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具有边缘缺陷石墨烯纳米结的自旋输运特性


第 27 卷 第 3 期 2012 年 6 月 Article ID: 10078827 ( 2012 ) 03018107

新 型 炭 材 料 NEW CARBON MATERIALS

Vol. 27 No. 3 Jun. 2012

The spin-dependent transport properties

of a zigzag graphene nanoribbon edge-defect junction
2, 3 AN Liping 1, , LIU Nianhua3

( 1 . Department of Physics,Shaoguan University,Shaoguan 512026 ,China; 2 . Department of Physics,Yanshan University,Qinhuangdao 066004 , China; 3 . Institute for Advanced Study,Nanchang University,Nanchang 330031 ,China)

Abstract: Firstprinciples calculation w as performed to investigate the transport properties of edgedefect junctions of graphene w ith Hterminated or bare edges,w hich w ere generated by removing edge carbon atoms from a perfect ribbon. The edge defect changes the electronic transport behavior of a zigzag graphene nanoribbon from spindegenerated for a perfect ribbon to highly spinpolarized for edgedefective ones at the Fermi level. The electronic local density of states isosurface calculations could help understand the transport results. These junctions could generate spinpolarized currents. Especially ,the bare edgedefect junction has a high spin filter efficiency regardless of the external bias. This behavior suggests a possible use of the edgedefective graphene in a spin filter system. Keywords: Graphene nanoribbon; Edgedefect junction; Spindependent transport Document code: A CLC number: TQ 127. 1+ 1

1

Introduction

In the last tw o decades,various forms of carbon nanostructures, namely , buckyballs, carbon nanotubes,and lately graphene,have attracted a great deal of interest for their novel fundamental properties and possible applications in electronics. With the developments in preparation and synthesis techniques, carbonbased nanostructures have emerged as one of the most promising materials for nonsilicon electronics. In recent experimental studies,graphene nanoribbons ( GNRs) w ith narrow w idth have been realized[1-2]. In addition to high carrier mobilities that are higher than those of silicon,the existence of w idthdependent energy band gaps makes the GNRs a potentially useful structure for various applications. The w idth dependence of the band gap and the transport properties in quasionedimensional narrow GNRs have been studied theoretically[3-10]. Defects in GNR structures, such as vacancy or doped atoms or StoneWales defect,w ere also reported to modify electronic properties of GNR significantly[11-16]. Since GNRs have long spincorrelation lengths and good ballistic transport characteristics,they can
Received date: 20110916 ; Revised date: 20111205

be considered a promising active material of spintronic devices[17]. In particular, zigzag GNRs ( ZGNRs ) have unique spinpolarized edge states[18]. These edge states may be tuned by applying electrical field or choosing edge functional groups, giving rise to halfmetallic properties[19-22]. M oreover, ZGNRbased gain magnetoresistance w as realized,indicating possible application of ZGNRs in digital storage[23]. In this w ork,w e study the spindependent electronic transport of an edgedefect ZGNR junction by performing firstprinciple calculation. The edge defect changes the electronic transport behaviors of ZGNR from the spin degenerated for perfect case to highly spinpolarized at the Fermi level. These junctions could generate spinpolarized currents. Especially , the bare edgedefect junction has higher spin filter efficiency , regardless of the external bias. These behaviors suggest them as possible candidates to be used in spin filter device.

2

M odel and method

In recent firstprinciple calculations, some groups indicated that vacancies on GNR edges are energetically preferred[12] w hich significantly suppresses

Foundation item: National Science Foundation of China ( 10832005 ) . Author introduction: AN LIping ( 1975 - ) ,female,Ph. D. ,Lecturer,engaged in the research of photonic crystals and nanostructure materials. Email: fox781209@ mail. ecust. edu. cn English edition available online ScienceDirect ( http: ??w w w . sciencedirect. com ?science?journal?18725805 ) . DOI: 10. 1016 / S18725805 ( 12 ) 600122

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GNRs ’ conductance[11]. Here, w e fabricate GNR edge defects by removing carbon atoms from the edges of 4ZGNR,w ith the dangling bonds saturated by hydrogen atoms as show n in Fig. 1a, w here the source and drain electrodes are composed of tw o semiinfinite ZGNRs w ith four zigzag carbon chains ( 4ZGNR ) . On the other hand, bare GNRs can exist in the laboratory , and they are stable even at sufficiently high temperature of 2 000 K from the tightbinding moleculardynamics simulation[24]. So w e also study the transport properties of bare ZGNR edgedefect junction as show n in Fig. 1b. Optimization result indicates that all carbon and hydrogen atoms in the defect region are still in the same plane after relaxation.

2 e μ r( V b) T ( E, V b ) dE , ( 1) ∫ h μ l( V b ) σ w here the σ = ↑( spin_up) and↓( spin_down) . The energy region is betw een - eV b /2 and + eV b /2 , w hich contributes to the current integral. For every spin σ , the electron transmission coefficient under external bias V b is as given below : R A Tσ ( E, V b ) = Tr [ ( 2) Γl G Γr G ] σ, R A w here G and G are the retarded and advanced Green’s functions and Γ l and Γ r are the contact broadening functions associated w ith the left and right electrodes,respectively. Iσ ( V b ) =

3

Results and discussion

Fig. 1 A schematic device model of ZGNR junction. The w hole device consists of a central scattering region and tw o corresponding perfect electrodes,w hich are ( a) Hterminated and ( b) bare edgedefect junction

In this w ork, w e explore the spindependent electron transport in edgedefect ZGNR junction ( see Fig. 1 ) . Our firstprinciple calculations are based on densityfunctional theory ( DFT ) combined w ith nonequilibruim Green’ s function ( NEGF ) as implemented in the ATK package[25-26]. Single ξ basis sets are used. The mesh cutoff is chosen as 150 Ry ,and a M onkhorstPack kmesh of 1 × 1 × 50 is used. Since the electronic devices usually w ork at room temperature,the electron temperature is set to 300 K in our calculations. The geometry optimization is performed for the scattering region using quasiNew ton method until the absolute value of force acting on each atom is less than 0. 5 eV / nm. dependent current Under external bias,the spinthrough the central scattering region can be calculated by LandauerBüttiker formula

We performed transport calculations using the relaxed structures show n in Fig. 1. The calculated spindependent transmission spectra of the Hterminated and bare edgedefect junctions at zero bias are show n in Fig. 2. The spin orientations of the leads are set parallel ( P) as in Figs. 2a and c, w hile those in Figs. 2b and d are set antiparallel ( AP) . It can be seen that there is no spinpolarization betw een spin_up and spin _dow n state in the Hterminated edgedefect junction if the spin orientations of the tw o leads are in antiparallel alignment. M oreover,both spin _ up and spin _ dow n channels are blocked at the Fermi level ( see Fig. 2b) . On the other hand,spinpolarization occurs w ith a large spin splitting energy ( show n in Figs. 2a, c and d ) and exhibits a strong spin anisotropy at the Fermi level. For the parallel configuration of electrode spins ( see Fig. 2a and c) ,the spin_up and spin _dow n transmittances ( T up and T dow n ) exhibited a decrease in magnitude around Fermi energy E f under zero bias w hen compared to T in the case of a perfect ribbon ( degenerate w ith one unit for both spins show n in Fig. 2a dot line ) . The Hterminated ZGNR edgedefect junction exhibits above 50% decrease in transmission at the E f . This is because the edge vacancies break the sixsided carbon rings and the C —C sp2 hybridization is substituted by the localized C —H bonds on the edge vacancy. On the other hand,the values of T up and T dow n in Fig. 2a are almost constant in the energy w indow of 0. 2 eV around Fermi level. For the antiparallel configuration of electrode spins in bare edgedefect junction ( see Fig. 2d ) ,the spin_up and spin _ dow n transmittances ( T up and T dow n ) exhibited an increase in magnitude around Fermi energy E f at zero bias w hen compared to T in the case of a perfect ribbon ( degenerate w ith zero transmittance for both spins show n in Fig. 2d dot line) ; how ever,the transmittance is not changed for the Hterminated edge -defect junction if electrode spins are antiparallel in

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Fig. 2

The spindependent transmission spectra of ( a, b) the Hterminated and ( c, d) bare edgedefect junctions at zero bias

configuration. The spin polarization at the Fermi level can be measured by[27] T up - T dow n . ( 3) ξ= T up + T dow n The value of ξ for each case is given in Fig. 2. The polarization for the bare edgedefect junction is higher than that for the Hterminated edgedefect junction, regardless of the spin orientations of the leads,and presented a spin polarization over 70% at zero bias for the tw o cases,w hich is a good candidate for spin filter because of its higher polarization. To help understand the transport result of the edgedefect junction at zero bias,w e also calculated the local density of states ( LDOS ) at the Fermi level. Fig. 3 presents LDOS isosurfaces of the Hterminated and bare edgedefect junctions. Comparing Figs. 3a and b,w e can see that the state of spin_dow n in bare edgedefect junction continuously distributed in the central region,enhancing the transmission. This explains w hy T dow n presented a high value. Although the states of spin_up in bare edgedefect junction show ed a clustering of states in some atoms and the complete absence of states in some atoms, the reduction of states in the central region reduced transmission,giv-

ing a low er value of T up than that of the Hterminated. From Fig. 3c,w e can see that the LDOS at the Fermi level is very small,w hich means no electron is traveling from one end to another w hen the bias is zero or below a finite bias. This corresponds to zero transmission for the case in Fig. 2b. But w e note an enhancement of states in Fig. 3d compared w ith that in Fig. 3c; thus,there is a low er transmittance as show n in Fig. 2d. Next,w e calculate the spindependent currentvoltage ( IV ) characteristics. The I - V curves of the edgedefect junction given by Eq. ( 1 ) are presented in Fig. 4 As can be seen,for the Hterminated edgedefect junction,both spin states of the parallel spin configuration of electrodes are metallic; moreover ,the current of spin_up ( I up ) is larger than that of spin_dow n ( I dow n ) ,because the value of T up is greater than that of T dow n . In the antiparallel spin configuration of electrodes,the I - V characteristics depend not only on the spin but also on the direction of bias as show n in Fig. 4a. It show s a semiconducting condition w ith a threshold voltage of 100 mV for the spin _ dow n state; the spin _ up state is insulating tow ard the positive bias. The behavior is opposite toward the negative bias. For the case of bare edgedefect junction, the I - V curves are same in the negative

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Fig. 3 LDOS isosurfaces at the Fermi level. Left and right panels display spin_up and spin_dow n,respectively ; ( a) and ( c) for the Hterminated edgedefect junction,( b) and ( d) for the bare edgedefect junction

and positive bias parts as show n in Fig. 4b. It is found that except the spin _ up state of the antiparallel spin configuration of electrodes is nearly insulating ; the others are all metallic. For comparison,w e ploted the I - V curves of the Hterminated and the bare edgedefect junction w ith the same spin configuration as in Fig. 4c and d. It is obvious that the current of spin_ dow n state in the bare edgedefect junction is the largest,regardless of the spin orientations of the leads. The transport property of the bare edgedefect junction may be originated from tw o factors. In addition to the broken perfect honeycomb structure in the defect region ( as presented in Fig. 1b,the edged C —C bond lengths are no longer identical to the ones in the perfect honeycomb structure, and the bond angles deviate from 120° after structure relaxation ) ,there are tw o extra bands existing in the band structure for bare

ZGNR , w hich originated from the dangling bond ( see the bands indicated by the arrow in Fig. 5b ) ,except for the edge state near the Fermi level,indicated by a circle ( see Fig. 5 ) . Thus,the coexistence of the edge state and dangling bond state provides transport convenience for electron. Finally ,w e take the definition of spin filter efficiency ( SFE ) = I up - I dow n / I up + I dow n ; the SFE of the edgedefect junction w ith the increase in bias is plotted in Fig. 6. It is found that for the antiparallel configuration of electrode spins in the Hterminated edgedefect junction,the SFE is increased by about 100% under larger bias. On the other hand,the bare edgedefect junction has higher spin filter efficiency at any external bias,w hich may be of great importance in designing the devices.

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Fig. 4

The spindependent I - V curves of the Hterminated and the bare edgedefect junctions w ith parallel / antiparallel spin orientations of the leads

Fig. 5

The band structures of the Hterminated and the bare ZGNR. The arrow s indicate the bands appearing due to the dangling bond state. The circle line indicates the edge state. The spin is unpolarized

4

Conclusions

We have investigated spindependent electronic transport using firstprinciple quantum transport calculations in molecular devices constructed by removing carbon atoms from the edges of ZGNR. The Hterminated and the bare edgedefect junctions have been considered. The existence of edgedefect changed the electronic transport behaviors of ZGNR from the spin degenerated for perfect case to highly spinpolarized

at the Fermi level. We also presented electronic LDOS isosurface calculations that helped to understand the transport results. These devices could generate spinpolarized currents under bias. Especially ,the bare edgedefect junction has higher spin filter efficiency regardless of the external bias. The study of ZGNR edgedefect junction benefits graphene integrated circuit engineering that might be realized by ultrafine GNR fabrication technologies in the future and

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[ 11]





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Gorjizadeh N ,Farajian A A ,Kaw azoe Y. The effects of defects on the conductance of graphene nanoribbons[J] . Nanotechnology , 2009 , 20 ( 1 ) : 015201.

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[ 14] Oeiras R Y ,AraújoMoreira F M ,da Silva E Z. Defectmediated halfmetal behavior in zigzag graphene nanoribbons[J]. Phys Rev B , 2009 , 80 : 073405. [ 15] Zheng X H,Rungger I,Zeng Z ,et al. Effects induced by sinFig. 6 The spin filter efficiency ( SFE) of the edgedefect junctions w ith different spin orientations of the leads [ 16] gle and multiple dopants on the transport properties in zigzagedged graphene nanoribbons [J]. Phys Rev B ,2009 , 80 : 235426. Zheng X H,Wang R N ,Song L L ,et al. Impurity induced spin filtering in graphene nanoribbons[J]. Appl Phys Lett, 2009 , 95 : 123109. [ 17] Delin A ,Tosatti E,Weht R. Magnetism in atomicsize palladium contacts and nanow ires[J] . Phys Rev Lett,2004 ,92 : 057201. [ 18] Castro Neto A H,Guinea F,Novoselov K S ,et al. The elec. Rev Mod Phys,2009 ,81 : tronic properties of graphene[J] [ 1] Han M Y ,?zyilmaz B , Zhang Y ,et al. Energy bandgap engiJ]. Phys Rev Lett, 2007 , 98 : neering of graphene nanoribbons[ 206805. [ 2] Li X L ,Wang X R,Zhang L ,et al. Chemically derived ultrasmooth graphene nanoribbon semiconductors [J ]. 2008 , 319 : 12291232. [ 3] Miyamoto Y ,Nakada K ,Fujita M . Firstprinciples study of edge states of Hterminated graphitic ribbons[J]. Phys Rev B , 1999 , 59 : 98589861. [ 4] Lee H, Son Y W , Park N , et al. Magnetic ordering at the edges of graphitic fragments: magnetic tail interactions betw een the edgelocalized states[J]. Phys Rev B , 2005 , 72 : 174431. [ 5] [ 6] Son Y W ,Cohen M L ,Louie S G. Energy gaps in graphene nanoribbons[J] . Phys Rev Lett, 2006 , 97 : 216803. Barone V ,Hod O ,Scuseria G E. Electronic structure and stability of semiconducting graphene nanoribbons[J] . Nano Lett, 2006 , 6 : 27482754. [ 7] Abanin D A ,Lee P A ,Levitov L S. Spinfiltered edge states and quantum Hall effect in graphene[ J] . Phys Rev Lett, 2006 , 96 : 176803. [ 8] Areshkin D A ,Gunlycke D ,White C T. Ballistic transport in graphene nanostrips in the presence of disorder: importance of edge effects[ J]. Nano Lett, 2007 , 7 : 204210. [ 9] Cresti A ,Grosso G ,Parravicini G P. Numerical study of electronic transport in gated graphene ribbons[J] . Phys Rev B , 2007 , 76 : 205433. [ 10] Ezaw a M . Peculiar w idth dependence of the electronic properties of carbon nanoribbons [J]. Phys Rev B , 2006 , 73 : 045432. [ 27] [ 26] [ 25] [ 24] [ 21] Science, [ 20] [ 19] 109162. Son Y W , Cohen M L , Louie S G. Halfmetallic graphene nanoribbons[ J]. Nature, 2006 , 444 : 347349. Guo J,Gunlycke D ,White C T. Field effect on spinpolarized transport in graphene nanoribbons[J] . Appl Phys Lett,2008 , 92 : 163109. Zeng M G ,Shen L ,Yang M ,et al. Charge and spin transport in graphenebased heterostructure[J]. Appl Phys Lett,2011 , 98 : 053101. [ 22] Gorjizadeh N ,Kaw azoe Y. Chemical functionalization of graphene nanoribbons[ J] . J Nanomater, 2010 , 2010 : 513501. [ 23] Kim W Y , Kim K S. Prediction of very large values of magnetoresistance in a graphene nanoribbon device[J] . Nat Nanotechnol, 2008 , 3 : 408412. Kaw ai T ,Miyamoto Y ,Sugino O. Graphitic ribbons w ithout hydrogentermination: Electronic structures and stabilities[J]. Phys Rev B , 2000 , 62 : R16349R16352. Brandbyge M ,Mozos J L , Ordejon P, et al. Densityfunctional method for nonequilibrium electron transport[J] . Phys Rev B, 2002 , 65 : 165401. Taylor J,Guo H, Wang J. Ab initio modeling of open systems: Charge transfer, electron conduction, and molecular sw itching of a C 60 device [J] . Phys Rev B , 2001 , 63 : 121104. Martins T B , Miw a R H, da Silva A J R, et al. Electronic and transport properties of borondoped graphene nanoribbons[J]. Phys Rev Lett, 2007 , 98 : 196803.

can be useful in novel spintronics. Acknowledgments This w ork is supported by the National Natural Science Foundation of China ( No. 10832005 ) .
References

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具有边缘缺陷石墨烯 纳米 结 的 自旋输运特性
安丽萍
1, 2, 3

, 刘念华3

( 1. 韶关大学 物理系, 广东 韶关 512026 ; 2. 燕山大学 物理系,河北 秦皇岛 066004 ; 3. 南昌大学 高等研究院,江西 南昌 330031 )



要:

利用第一性原理研究了两种具有边缘缺陷石墨烯纳米结的自旋输运 , 即 边 界 氢 原 子 饱 和和 未 被 饱 和 两

种情况。结果表明: 边缘缺陷改变了电子的输运行 为。 对 于 完 整 的石墨烯纳米 带, 两 种 自旋的 电子 在 费 米 能 级 附 近是完全简并的; 对于含有边缘缺陷的石墨烯纳米结 , 两 种 自旋的 电子 在 费 米 能 级 附 近 的 很 大 能 量 范围 内 表 现 出 自旋分离。电子局域态密度可进一步说明这种 输运 行 为。 这 些 纳米结 可 产 生 与 自旋相 关 的 极 化 电 流。 特 别 对 于 未饱和的缺陷结, 在任何偏压下都有较高的自旋滤波效率。 关键词: 石墨烯纳米带; 边缘缺陷结; 自旋输运

基金项目: 国家自然科学基金( 10832005 ) . mail: fox781209@ sina. com. cn 作者简介: 安丽萍( 1975 - ) ,女, 山西平遥人, 博士研究生, 讲师, 主要从事光子晶体和纳米材料的研究. E-

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