the α-spinstate. Here, our results are consistent with the previous simula-tion performed by spin-polarized calculations [22]. The simulationresults reveal that the perfect ZGNRs are semimetallic owing tothe presence of edge states [14]. In addition, the splitting betweenthe α- and β-spin states in the CNP also indicates that the per-fect ZGNRs are antiferromagnetic [23]. The remarkable DOS peakslocated around ±1.2 eV are responsible for the enhancement ofquantum conductance. In the case of the symmetric pattern GNRshown in Fig. 1(b), the sharp peak derived from the edge state isremarkably decreased and moves toward the CNP, which is dueto the breaking of edge states. Such a modification has importantinfluence to the electronic transport properties around the CNPin this configuration, which is verified by the transmission resultshown in Fig. 3. The DOS peak at −1.5 eV is much higher thanthat of the pristine, which is associated with the emergence of

Fig. 1. (Color online.) Geometrical profile of all structural configurations. (a) Thetop figure on the left side is the pristine nanostructure. (b) The top figure on theright side is the symmetric pattern with missing atoms, named as multichannelconfiguration. (c) The bottom figure on the left side is the symmetric nanostructureinitiated by removing more atoms, named as 2-channel configuration. (d) The bot-tom figure on the left side is the asymmetric nanostructure initiated by removingmore atoms, named as asymmetric configuration.

Fig. 2. (Color online.) The spin-polarized density of states (DOS) for (a) the pris-tine, (b) the multichannel configuration, (c) the 2-channel configuration, and (d) theasymmetric configuration. The α-spin DOS (top panel) and β-spin DOS (bottompanel) are shown by solid line (red color online) and dotted line (blue color on-line), respectively. The charge neutrality point (CNP) is denoted by the zero.

localization due to the charge transfer from the edge state. Addi-tionally, the results of α-spin state and β-spin state that far fromthe CNP are symmetric. It is found that two smooth DOS dips arelocated at about ±1.34 eV in both the α- and β-spin states, whosefeatures are dominated by the symmetry of the atomic nanostruc-ture. The DOS far from the CNP resembles the pristine, leadingto the similar transport behavior compared with the pristine re-sults. As for the configuration shown in Fig. 1(c), it is clear thatthe electronic structure of this configuration is very similar to thesituation in the multichannel configuration although there are nu-merical differences between them. The main change taking placein the electronic structure is the emergence of prominent energygap at the Fermi level. Compared to the smooth channel config-uration, the smooth DOS gap at 0.39 eV in the α-spin state issubstantially increased, and correspondingly similar result is also

H. Zeng et al. / Physics Letters A 376 (2012) 3277–3280 3279

Fig. 3. (Color online.) Electronic transmission coefficients of the defective ZGNRs,which are shown by solid line (blue color online). (a) The pristine, (b) the mul-tichannel configuration, (c) the 2-channel configuration, and (d) the asymmetricconfiguration. The charge neutrality point (CNP) is denoted by the dotted line.

observed at about −0.39 eV in the β-spin state. We attribute thedistinct results to the enhancement of resonant energies arisingfrom the different coupling due to the tailored nanostructure. Ana-logically, an impurity in the graphene as well as GNR can alsoyield clearly observable resonant states around the CNP [24–27].The asymmetric configuration is formed by removing more atomsfrom the previous symmetric nanoconfiguration. In general, theband structure near the Fermi level does not experience muchchange. However, the energy gap at the Fermi level in the β-spinstate becomes distinctive. The modifications in the band structureresults suggest that the electronic transport can be improved bytopological design in terms of energetic particle irradiation tailor-ing.

The transmission spectrum of the defective GNRs is displayedin Fig. 3. For the pristine GNR, the edge state in the CNP con-tributes 3G0 conductance, which is consistent with the previ-ous study [26,28]. The symmetric geometry of the pristine GNRleads to perfect symmetric transmission with respect to the CNP.The quantum transmission enhancement is ascribed to the pres-ence of van Hove singularity in DOS results. For the multichan-nel configuration, the transmission coefficient at CNP is remark-ably decreased to less than 1. Although the first transmissionplateau resembles the pristine, the transmission coefficient is de-creased to smaller than 0.5. Moreover, there occurs a transmis-sion dip tiny below the CNP and two sharp peaks observed at±1.48 eV arising from the localized electrons at this region. Itcan be seen clearly that the transmission spectrum has sym-metric line shapes with respect to the CNP except for the tinysharp transmission gap. In the case of 2-channel configuration,the transmission peak at the CNP is eventually evanescent. Thefirst transmission plateau is lowered to zero, indicating the metal–semiconductor transition, which is in good agreement with theprevious report in the asymmetric pattern [29]. Our results sug-gest a strategy to tune the band gap in GNR-based electronic interms of precise irradiation engineering to decorate the nanostruc-ture, which is specifically crucial for the potential application ofGNR-based quantum dots (QDs) [13]. The additional transmissiongap below the CNP becomes obscure in contrast to the previ-ous defective nanostructure. It is noted that the presence of twosymmetric transmission peaks located at ±1.6 eV, which are at-tributed to the extended states according to the correspondingDOS analysis. As for the asymmetric configuration, the M–S tran-sition is also observed for the presence of transmission gap ex-tending from −1.2 eV to 1.2 eV. This can be explained in termsof the asymmetric nanostructure somehow relieving the degener-

Fig. 4. I–V characteristics of the defective ZGNRs after tailoring structural atoms.(a) The pristine, (b) the multichannel configuration, (c) the 2-channel configuration,and (d) the asymmetric configuration.

acy among the various van Hove singularities, and similar resultcan be found in the cases of graphene and carbon nanotube [30,31]. The second symmetric transmission plateau emerges rang-ing from ±−1.2 eV to ±−1.48 eV, in contrast to the 2-channelcase in which such a feather is evanescent. As a consequence, thecurrent of this nanostructure at this bias region, paradoxically, islarger than that of the 2-channel nanoconfiguration. In addition,the transmission peaks at ±1.6 eV maintained but the values aredecreased.

Fig. 4 shows the I–V characteristics of the various defectiveGNRs, including the pristine GNRs result for comparison. The I–Vcurves of the pristine GNRs manifests oscillate characteristics atthe range of −1.4 V to 1.4 V because of the increase in trans-mission gap, and the current is determined by the competitionbetween the bias and the transmission gap [32]. Beyond this range,the current starts to increase tempestuously. The I–V curve ofthe pristine case is shown to be symmetric with respect to theV bias = 0 as a result of its symmetric nanostructure. The oscilla-tion characteristics of the I–V curve also present in the multi-channel configuration, within the same range −1.4 V to 1.4 V,which is in consistence with the result of the pristine. However,the oscillation intensity has substantially decreased. The main dif-ference in the I–V curve between the pristine and the multi-channel configurations is that the electronic transport has sig-nificantly deteriorated due to the atomic geometry of the multi-channel configuration. The 2-channel configuration is correspond-ing to more missing atoms; the oscillation characteristics of itsI–V curve is almost evanescent, but it has a long plateau rangedfrom −1.2 V to 1.2 V originated from geometry change. Comparedwith the results of the pristine case, the I–V curve illustratesthat the tailoring atoms could effectively lead to the M–S tran-sition. As for the asymmetric nanostructure, it is interesting tofound that the current at the bias region of 1.4–2.0 V is largerthan that of the 2-channel configuration, which is consistent withthe previous transmission results. The I–V curve of this configu-ration, associated with asymmetric nanostructure, is asymmetricalthough the differences are not distinct. In detail, the currentis 4.29 μA at the bias 1.6 V in contrast with the 3.30 μA cur-rent at bias −1.6 V, which can be ascribed to the electron scat-tering induced by the strong interaction between the right leadand the central region. The asymmetric I–V characteristics areexpected be present provided that more atoms are tailored. There-fore, the calculation results of GNRs with channels indicate that itis possible to obtain particular electronic and transport propertiesthrough pre-design or tailoring to utilize GNRs as diode or othernanodevice.

3280 H. Zeng et al. / Physics Letters A 376 (2012) 3277–3280

4. Conclusion

In conclusion, we have studied the electronic transport prop-erties of the tailored defective ZGNRs with pre-designed geome-try. The electronic band gaps are found to increase in the defec-tive GNRs after tailoring atoms with respect to the pristine GNR,which could lead to metal-semiconducting transition with increas-ing number of missing atoms. The I–V characteristics revealed thatsymmetric nanostructures present symmetric pattern with respectto the V bias = 0. More importantly, the asymmetric I–V curve pat-terns in virtue of the symmetry break during geometrical recon-struction suggest that this nanostructure can be used in the designof future nanodevice.

Acknowledgements

The authors acknowledge Dr. M. Kuroda and Prof. K.-L. Yaofor technical assistance on carrying out ab initio transport prop-erties and the relax calculation in the Mac OS X Turing cluster.We also thank Prof. D.-H. Xu for fruitful discussion. This workis supported by the National Science Foundation of China (GrantNos. 11047176, 11204391, 61006077), and the Research Founda-tion of Education Bureau of Hubei Province of China (Grant Nos.Q20111305, B20101303, T201204).

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