Semiconducting to Half-Metallic to Metallic Transition on Spin

Jul 8, 2010 - ... and Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154. J. Phys...
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Semiconducting to Half-Metallic to Metallic Transition on Spin-Resolved Zigzag Bilayer Graphene Nanoribbons Yufeng Guo,*,†,‡ Wanlin Guo,*,† and Changfeng Chen*,‡ Institute of Nanoscience, Nanjing UniVersity of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China, and Department of Physics and High Pressure Science and Engineering Center, UniVersity of NeVada, Las Vegas, NeVada 89154 ReceiVed: March 10, 2010; ReVised Manuscript ReceiVed: June 1, 2010

Our first-principles calculations show that the electronic properties of spin-resolved zigzag bilayer graphene nanoribbons (ZBGNRs) of antiferromagnetic edges are highly sensitive to the interlayer distance between nanoribbons. The energy gap of the antiferromagnetic ZBGNR decreases and the semiconducting ZBGNR finally becomes a metal with decreasing interlayer spacing. Coupling with a transverse electric field, the ZBGNR exhibits a semiconducting to half-metallic to metallic transition via interlayer distance compression. The charge redistribution of spin-up and spin-down and the change of the density of states on the edge atoms, which are driven by the coupled effect of nanomechanical compression and the electric field, contribute to the exceptional modification on the band structure of the ZBGNR. Introduction A graphene nanoribbon, a one-dimensional structure or a strip of graphene of nanometers in width, exhibits various remarkable physical and chemical properties because of its special edge states and size effects.1-7 Zigzag and armchair edge geometries of monolayer GNRs give rise to largely different electronic properties. Armchair graphene nanoribbons are found to be metallic or semiconducting depending on their width.8-10 Meanwhile, zigzag graphene nanoribbons (ZGNRs) possess edge magnetism,8-11 and theoretical studies suggest that the ZGNRs of an antiferromagnetic (AF) edge state show a semiconducting to half-metallic transition in the presence of a transverse electric field across the nanoribbon width.12-14 The ZGNRs are then expected to have great potential applications in nanosensors, spin-filter devices, and spinelectronics. Bilayer graphene, a Bernal stacking (AB stacking) of two single graphene layers, is a gapless semiconductor, but an electronic gap will be induced by interaction with the substrate15-17 or externally in the presence of a vertical electric field,18-23 and the field-induced gap can be effectively tuned in a larger range by changing its interlayer spacing.24,25 Another experiment reports that the interlayer conduction of an epitaxial bilayer graphene is significantly modified by nanomechanical interlayer compression.26 Previous theoretical studies revealed that bilayer graphene nanoribbons of zigzag geometrical termination possess edge magnetism27,28 when bilayer graphene is cut into bilayer nanoribbons. However, the interlayer stacking arrangement and coupling significantly affect the localized edge spin states and magnetism.28-31 Tuning electronic properties of graphene nanoribbons is an intriguing aspect of fundamental research in graphene materials and functional device design. As electric and mechanical methods or their coupled effects become feasible ways to tune graphene properties, the sensitivity of the electronic structure and edge spin configuration of bilayer graphene * To whom correspondence should be addressed. E-mail: [email protected] (Y.G.), [email protected] (W.G.), [email protected] (C.C.). Phone: 86-25-84890513 (Y.G.). Fax: 86-25-84895827 (Y.G.). † Nanjing University of Aeronautics and Astronautics. ‡ University of Nevada.

nanoribbons to nanomechanical compression and an external field as well as the underlying physical mechanism needs to be further explored. In this study, we use density functional theory (DFT)-based first-principles calculations to systematically investigate the response of the electronic structure of spin-resolved zigzag bilayer graphene nanoribbons (ZBGNRs) of AF edges to the interlayer spacing compression in the presence or absence of a transverse electric field. The AF ZBGNR transforms from a semiconductor into a metal solely with interlayer distance decreases. When a transverse electric field is applied, the AF ZBGNR displays a semiconducting to half-metallic to metallic transition via the compression of the interlayer spacing. The underlying mechanisms for modification of the electronic properties are explained by the interlayer shift of spin-polarized edge electrons and the change of the local density of states on edge atoms, which is caused by the coupling between interlayer compression and field effects. Model and Method We consider a unit of an AB stacking 8-ZBGNR in which a periodic boundary condition is applied in the longitudinal direction. The 8-ZBGNR in such a supercell includes 32 carbon atoms, and the width of each graphene nanoribbon layer is 1.56 nm. The edge carbon atoms are terminated by hydrogen atoms. We consider three cases for the ZBGNR: (1) spin-unpolarized and two spin-resolved situations (R-spin and β-spin, or spin-up and spin-down are resolved), (2) antiferromagnetic (AF), and (3) ferromagnetic (FF) edge spin orientations, as shown in Figure 1. For the spin-resolved situations, the spin orientations at the edge atoms along the longitudinal direction are all ferromagnetic. The electronic structures of the ZBGNR are investigated by using the first-principles DFT computational VASP code with the ultrasoft pseudopotential and local (spin) density approximation [L(S)DA] for the exchange-correlation potential.32-34 An energy cutoff of 400 eV and a sufficient number of special 70 k-points that are uniformly sampled along the 1D Brillouin zone are employed for the 8-ZBGNR. The vacuum regions in the supercell between edges and planes are larger than 1.6 and 1.4

10.1021/jp102147a  2010 American Chemical Society Published on Web 07/08/2010

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Figure 1. Band structures of an 8-ZBGNR with (a) spin-unpolarized, (b) antiferromagnetic, and (c) ferromagnetic states. The carbon atoms at the left and right edges are denoted by L1, L2, R1, and R2, respectively. The black arrows show the directions of spin magnetic moments for edge atoms. In (b) and (c), the black lines represent R-spin and the red lines represent β-spin. The Fermi level is set to zero.

nm, respectively, to avoid any intercell interaction. The external electric field is modeled by adding a sawtooth-like potential along the transverse direction of the ZBGNR.35 The geometry for the ZBGNR is fully relaxed until the force on each atom is less than 0.1 eV/nm, and the equilibrium interlayer distance is 0.334 nm. To achieve an AF state, we initially set an up magnetic moment at each left edge carbon atom and a down magnetic moment at right edge atoms so that the R-spin (spinup) is dominant at the left edge, whereas the β-spin (spin-down) is dominant at the right edge, as shown in Figure 1b. The FF state is obtained by the same way. Results and Discussion The band structures of the spin-unpolarized and spin-polarized ZBGNRs in the absence of an electric field are shown in Figure 1. The spin-unpolarized ZBGNR is metallic, and its band structure is similar to that of single-layer ZGNRs.11 For the spinresolved situations, the ZBGNRs of the AF and FF edge spin configurations are semiconducting and metallic, respectively, (Figure 1b,c). The total energy of the AF state is 18.1 meV per edge atom lower than that of the spin-unpolarized one, and the FF state is 16.6 meV/atom lower. When the interlayer distance of the 8-ZBGNR is compressed to 0.24 nm, the total energy of the AF state is 4.85 meV per edge atom lower than that of the spin-unpolarized state, and the FF state is 4.4 meV/atom lower. In the presence of a transverse electric field of 2 V/nm, the total energy of the AF state is 1.4 meV per edge atom lower than that of the FF state. Therefore, the 8-ZBGNR with the AF edge is favored as the ground state, and in the following, we focus on investigating the effects of interlayer compression and an external field on the AF ZBGNRs. Figure 2 shows the band structures of the AF 8-ZBGNR of which the interlayer spacing d is compressed. At d ) 0.27 nm, the AF 8-ZBGNR is still a semiconductor (Figure 2a), but the energy gap is significantly reduced and the bands around the Fermi level are obviously deformed. When the interlayer distance decreases to 0.24 nm, the AF 8-ZBGNR totally transforms into a metal, as shown by Figure 2b. Interlayer compression significantly modifies the electronic properties of the AF ZBGNR. As explored by previous studies, the electronic and magnetic characteristics of graphene nanoribbons are mainly determined by its edge atom states.8-11 To unveil the physical mechanisms of interlayer compression induced band structure transition, the

Figure 2. Band structures of the AF 8-ZBGNR with the interlayer distance compressed to (a) 0.27 and (b) 0.24 nm. The inset shows the band structure around the Fermi level.

local density of states (LDOS) of R-spin and β-spin at the left and right edge carbon atoms are plotted in Figure 3. At equilibrium, d ) 0.334 nm, the AF ZBGNR is semiconducting. On the L1, L2, R1, and R2 edge atoms, there are two LDOS peaks below or two peaks above the Fermi level for both R-spin and β-spin. The R-spin states are occupied on the left L1 and L2 edge atoms (Figure 3a) and, oppositely, the occupied β-spin states appear on the right R1 and R2 edge atoms (Figure 3d), owing to the initial setting of the AF edge state. With the interlayer spacing compressed to 0.24 nm, the LDOS of R-spin on the L2 atom crosses the Fermi level and exhibits two peaks below and above the Fermi level, and the same change is also observed for the LDOS of β-spin on the R1 atom, as shown by Figure 3e,h. The semiconductor-to-metal transition of ZBGNRs induced by interlayer compression can be attributed to the modification of edge states localized on the L2 and R1 carbon atoms. To further understand the interlayer compression effect on the AF 8-ZBGNR, it is instructive to examine the response and redistribution of the spin-polarized charge density on edge atoms. Figure 4 shows the spatial distribution of the charge density difference, ∆F( ) FR(r) - Fβ(r), between R-spin and β-spin of the AF 8-ZBGNRs with different interlayer distances. Here, positive and negative ∆F only represent the opposite spin orientation. For the ZBGNR with d ) 0.334 nm, ∆F+ mainly distributes on the left edges, where ∆F- distributes on the right

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Figure 3. Local density of states (in units of states/atom) of R-spin and β-spin at the left L1, L2 and right R1, R2 edge atoms of the AF 8-ZBGNR with (a-d) d ) 0.334 nm and (e-h) d ) 0.24 nm.The Fermi level is set to zero.

Figure 4. Contour plots of the two-dimensional (2D) projection of the charge density difference [in units of e/(Å)3] between R-spin and β-spin of the AF 8-ZBGNRs. Yellow, red colors represent the positive charge density difference from lower to higher, whereas cyan, blue colors represent the negative charge density difference from higher to lower. Here, dark blue dots are carbon atoms and dark red dots are hydrogen atoms.

edges, resulting in the AF edge states. However, ∆F+ and ∆Fon the L2 and R1 carbon atoms gradually decrease with decreasing interlayer distance, as shown in Figure 4. On the contrary, the corresponding charge densities on the L1 and R2 atoms increase with interlayer distance decreases. The charge density shift is also proved by the increase or decrease of the LDOS on these edge atoms (Figure 3). The L2 and R1 atoms just locate above or beneath another carbon atom that belongs to the adjacent nanoribbon layer. Interlayer compression strengthens the interlayer coupling and, accordingly, the interaction between the L2 and R1 atoms with their related atoms. This leads to the interlayer transfer of some spin-up electrons from the L2 to the L1 atom and some spin-down electrons from the R1 to the R2 atom. As a result, the AF ZBGNR gradually transforms from a semiconductor into a metal. Moreover, the energy gap of the AF ZBGNR monotonically decreases with the reducing interlayer spacing until the ZBGNR completely becomes a metal. The electronic structure of the AF ZBGNR, in particular, for its edge states, is sensitive to interlayer compression. Previous studies have revealed that single-layer zigzag graphene nanoribbons of the AF edges display a semiconducting to halfmetallic transition in the presence of transverse electric fields.12 For the AF 8-ZBGNR, a similar electronic structure transition occurs if external electric fields are applied across the width of the graphene nanoribbons. Under a transverse electric field Et of 3 V/nm, the band structures of R-spin and β-spin of the AF ZBGNR are apparently split (Figure 5a) due to higher and lower electrostatic potentials formed at the left and right edges. The ZBGNR finally becomes half-metallic when the electric field Et increases to 5 V/nm (Figure 5b). On the other hand, the interlayer compression, as

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Figure 5. Band structures of the AF 8-ZBGNRs with an interlayer distance d ) 0.334 nm under (a) 3 and (b) 5 V/nm and (c) d ) 0.27 nm under 3 V/nm. The insets show the band structures around the Fermi level, which is set to zero.

Figure 6. Local density of states of R-spin and β-spin at the left and right edge atoms of the 8-ZBGNR with d ) 0.334 nm in the presence of electric fields. The Fermi level is set to zero.

mentioned above, can significantly influence the edge states of bilayer graphene nanoribbons. Thus, the coupled effect of the transverse electric field and interlayer spacing compression may produce a stronger modification on the electronic properties of the ZBGNR. Figure 5c shows the band structure of the AF ZBGNR with an interlayer distance of 0.27 nm under Et ) 3 V/nm. Different from the semiconducting in that d ) 0.334 nm, the compressed ZBGNR becomes half-metallic in the presence of the same electric field. This means that the half-metallicity of the ZBGNR, which was induced by the applied electric fields, as well as the critical field strength, can be effectively tuned via adjusting the interlayer distance. Figure 6 shows the LDOS of R-spin and β-spin on the left and right edge atoms in the presence of 3 and 5 V/nm electric

fields. At an equilibrium interlayer distance of 0.334 nm, the electric field Et of 3 V/nm moves the occupied and unoccupied states of R-spin on the edge atoms closer but moves the occupied and unoccupied states of β-spin apart, as shown by the peak shift of the LDOS in Figure 6a-d. When the Et increases to 5 V/nm, the LDOS curves of R-spin on the L1, L2, R1, and R2 atoms, including the occupied and unoccupied states, approximately overlap at the Fermi level (Figure 6e,f), but the corresponding LDOS curves of β-spin become more apart (Figure 6g,h), suggesting the half-metallic transition. This change is due to different electrostatic potentials and charge transfer between the left and right sides. To elucidate the mechanism for the interlayer compression caused half-metallicity at a lower field, Figure 7 shows the

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Figure 7. Local density of states of R-spin and β-spin at the left and right edge atoms of the 8-ZBGNR with d ) 0.27 nm under Et ) 3 V/nm. The Fermi level is set to zero.

LDOS of R-spin and β-spin under Et ) 3 V/nm, and the interlayer distance is compressed to 0.27 nm. The LDOS curves of the occupied and unoccupied states of R-spin on the L2 and R2 atoms move together and overlap at the Fermi level (Figure 7a,b). Compared with the case that d ) 0.334 nm and Et ) 3 V/nm, the interlayer compression also makes the occupied state of β-spin on the R1 atom and the unoccupied state of β-spin on the L1 atom closer (Figure 7c,d) as the interlayer charge transfer occurs. Therefore, the half-metallicity of the compressed ZBGNR under a lower critical electric field originates from the compression-induced interlayer charge transfer and the redistribution of R-spin on the L2 and R2 edge atoms.

Figure 8. (a) The band gap of R-spin and β-spin of the AF 8-ZBGNR with different interlayer spacings versus transverse electric field. (b) The variations of the band gap of R-spin and β-spin with interlayer distance in the presence of a 2 V/nm electric field. (c) Interlayer force of the 8-ZBGNR with interlayer distance in the absence of an electric field.

Figure 9. Total energy of the AF 8-ZBGNR with (a) a transverse electric field for d ) 0.27 and 0.334 nm and (b) interlayer distance in the absence and presence of an electric field of 2 V/nm.

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Figure 10. Band structures of an AF 8-ZBGNR with an interlayer antiparallel spin arrangement (AF-AP) (a) in the absence of an electric field, (b) with the interlayer distance compressed to 0.27 nm, and (c) under Et ) 2 V/nm.

Figure 11. Band structures of an AA stacking 8-ZBGNR with (a) spin-unpolarized, (b) antiferromagnetic, and (c) ferromagnetic states.

The systematic responses of the energy band gaps of R-spin and β-spin to the combined effects of interlayer spacing compression and the transverse electric field are given in Figure 8. Here, ∆R represents the gap of the band structure of R-spin and ∆β that of β-spin. For d ) 0.334 nm, ∆Rdecreases with transverse electric field increases and the ZBGNR becomes halfmetallic at Et ) 5 V/nm. Meanwhile, ∆β increases with Et increases. When the interlayer distance d is compressed to 0.27 nm, ∆R reduces to 0 at Et ) 3 V/nm, and ∆β is much lower than that of d ) 0.334 nm, as shown in Figure 8a. Interlayer compression remarkably decreases the critical electric field to induce half-metallicity in the ZBGNR. Figure 8b shows the variations of energy gap with the change of interlayer distance under Et ) 2 V/nm. Both ∆R and ∆β decrease with interlayer distance decreases. At d ) 0.255 nm, ∆Rdecreases to 0, but ∆β becomes 0 at d ) 0.24 nm. Thus, the compressed AF ZBGNR displays a semiconducting to half-metallic to metallic transition in the presence of an electric field of 2 V/nm. The tuning of the electronic structure of the ZBGNR can be realized not only by applying an external electric field but also by interlayer spacing compression. Figure 8c shows the variation of the force between two graphene nanoribbons. It increases sharply with an interlayer distance less than 0.3 nm. A recent experiment reported that the interlayer spacing between graphene layers can be reduced to 0.1 nm by nanomechanical compression.26 It is, therefore, possible to change the interlayer distance between two graphene nanoribbons over 25%.

To understand the effects of an external field and interlayer compression on the energy change of the AF 8-ZBGNR, the total energetics with an electric field and interlayer distance are shown in Figure 9. The transverse electric field decreases the total energy of the ZBGNR because of charge transfer between left and right edges, but the energy for a smaller interlayer spacing is higher (Figure 9a). The total energy increases with decreasing interlayer distance, as shown in Figure 9b. Compared with interlayer compression, the electric field effects on the energy of the AF 8-ZBGNR are rather low. Except for the AF and FF edge states, the ZBGNR may have other edge spin configurations. Figure 10a presents the band structure of an AF 8-ZBGNR with an interlayer antiparallel spin arrangement (AF-AP). The AF-AP ZBGNR is a semiconductor but transforms into metallic under interlayer compression (Figure 10b) or in the presence of a transverse electric field of 2 V/nm (Figure 10c). For the cases of d ) 0.334 and 0.27 nm and Et ) 2 V/nm shown in Figure 10, the total energetics of the AF-AP ZBGNR are 2.15, 2.9, and 4.48 meV per edge atom higher than that of the AF state, respectively. Thus, the AF state of the ZBGNR is always the ground state even under nanomechanical compression and an external field. The interlayer stacking arrangement is important for the electronic structures of the edge states on the graphene nanoribbons.28,29 Here, we have also investigated an AA stacking 8-ZBGNR, and its band structures of spin-unpolarized, antiferromagnetic, and ferromagnetic edge states are given in Figure

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Figure 12. Band structures of the AF 16-ZBGNRs with an interlayer distance d ) 0.334 nm (a) in the absence of an electric field, (b) under 4 V/nm, and (c) d ) 0.27 nm under 1 V/nm. The insets show the band structures around the Fermi level, which is set to zero.

11. The AA stacking ZBGNR is metallic for both edge spinunpolarized and edge polarized configurations, without obvious differences in the band structures. The energy of the AF state is only 0.005 meV per edge atom lower than that of the spinunpolarized state, whereas the FF state is 0.03 meV/atom higher. Such small energy differences means that there is no edge magnetism on the AA stacking ZBGNR. Moreover, a previous study revealed that the edge magnetism of zigzag bilayer graphene nanoribbons depends not only on the interlayer stacking arrangement but also on the exchange-correlation approximation chosen in DFT calculations.28 In that study,28 the LDA R-aligned ribbons were found to be nonmagnetic, but edge magnetism was obtained using GGA, whereas for β-aligned ribbons, both LDA and GGA predict the magnetic ground state. This indicates that the interlayer stacking arrangement plays a more important role in the edge magnetism of the bilayer nanoribbons. The AB stacking ZBGNR in our study (Figure 1) corresponds to the β-aligned zigzag bilayer ribbons shown in ref, 28 and the electronic structures and edge magnetism prediction are consistent with the results in ref28 as well. Therefore, the change of the electronic structures of the edge states predicted by our DFT calculations using LDA is qualitatively reliable for the ZBGNR. The size effect of the graphene nanoribbon on the electronic properties has been studied as well. Similar to the 8-ZBGNR, we consider a unit of an AB stacking 16-ZBGNR, which includes 64 carbon atoms, and the width of each graphene nanoribbon layer is 3.23 nm and the edge carbon atoms are terminated by hydrogen atoms. The equilibrium interlayer distance for the 16-ZBGNR is 0.334 nm, and the AF edge state is still the most stable state. As shown in Figure 12a,b, the AF 16-ZBGNR is a semiconductor and becomes half-metallic when a transverse electric field of 4 V/nm is applied. The critical electric field needed for transition is lower than that of the AF 8-ZBGNR. When the interlayer distance reduces to 0.27 nm, the AF 16-ZBGNR transforms into half-metallic under 1 V/nm (Figure 12c). The 16-ZBGNR exhibits a similar electronic structure transition as that of the 8-ZBGNR under the combination effect of electric field and interlayer compression. However, increasing the width of the graphene nanoribbon remarkably decreases the critical electric field. Conclusions Using first-principles calculations, we study the intrinsic electronic structure of the 8-ZBGNR with the AF edge spin orientations under nanomechanical compression and an external

field. In the presence of a moderate transverse electric field, the 8-ZBGNR exhibits semiconducting, half-metallic, and metallic properties depending on the interlayer distance variation. The interlayer spacing compression dramatically decreases the critical electric field to induce the half-metallicity in the AF ZBGNR. The underlying mechanism is unveiled by examining the external electric field and interlayer coupling induced total charge redistribution and changes in the charge densities of spin-up and spin-down at edge atoms. Adjusting the interlayer spacing becomes a viable way to tune the electronic properties of the spin-resolved ZBGNR. The present results may provide some insights into the fundamental electronic and magnetic properties of bilayer graphene nanoribbons and suggest potential applications in spin sensor and nanoscale mechanical-electricspintronics devices. Acknowledgment. This work is supported by DOE Cooperative Agreement DE-FC52-06NA26274 at UNLV, the 973 Program (2007CB936204), the NSF (10732040, 10947156), the Jiangsu NSF (BK2009365) of China at NUAA, and the Innovation Fund of NUAA. References and Notes (1) Novoselov, K. Nat. Mater. 2007, 6, 720. (2) Han, M. Y.; Oezyilmaz, B.; Zhang, Y.; Kim, P. Phys. ReV. Lett. 2007, 98, 206805. (3) Qian, H.; Negri, F.; Wang, C.; Wang, Z. J. Am. Chem. Soc. 2008, 130, 17970. (4) Novikov, D. S. Phys. ReV. Lett. 2007, 99, 056802. (5) Wang, X.; Ouyang, Y.; Li, X.; Wang, H.; Guo, J.; Dai, H. Phys. ReV. Lett. 2008, 100, 206803. (6) Dalosto, S. D.; Levine, Z. H. J. Phys. Chem. C 2008, 112, 8196. (7) Zhang, X. W.; Yang, G. W. J. Phys. Chem. C 2009, 113, 4662. (8) Nakada, K.; Fujita, M.; Dressslhaus, G.; Dresselhaus, M. S. Phys. ReV. B 1996, 54, 17954. (9) Yang, L.; Park, C.; Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. ReV. Lett. 2007, 99, 186801. (10) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. ReV. Lett. 2006, 97, 216803. (11) Pisani, L.; Chan, J. A.; Montanari, B.; Harrison, N. M. Phys. ReV. B 2007, 75, 064418. (12) Son, Y. W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (13) Hod, O.; Barone, V.; Peralta, J. E.; Scuseria, G. E. Nano Lett. 2007, 7, 2295. (14) Dutta, S.; Manna, A. K.; Pati, S. K. Phys. ReV. Lett. 2009, 102, 096601. (15) Mattausch, A.; Pankratov, O. Phys. ReV. Lett. 2007, 99, 076802. (16) Varchon, F.; Feng, R.; Hass, J.; Li, X.; Ngoc Nguyen, B.; Naud, C.; Mallet, P.; Veuillen, J. Y.; Berger, C.; Conrad, E. H.; Magaud, L. Phys. ReV. Lett. 2007, 99, 126805. (17) Oostinga, J. B.; Heersche, H. B.; Liu, X.; Morpurgo, A. F.; Vandersypen, L. M. K. Nat. Mater. 2008, 7, 151.

Semiconducting to Metallic Transition on ZBGNRs (18) Ohta, T.; Bostwick, A.; Seyller, T.; Horn, K.; Rotenberg, E. Science 2006, 313, 951. (19) Castro, E. V.; Novoselov, K. S.; Morozov, S. V.; Peres, N. M. R.; Lopes dos Santos, J. M. B.; Nilsson, J.; Guinea, F.; Geim, A. K.; Castro Neto, A. H. Phys. ReV. Lett. 2007, 99, 216802. (20) Ohta, T.; Bostwick, A.; McChesney, J. L.; Seyller, T.; Horn, K.; Rotenberg, E. Phys. ReV. Lett. 2007, 98, 206802. (21) Zhang, Y. B.; Tang, T. T.; Girit, C.; Hao, Z.; Martin, M. C.; Zettl, A.; Crommie, M. F.; Shen, Y. R.; Wang, F. Nature 2009, 459, 820. (22) Li, Z. Q.; Henriksen, E. A.; Jiang, Z.; Hao, Z.; Martin, M. C.; Kim, P.; Stormer, H. L.; Basov, D. N. Phys. ReV. Lett. 2009, 102, 037403. (23) Mak, K. F.; Lui, C. H.; Shan, J.; Heinz, T. F. Phys. ReV. Lett. 2009, 102, 256405. (24) Guo, Y. F.; Guo, W. L.; Chen, C. F. Phys. ReV. B 2009, 80, 085424. (25) Guo, Y. F.; Guo, W. L.; Chen, C. F. Appl. Phys. Lett. 2008, 92, 243101.

J. Phys. Chem. C, Vol. 114, No. 30, 2010 13105 (26) Sutter, P. W.; Flege, J.; Sutter, E. A. Nat. Mater. 2008, 7, 406. (27) Castro, E. V.; Peres, N. M. R.; Lopes dos Santos, J. M. B. arXiv: 0801.2788, 2008. (28) Sahu, B.; Min, H.; MacDonald, A. H.; Banerjee, S. K. Phys. ReV. B 2008, 78, 045404. (29) Miyamoto, Y.; Nakada, K.; Fujita, M. Phys. ReV. B 1999, 59, 9858. (30) Lee, H.; Park, N.; Son, Y. W.; Han, S.; Yu, J. Chem. Phys. Lett. 2004, 398, 207. (31) Lee, H.; Son, Y. W.; Park, N.; Han, S.; Yu, J. Phys. ReV. B 2005, 72, 174431. (32) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (33) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251. (34) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (35) Neugebauer, J.; Scheffler, M. Phys. ReV. B 1992, 46, 16067.

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