Z-like Conducting Pathways in Zigzag Graphene Nanoribbons with

Article pubs.acs.org/JPCC

Z-like Conducting Pathways in Zigzag Graphene Nanoribbons with Edge Protrusions Yipeng An,† Wei Ji,‡ and Zhongqin Yang*,† †

State Key Laboratory of Surface Physics and Key Laboratory for Computational Physical Sciences (MOE) & Department of Physics, Fudan University, Shanghai 200433, China ‡ Department of Physics, Renmin University of China, Beijing 100872, China ABSTRACT: Electronic transport properties of zigzag graphene nanoribbons (ZGNRs) with one or two triangle protrusions at the edges are studied by using density functional theory combined with nonequilibrium Green’s function method. We find the protrusion generally breaks down the edge state along the same edge, which carries the most current in the junction. For the graphene ribbons having even number of zigzag chains, however, the protrusions can increase or decrease significantly the conductance with different relative position of the two protrusions, accompanied by negative differential resistance characteristics. The abnormal increase of the conductance is ascribed to the forming of a new Z-like conducting pathway as well as the ruining of the mirror symmetry of the ribbons. In terms of odd ZGNRs, the introduction of edge protrusions only suppresses current flow and linear I−V curves are achieved. These edgemodified ways make the graphene-based nanomaterials present more abundant electronic transport phenomena and can be useful for the design of future nanoelectronic devices.

1. INTRODUCTION Graphene has attained extensive interest since its successful fabrication in 20041,2 due to its special electronic structures and fantastic electronic transport behaviors,3−5 including anomalous quantum Hall effect,6 quantum confinement effect,7 etc. Graphene sheets need to be tailored into certain geometries to fit the requirement of future device applications. Graphene nanoribbons are one category of the promising candidates8−10 for coming nanodevices. Several prototype devices based on graphene nanoribbons have been fabricated,11−14 and transport properties in various devices have been theoretically investigated, e.g., field-effect transistors (FET),15 negative differential resistance (NDR) behaviors,8,16 gas sensors,17 and the effect of graphene coupled on metallic electrode.18 For graphene nanoribbons with zigzag edges (ZGNRs), the edge states are full of significance, which generally dominate the electronic structures around the Fermi level (EF) and thus primarily influence the transport characteristics of ZGNR-based devices. Attractive properties were obtained by modifying the edges of ZGNRs. For instance, the electronic transport behaviors of some T-shaped and crossed ZGNR junctions were modeled by first-principles calculations. It was demonstrated that these ZGNR-based nanostructures could present some interesting phenomena,19 e.g., showing a metallic behavior and controlling the electronic transport by selective doping of B or N atoms. A junction, comprised of a graphene diamond nanofragment with hydrogenated zigzag edges interconnected to two semi-infinite non-hydrogenated-reconstructed graphene nanoribbons, was predicted to show the field-effect transistors characteristic.20 How the O adsorption and structural modifications at the edges of graphene © 2012 American Chemical Society

nanoribbons affect the spin-polarized transport properties at zero bias has been explored by Saloriutta et al. The O adsorption was found to dominate the transport of the armchair graphene nanoribbons, while the structural modifications could tune markedly the transport of ZGNRs.21 However, not all ZGNRs behave similarly. The ZGNRs containing even number of zigzag chains in width, present completely different electronic transport characteristics from those of odd number.22 Thus, the edge-modifying operation is expected to produce very different electronic transport properties of the two kinds of ZGNRs, although the details that how it affects the transport properties are still ambiguous. In this paper, to shed more light on the role of edge modifications, we reported a theoretical study of the electronic transport properties of the both categories, namely even and odd, of ZGNRs whose edges are modified by one or two triangle protrusions (TPs). These configurations are different from those in refs 19−21. As shown in Figure 1, two perfect ZGNRs, one containing 4 zigzag chains (4-ZGNR) and the other, 5 (5-ZGNR), are adopted as the original samples. The role of how the TPs affect the electronic transport properties of the two kinds of ZGNRs is explored. Our first-principles calculations show that the TPs usually break down the conductive edge states of the edges modified by TPs. However, under certain conditions, one new conducting pathway of Zlike can be formed, which can drastically increase the conductance of the junction. The interesting NDR characterReceived: January 11, 2012 Revised: February 14, 2012 Published: February 18, 2012 5915

dx.doi.org/10.1021/jp3003646 | J. Phys. Chem. C 2012, 116, 5915−5919

The Journal of Physical Chemistry C

Article

each atom is less than 0.05 eV/Å. To preserve a precise description of π-conjugated bonds, double-ζ plus polarization (DZP) basis set was used for all atoms. The Norm-conserving Troullier−Martins pseudopotentials26 were used to describe the core electrons. The Brillouin zone of the electrode was sampled with 1 × 1 × 100 points within the Monkhorst−Pack K-point sampling scheme, and the mesh cutoff was chosen as 150 Ry. The current through the transport system was calculated from the Landauer−Büttiker formula.27 Details of the calculation method can be available in the previous literatures.23−25

3. RESULTS AND DISCUSSION Current−voltage (I−V) characteristics of the 4-ZGNR-based nanojunctions were calculated as the bias voltage varies from 0.0 to 1.0 V in a step of 0.1 V, as shown in Figure 2a. These

Figure 1. Schematic diagram of the ZGNR based nanojunctions. (a) refers to the perfect and edge-modified (with one or two triangle protrusions) 4-ZGNR based nanojunctions, labeled as GE0, GE1, and GE21−GE24. (b) refers to the case for 5-ZGNR, labeled as GO0, GO1, GO21, and GO22. The shadowed areas indicate the left (L) and right (R) electrodes, between which is the central scattering region (containing the sample and three unit cells for every buffer layer near the electrodes).

istics are obtained for the 4-ZGNR nanojunctions. Dissimilarly, 5-ZGNR displays linear I−V curves, and TPs consistently suppress the electron transmission in this case. Although spinpolarized states may appear in ZGNRs with or without protrusions,21 they usually would become unstable with respect to the spin-unpolarized states at finite temperature due to the weakness of the magnetism.22 Thus, only spin-unpolarized calculations were performed in this work to obtain the experimentally detectable transport properties.

Figure 2. (a) and (b) refer to the I−V characteristics and transmission spectra at zero bias for these 4-ZGNR based nanojunctions, respectively. The Fermi level is set at zero.

2. MODELS AND METHOD Figures 1a and 1b display the schematic diagram of the 4ZGNR (with even zigzag chains) and 5-ZGNR (with odd zigzag chains) based two-probe transport systems, respectively. For both cases, the perfect nanoribbons (without triangle protrusions), the nanoribbons with only one edge occupied by one protrusion, and the nanoribbons with both edges occupied by protrusions are considered in our calculations. The perfect 4-ZGNR and 5-ZGNR junctions are labeled as GE0 and GO0, respectively. When only one edge of the ribbon is occupied by the protrusion, the junction is labeled as GE1 or GO1, as indicated in Figure 1. GE21−GE24 and GO21−GO22 express the 4-ZGNR and 5-ZGNR junctions, respectively, who have two protrusions at the edges with different relative distances between them. In the calculations, a two-probe transport system is comprised of three parts, i.e., the left electrode (L), the right electrode (R), and the central scattering region (C). The steady state quantum transport calculations are performed using the first-principles density functional theory (DFT) with the local density approximation combined with the nonequilibrium Green’s function (NEGF) formalism as implemented in the Atomistix ToolKit (ATK) program package.23−25 The structural relaxations of each two-probe system are performed in advance and allowed until the absolute value of force acting on

edge-modified ZGNRs nanojunctions present different I−V characteristics, compared with GE0, a perfect ribbon, which shows a current-limited effect due to a conductance gap (Cg) presenting under the applied bias.22 The two-probe system GE1, in which an edge of the ribbon is modified with a TP, shows a better electron transmission ability than the perfect GE0 and an interesting NDR characteristic. The current through GE1 is first quickly increased when applying a bias voltage from 0.0 to 0.4 V. If the voltage is beyond 0.4 V, the current decreases, but still larger than that of GE0, at least until the voltage reaching 1.0 V. Similar NDR behaviors are also observed in systems GE21 to GE23 where both edges of a 4ZGNR are modified by two TPs with different relative distances between them. System GE24 is a special case that appears an insulating characteristic. With respect to the decrease of the relative distance, more importantly, the conductance increases gradually from GE21 to GE23 and abruptly drops to a very small value, even smaller than GE0, in GE24. We look into the transmission curves of these 4-ZGNRbased nanojunctions for a better understanding of the obtained I−V curves, since the current is determined by the transmission spectra, as shown in Figure 2b. Although there is a sharp transmission peak, stemmed from the flat bands near the Fermi level,28 sitting around the EF at equilibrium in the transmission 5916



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spectrum of GE0, an obvious conductance gap (Cg) was found under certain biases, which normally enlarges with the bias voltage increasing.22 The reason why a gap was induced by bias voltages was ascribed to the different parities of the π (filled, odd parity) and π* (empty, even parity) states around the EF, hindering the hopping of electrons from the source to the drain.22 It thus leads to a current−limited effect of GE0 that only the transmission channels around the boundaries of the bias window contribute to the current. Comparing the transmission curves of GE0 and GE1 in Figure 2b, one can find at zero bias one protrusion at the edge of the ZGNR can decrease much the transport ability of the system. This trend is consistent with the result obtained in ref 21. The sharp transmission peak in GE0 becomes broader in GE1, implying GE0 a more conductive junction under a relatively low applied bias. The substantial difference between GE1 and GE0 geometries is that the former has no mirror symmetry along the width of the ribbon, while the latter has. As a result, the parity limitation22 to the current is canceled in GE1, unlike in GE0, which guarantees the electrons in GE1 can easily jump from the source to the drain through the paritybroken transport channels, e.g., the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO) of the central scattering region, as shown in Figure 3.

become more conductive from GE21 to GE23, but fairly localized for GE24 in which no appreciable conducting state is found from −1.8 to 1.8 eV in its transmission spectrum (Figure 2b). From GE21 to GE23, the shorter the relative distance of the two TPs, the stronger the coupling between them, which was confirmed by the broadening of the density of states (DOS) near the EF shown in Figure 4. Distributions of

Figure 4. DOSs of the sample parts of GE21, GE22, and GE23 nanojunctions.

scattering states can help understanding those results. The edge state at a side of a ribbon degrades incompletely, due to the scattering of the TP. Both incomplete edge states at the two sides of a ribbon, however, connect together with the region between the two TPs, forming a new state, via the interactions between them. As shown in Figure 3, the scattering state distribution of the newly formed state in real space indicates a Z-like conducting pathway of the ribbon, which enhances the conductance of the devices. Such Z-like pathway is clearly seen in Figure 3, especially for GE23, where both the HOMO and LUMO present the best electronic conduction ability. The formation of the Z-like pathway, that relevant with the distance between the two TPs, explains the growing conductance from GE21 to GE23. However, when the distance between the two TPs gets closer and eventually reaches the case of GE24, the mirror symmetry along the width direction resumes, which kills the Z-like pathway, since it does not satisfy the mirror symmetry. The destroyed pathway leads to the rather localized HOMO and LUMO of GE24, as illustrated by Figure 3, giving rise to the abruptly dropped conductance of GE24 from that of GE23 (see Figure 2a). In terms of the 5-ZGNR-based devices, electronic transport properties of the two-TP modified devices are more or less similar to that of the 4-ZGNR, while that for TP-free and oneTP modified devices are opposite to that of the 4-ZGNR. Current−voltage curves of the four nanojunctions, i.e., GO0, GO1, GO21, and GO22, are plotted in Figure 5a. It was found that the linear I−V curve of GO0 exhibits the maximum conductance among all the four devices due to the lack of mirror-symmetry-induced current limitation, which is consistent with the previous report.22 The conductance of the other three devices is consistently decreased not only for the one-TP case (GO1) but also for both two-TP cases (GO21 and GO22). As illustrated in Figure 5b, the electron transmission is strongly suppressed when TP (s) is (are) fabricated at the edge(s) due to the breakdown of the traditional edge states. The conductance thus decreases from GO0, GO1, to GO21 in Figure 5a. Although the two TPs are fairly close in GO22, it still does not satisfy the mirror symmetry, so that no symmetryinduced current limitation exists.22 The formed Z-like conducting pathway, more conductive than GO21, persists in

Figure 3. HOMO and LUMO eigenstates of central scattering region of the 4-ZGNR-based nanojunctions. The isovalue of molecular orbitals is 0.03 Å−3/2. The red/blue color expresses the positive/ negative wave functions.

From the extended behavior of HOMO and LUMO of GE1, it is found that the conducting capability of HOMO is much stronger than that of LUMO. Thus, it is the HOMO, distributing mostly along the TP-free edge, mainly conducts the GE1 device. Because of the existence of a TP, the edge state on another edge of the ribbon is destroyed. Even so, due to the cancellation of parity limitation and the conducting behavior of the remaining edge state, the largest current carried by GE1 is twice to that of GE0. From GE21 to GE24, each edge of a 4-ZGNR is modified by a TP with tapering distances between the two TPs. Their conductance increases gradually from GE21 to GE23 and abruptly drops to a very small value, even smaller than GE0, in GE24, consistent with the transmission behaviors of those junctions illustrated in Figure 2b. The states near the EF 5917



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the blockade of almost all eigenstates (the small triangles) in the bias window as shown in Figure 6a, bottom. Other NDR features found in GE21−GE23 and linear I−V curves for GO series can be understood by similar analysis routines. Note that the different transport behaviors of ZGNRs with even or odd number of zigzag chains only appear at finite biases. The difference may be undetectable for the two kinds of ZGNRs at zero bias.21 These results suggest that the one-TP 4-ZGNR based nanojunctions may likely be candidates for two-terminal NDR devices, e.g., high-frequency oscillators,29 mixers, multipliers, logic,30 and analog-to-digital converters.31 For 5-ZGNRbased junctions, the linear I−V curves can be effectively tuned through the edge protrusions, which should also be helpful in future graphene applications.

4. CONCLUSIONS We investigated the electronic transport properties of the two categories of zigzag graphene nanoribbons (with even and odd chains) whose edges are modified by one or two triangle protrusions, using a first-principles method. The edge protrusions were found to drastically tune the transport properties of the ribbons. They generally destroy the traditional edge states at the same side of the ribbons and decrease the conducting ability of the junctions. A brand new Z-like transport pathway, however, can be formed in the ribbons with two closer protrusions at the two edges, which can enhance much the conducting capability of the circuit. The 4ZGNRs with protrusions almost show NDR effect, while approximate linear I−V curves are found for 5-ZGNR-based nanojunctions. The difference is ascribed to the parity limitation from the structural symmetry in the former, but not in the latter. Our findings indicate such edge-modified tactics can control effectively the electron transport properties and make the GNRs based nanomaterials present more diversified functions.

Figure 5. (a) and (b) refer to the I−V characteristics and transmission spectra at zero bias for these 5-ZGNR-based nanojunctions, respectively. The Fermi level is set at zero. The insets of the lower two pictures in (b) present the HOMO and LUMO eigenstates of the nanojunctions.

GO22, which has the smallest distance between the two TPs, as shown in the insets of the lower two pictures of Figure 5b. Such pathway causes a much higher conductance of GO22 than that of GO21 in Figure 5a. The NDR seems a unique I−V feature for 4-ZGNR-based devices, while 5-ZGNR-based devices show almost linear I−V curves. Systems GE1 and GO1 are chosen, as representative systems, to reveal the underlying mechanism. Transmission spectra of GE1 and GO1 under various biases are given in Figures 6a and 6b, respectively. When increasing the bias, e.g.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under Grants 10674027 and 11004244, 973-project under Grants 2011CB921803 and 2012CB932704, Beijing Natural Science Foundation (BNSF) under Grant 2112019, Fudan High-end Computing Center, and Beijing Computing Center. Wei Ji was supported by Program for New Century Excellent Talents in University.

Figure 6. Transmission spectra of GE1 (a) and GO1 (b) nanojunctions under the biases of 0.0, 0.4, and 1.0 V. The small triangles indicate the eigenstate positions of the scattering region in the bias window.

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to 0.4 V, several eigenstate channels (labeled by the triangles) entered into the bias window for both GE1 and GO1. The current of either case, therefore, goes larger with the bias increasing to 0.4 V. When the applied bias exceeds 0.4 V, the trend of GO1 continues; however, that of GE1 does not due to the mirror symmetry induced current limitation. Under a bias of 1.0 V, the states near the EF, e.g. HOMO, on the TP-free edge in GE1 tend to be localized at the left side of the ribbon. The eigenstate distribution along the graphene core, excluding the protrusion part, of the ribbon shows distinct mirror symmetry. Therefore, the current limitation from the mirror symmetry of 4-ZGNR comes back under high biases, leading to

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Z-like Conducting Pathways in Zigzag Graphene Nanoribbons with

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