The spin-dependent transport properties of zigzag graphene nanoribbon edge-defect junction

NEW CARBON MATERIALS Volume 27, Issue 3, Jun 2012 Online English edition of the Chinese language journal Cite this article as: New Carbon Materials, 2012, 27(3):181–187.

RESEARCH PAPER

The spin-dependent transport properties of zigzag graphene nanoribbon edge-defect junction AN Li-ping1,2,*, LIU Nian-hua1 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: First-principles calculation was performed to investigate the transport properties of edge-defect junctions of graphene with H-terminated or bare edges, which were generated by removing edge carbon atoms from a perfect ribbon. The edge defect changes the electronic transport behavior of a zigzag graphene nanoribbon from spin-degenerated for a perfect ribbon to highly spin-polarized for edge-defective ones at the Fermi level. The electronic local density of states isosurface calculations could help understand the transport results. These junctions could generate spin-polarized currents. Especially, the bare edge-defect junction has a high spin filter efficiency regardless of the external bias. This behavior suggests a possible use of the edge-defective graphene in a spin filter system. Key Words: Graphene nanoribbon; Edge-defect junction; Spin-dependent transport

1

Introduction

In the last two 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, carbon-based nanostructures have emerged as one of the most promising materials for nonsilicon electronics. In recent experimental studies, graphene nanoribbons (GNRs) with narrow width have been realized[1-2]. In addition to high carrier mobilities that are higher than those of silicon, the existence of width-dependent energy band gaps makes the GNRs a potentially useful structure for various applications. The width dependence of the band gap and the transport properties in quasi-one-dimensional narrow GNRs have been studied theoretically[3-10]. Defects in GNR structures, such as vacancy or doped atoms or Stone–Wales defect, were also reported to modify electronic properties of GNR significantly[11-16]. Since GNRs have long spin-correlation lengths and good ballistic transport characteristics, they can be considered a promising active material of spintronic devices[17]. In particular, zigzag GNRs (ZGNRs) have unique spin-polarized edge states[18]. These edge states may be tuned by applying electrical field or choosing edge functional groups, giving rise to half-metallic properties[19-22]. Moreover, ZGNR-based gain

magnetoresistance was realized, indicating possible application of ZGNRs in digital storage[23]. In this work, we study the spin-dependent electronic transport of an edge-defect ZGNR junction by performing first-principle calculation. The edge defect changes the electronic transport behaviors of ZGNR from the spin degenerated for perfect case to highly spin-polarized at the Fermi level. These junctions could generate spin-polarized currents. Especially, the bare edge-defect 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

Model and method

In recent first-principle calculations, some groups indicate that vacancies on GNR edges are energetically preferred[12], which significantly suppresses GNRs’ conductance[11]. Here, we fabricate GNR edge defects by removing carbon atoms from the edges of 4-ZGNR, with the dangling bonds saturated by hydrogen atoms as shown in Fig. 1a, where the source and drain electrodes are composed of two semi-infinite ZGNRs with four zigzag carbon chains (4-ZGNR). 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 tight-binding molecu

Received date: 16 September 2011; Revised date: 05 December 2011 * Corresponding author: AN Li-ping (1975- ), female, Ph.D., Lecturer，engaged in the research of photonic crystals and nanostructure materials. E-mail: [email protected] Copyright©2012, Institute of Coal Chemistry, Chinese Academy of Sciences. Published by Elsevier Limited. All rights reserved. DOI: 10.1016/S1872-5805(12)60012-2

AN Li-ping et al. / New Carbon Materials, 2012, 27(3): 181–187

In this work, we explore the spin-dependent electron transport in edge-defect ZGNR junction (see Fig. 1). Our first-principle calculations are based on density-functional theory (DFT) combined with 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 Monkhorst–Pack k-mesh of 1 × 1 × 50 is used. Since the electronic devices usually work at room temperature, the electron temperature is set to 300 K in our calculations. The geometry optimization is performed for the scattering region using quasi-Newton method until the absolute value of force acting on each atom is less than 0.5 eV/nm. Under external bias, the spin-dependent current through the central scattering region can be calculated by Landauer–Büttiker formula

I σ (V b ) = Fig. 1 A schematic device model of ZGNR junction. The whole device consists of a central scattering region and two corresponding perfect electrodes, which are (a) H-terminated and (b) bare edge-defect junction

lar-dynamics simulation[24]. So we also study the transport properties of bare ZGNR edge-defect junction as shown in Fig. 1b. Optimization result indicates that all carbon and hydrogen atoms in the defect region are still in the same plane after relaxation.

2e h

µ r (V b )

∫µ

l

(Vb )

T σ ( E , V b ) dE ,

(1)

where the σ =↑ ( spin _ up )and ↓ ( spin _ down ) . The energy region is between − eVb 2 and + eVb 2 , which contributes to the current integral. For every spin σ , the electron transmission coefficient under external bias Vb is Tσ ( E ,Vb ) as given below: R

Tσ ( E ,Vb ) = Tr[Γl G R Γr G A ]σ ,

(2)

where G and G are the retarded and advanced Green’s functions and Γl and Γr are the contact broadening functions associated with the left and right electrodes, respectively. A

Fig. 2 The spin-dependent transmission spectra of (a,b) H-terminated and (c,d) bare edge-defect junction

AN Li-ping et al. / New Carbon Materials, 2012, 27(3): 181–187

Fig. 3 LDOS isosurfaces at the Fermi level. Left and right panels display spin_up and spin_down, respectively; (a) and (c) for the H-terminated edge-defect junction, (b) and (d) for the bare edge-defect junction

3

Results and discussion

We performed transport calculations using the relaxed structures shown in Fig. 1. The calculated spin-dependent transmission spectra of the H-terminated and bare edge-defect junctions at zero bias are shown in Fig. 2. The spin orientations of the leads are set parallel (P) as in Figs. 2a and c, while those in Figs. 2b and d are set antiparallel (AP). It can be seen that there is no spin-polarization between spin_up and spin_down state in the H-terminated edge-defect junction if the spin orientations of the two leads are in antiparallel alignment. Moreover, both spin_up and spin_down channels are blocked at the Fermi level (see Fig. 2b). On the other hand, spin-polarization occurs with a large spin splitting energy (shown 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.2 a and c), the spin_up and spin_down transmittances ( Tup and Tdown ) exhibited a decrease in magnitude around Fermi energy E f under zero bias when compared to T in the case of a perfect ribbon (degenerate with one

unit for both spins shown in Fig. 2a dot line). The H-terminated ZGNR edge-defect junction exhibits above 50% decrease in transmission at the E f . This is because the edge vacancies break the six-sided 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 Tup and Tdown in Fig. 2a are almost constant in the energy window of 0.2 eV around Fermi level. For the antiparallel configuration of electrode spins in bare edge-defect junction (see Fig. 2d), the spin_up and spin_down transmittances ( Tup and Tdown ) exhibited an increase in magnitude around Fermi energy E f at zero bias when compared to T in the case of a perfect ribbon (degenerate with zero transmittance for both spins shown in Fig. 2d dot line); however, the transmittance is not changed for the H-terminated edge-defect junction if electrode spins are antiparallel in configuration. The spin polarization at the Fermi level can be measured by

[27]

AN Li-ping et al. / New Carbon Materials, 2012, 27(3): 181–187

Fig. 4 The spin-dependent I-V curves of the H-terminated and the bare edge-defect junctions with parallel/antiparallel spin orientations of the leads

Fig. 5 The band structures of the H-terminated and the bare ZGNR. The arrows indicate the bands appearing due to the dangling bond state. The circle line indicates the edge state.The spin is unpolarized

ξ=

Tup − Tdown Tup + Tdown

The value of ξ for each case is given in Fig. 2. The polarization for the bare edge-defect junction is higher than that for the H-terminated edge-defect junction, regardless of the spin orientations of the leads, and presented a spin polarization over 70% at zero bias for the two cases, which is a good candidate for spin filter because of its higher polarization. To help understand the transport result of the edge-defect junction at zero bias, we also calculated the local density of states（LDOS）at the Fermi level. Fig. 3 presents LDOS

isosurfaces of the H-terminated and bare edge-defect junctions. Comparing Figs. 3a and b, we can see that the state of spin_down in bare edge-defect junction continuously distributed in the central region, enhancing the transmission. This explains why Tdown presented a high value. Although the states of spin_up in bare edge-defect junction showed a clustering of states in some atoms and the complete absence of states in some atoms, the r eduction of states in the central region reduced transmission, giving a lower value of Tup than that of the H-terminated. From Fig. 3c, we can see that the LDOS at the Fermi level is very small, which means no electron is traveling from one end to another when the bias is zero or below a finite bias. This corresponds to zero transmission

AN Li-ping et al. / New Carbon Materials, 2012, 27(3): 181–187

(SFE) = I up − I down I up + I down ; the SFE of the edge-defect junction with the increase in bias is plotted in Fig. 6. It is found that for the antiparallel configuration of electrode spins in the H-terminated edge-defect junction, the SFE is increased by about 100% under larger bias. On the other hand, the bare edge-defect junction has higher spin filter efficiency at any external bias, which may be of great importance in designing the devices.

4

Fig. 6 The spin filter efficiency (SFE) of the edge-defect junctions with different spin orientations of the leads

for the case in Fig. 2b. But we noted an enhancement of states in Fig. 3d compared with that in Fig. 3 c; thus, there is a lower transmittance as shown in Fig. 2d. Next, we calculate the spin-dependent current–voltage (I-V) characteristics. The I-V curves of the edge-defect junction given by Eq. (1) are presented in Fig. 4. As can be seen, for the H-terminated edge-defect 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_down ( I down ), because the value of Tup is greater than that of Tdown . 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 shown in Fig. 4a. It shows a semiconducting condition with a threshold voltage of 100 mV for the spin_down state; the spin_up state is insulating toward the positive bias. The behavior is opposite toward the negative bias. For the case of bare edge-defect junction, the I-V curves are same in the negative and positive bias parts as shown 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, we ploted the I-V curves of the H-terminated and the bare edge-defect junction with the same spin configuration as in Fig. 4c and d. It is obvious that the current of spin_down state in the bare edge-defect junction is the largest, regardless of the spin orientations of the leads. The transport property of the bare edge-defect junction may be originated from two 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 two extra bands existing in the band structure for bare ZGNR, which 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, we take the definition of spin filter efficiency

Conclusions

We have investigated spin-dependent electronic transport using first-principle quantum transport calculations in molecular devices constructed by removing carbon atoms from the edges of ZGNR. The H-terminated and the bare edge-defect junctions have been considered. The existence of edge-defect changed the electronic transport behaviors of ZGNR from the spin degenerated for perfect case to highly spin-polarized at the Fermi level. We also presented electronic LDOS isosurface calculations that helped to understand the transport results. These devices could generate spin-polarized currents under bias. Especially, the bare edge-defect junction has higher spin filter efficiency regardless of the external bias. The study of ZGNR edge-defect junction benefits graphene integrated circuit engineering that might be realized by ultrafine GNR fabrication technologies in the future and can be useful in novel spintronics. Acknowledgements This work is supported by the National Natural Science Foundation of China (No.10832005).

References [1] Han M Y, Özyilmaz B, Zhang Y, et al. Energy band-gap engineering of graphene nanoribbons[J]. Phys Rev Lett, 2007, 98: 206805. [2] Li X L, Wang X R, Zhang L, et al. Chemically derived ultrasmooth graphene nanoribbon semiconductors[J]. Science, 2008, 319: 1229-1232. [3] Miyamoto Y, Nakada K, Fujita M. First-principles study of edge states of H-terminated graphitic ribbons[J]. Phys Rev B, 1999, 59: 9858-9861. [4] Lee H, Son Y W, Park N, et al. Magnetic ordering at the edges of graphitic fragments: Magnetic tail interactions between the edge-localized states[J]. Phys Rev B, 2005, 72: 174431. [5] Son Y W, Cohen M L, Louie S G. Energy gaps in graphene nanoribbons[J]. Phys Rev Lett, 2006, 97: 216803. [6] Barone V, Hod O, Scuseria G E. Electronic structure and stability of semiconducting graphene nanoribbons[J]. Nano Lett, 2006, 6: 2748-2754. [7] Abanin D A, Lee P A, Levitov L S. Spin-filtered 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: 204-210.

AN Li-ping et al. / New Carbon Materials, 2012, 27(3): 181–187

[9] Cresti A, Grosso G, Parravicini G P. Numerical study of electronic transport in gated graphene ribbons[J]. Phys Rev B, 2007, 76: 205433(1-8). [10] Ezawa M. Peculiar width dependence of the electronic properties of carbon nanoribbons[J]. Phys Rev B, 2006, 73: 045432. [11] Gorjizadeh N, Farajian A A, Kawazoe Y. The effects of defects on the conductance of graphene nanoribbons[J]. Nanotechnology, 2009, 20 (1): 015201. [12] Topsakal M, Aktürk E, Sevinçli H. First-principles approach to monitoring the band gap and magnetic state of a graphene nanoribbon via its vacancies[J]. Phys Rev B, 2008, 78: 235435.

properties of graphene[J]. Rev Mod Phys, 2009, 81: 109-162. [19] Son Y W, Cohen M L, Louie S G. Half-metallic graphene nanoribbons[J]. Nature, 2006, 444: 347-349. [20] Guo J, Gunlycke D, White C T. Field effect on spin-polarized transport in graphene nanoribbons[J]. Appl Phys Lett, 2008, 92: 163109. [21] Zeng M G, Shen L, Yang M, et al. Charge and spin transport in graphene-based heterostructure[J]. Appl Phys Lett, 2011, 98: 053101. [22] Gorjizadeh N, Kawazoe Y. Chemical functionalization of graphene nanoribbons[J]. J Nanomater, 2010, 2010: 513501(1-7).

[13] Ren Yun, Chen Ke-Qiu. Effects of symmetry and Stone–Wales

[23] Kim W Y,Kim K S. Prediction of very large values of magne-

defect on spin-dependent electronic transport in zigzag graphene

toresistance in a graphene nanoribbon device[J]. Nat Nanotech-

nanoribbons[J]. J Appl Phys, 2010, 107: 044514.

nol, 2008, 3: 408-412.

[14] Oeiras R Y, Araújo-Moreira F M, da Silva E Z. Defect-mediated

[24] Kawai T, Miyamoto Y, Sugino O. Graphitic ribbons without

half-metal behavior in zigzag graphene nanoribbons[J]. Phys

hydrogen-termination: Electronic structures and stabilities[J].

Rev B, 2009, 80: 073405. [15] Zheng X H, Rungger I, Zeng Z, et al. Effects induced by single and multiple dopants on the transport properties in zigzag-edged graphene nanoribbons[J]. Phys Rev B, 2009, 80: 235426.

Phys Rev B, 2000, 62: R16349-R16352. [25] Brandbyge M, Mozos J L, Ordejon P, et al. Density-functional method for nonequilibrium electron transport[J]. Phys Rev B, 2002, 65: 165401.

[16] Zheng X H, Wang R N, Song L L, et al. Impurity induced spin

[26] Taylor J, Guo H,Wang J. Ab initio modeling of open systems:

filtering in graphene nanoribbons[J]. Appl Phys Lett, 2009, 95:

Charge transfer, electron conduction, and molecular switching of

123109. [17] Delin A, Tosatti E, Weht R. Magnetism in atomic-size palladium contacts and nanowires[J]. Phys Rev Lett, 2004, 92: 057201. [18] Castro Neto A H, Guinea F, Novoselov K S, et al. The electronic

a C60 device[J]. Phys Rev B, 2001, 63: 121104. [27] Martins T B, Miwa R H, da Silva A J R, et al. Electronic and transport properties of boron-doped graphene nanoribbons[J]. Phys Rev Lett, 2007, 98: 196803.