ARTICLE pubs.acs.org/JPCC
Electronic Structures of BC2N Nanoribbons Peng Lu, Zhuhua Zhang, and Wanlin Guo* Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China ABSTRACT: We reveal a rich variety of electronic and magnetic properties of H-terminated BC2N nanoribbons (BC2NNRs) by using extensive first-principles calculations. Zigzag edged BC2NNRs (z-BC2NNRs) can be semiconducting or metallic depending on the alignment of edge atoms. In particular, magnetic and even half-metallic behaviors can appear in some edged z-BC2NNRs when the ribbon width is over a critical value. Armchair-edged BC2NNRs also can be semiconducting or metallic but determined by the proportion of carbon, nitrogen, and boron atoms in the ribbons. The band gaps of all semiconducting BC2NNRs can be explained by a universal mechanism that is due to the charge polarization between the opposite edges, which is impaired with increasing ribbon width.
1. INTRODUCTION For applications in nanodevices, quasi-one-dimensional materials are superior to other types of materials in unique structures and distinct properties.1-18 Recently, a new type of one-dimensional (1D) materials, nanoribbons, have been one of the most studied materials, as these materials are only one atomic layer in thickness and thereby inherit many outstanding properties and functions from their two-dimensional counterparts.2-18 Of all studied nanoribbons, graphene nanoribbons (GNRs), the strip of a single graphite layer, have stimulated extensive research interest due to their great promise for developing electronic and spintronic devices.2-10 In particular, zigzag GNRs show magnetic edge states, which can give rise to many unusual properties such as giant magnetoresistance effect,4 half-metallic and magnetoelectric effects,5 and promising applications. Another type of nanoribbon attracting wide research interest is boron nitride nanoribbons (BNNRs).15-18 Previous studies have shown that both zigzag and armchair BNNRs are nonmagnetic wide gap semiconductors when all the edges are terminated by hydrogen atoms, but their energy gaps can be closed by applying an in-plane transverse electric field.15 Interestingly, the zigzag BNNRs can also exhibit half-metallic nature when only one edge is passivated as well as field-dependent magnetic behavior when both of the edges are unpassivated.16-18 To bridge the large gap in properties between the BNNRs and GNRs and designing new 1D nanomaterials with more ample properties, it is promising to explore stoichiometric nanoribbons consisting of B, C, and N elements. Early experiments based on X-ray diffraction or scanning tunneling microscopy indicated that BC2N materials possess irregularly stacked hexagonal sheets, with an interlayer distance of 3.34 Å.19-22 This interlayer distance is similar to 3.35 Å in graphite and slightly larger than 3.17 Å of the layered h-BN sheets. It has been proved long before that the BC2N sheet is one of the most stable structures among the layered compound materials composed of B, C, and N elements.19-22 There exist three types of isomers for the BC2N sheets, which are denoted as type I, type II, and type III, respectively.23 Theoretical calculations predict that the r 2011 American Chemical Society
type II BC2N sheets are the most stable ones among the three isomers as the C-C and B-N bonds in this structure are optimally matched. As a result, the C atoms and BN pairs form zigzag atomic chains along the [010] direction. As in the way of producing GNRs, the BC2N nanoribbons (BC2NNRs) should also be available by patterning the BC2N sheet along certain crystallographic orientation.24-26 Because of the more ample atomic alignments, the BC2NNRs may show many interesting properties that outperform those in GNRs and BNNRs. Still, a systematic study on the electronic and possible magnetic properties of the BC2NNRs is missing. In this work, using comprehensive first-principles calculations, we investigate the electronic properties of the BC2NNRs and unravel important mechanisms for the gap opening in semiconducting BC2NNRs. It is found that the BC2NNRs can show semiconducting or metallic properties depending on the structure and alignment of edge atoms. The energy gap of the semiconducting BC2NNRs decreases with increasing the ribbon width, because of the widthdependent Coulomb interaction between the opposite edges. Interestingly, some of the wide semiconducting z-BC2NNRs can fall into a magnetic ground state and even show spontaneous halfmetallic properties, because of the enhanced spin polarization effect at the opposite edges.
2. COMPUTATIONAL METHOD All the calculations are carried out using Vienna Ab initio Simulation Package (VASP) code.27-29 Ultrasoft pseudopotentials30 with the plane-wave basis are chosen for the spin-unrestricted density functional theory (DFT) computation, and the cutoff energy for the basis set is set to 417.4 eV. In the calculations, the local (spin) density approximation is used for the exchange-correction potential. We model the BC2NNRs using a supercell method within 1D periodic boundary condition. Received: October 26, 2010 Revised: December 4, 2010 Published: February 10, 2011 3572
dx.doi.org/10.1021/jp110217t | J. Phys. Chem. C 2011, 115, 3572–3577
The Journal of Physical Chemistry C
Figure 1. (a) Atomic and (b) electronic structures of type II BC2N sheet. (c) Contour plots of charge densities for the VBM and CBM, respectively. (d) Schematic energy diagram for the π orbitals hybridization of the C, B, and N atoms in the BC2N sheet. Antibonding states of C-B and C-N are represented by a-CB and a-CN, respectively. Bonding states of C-B and C-N are represented by b-CB and b-CN, respectively.
All dangling bonds at ribbon edges are terminated with hydrogen atoms. Two adjacent ribbons are separated by a vacuum region of at least 10 Å. The Brillouin-zone integration is sampled by up to 20 special k points for atomic structure relaxation and a total of 50 k points for electronic structure calculation. All the atoms in the unit cell are fully relaxed using conjugate gradient method until the force on each atom is less than 0.1 eV/nm.
3. RESULTS AND DISCUSSION 3.1. Electronic Properties of 2D Hexagonal BC2N sheet. The atomic and electronic structures of a 2D hexagonal type II BC2N sheet are shown in Figures 1a and 1b, respectively. Our calculations show that the binding energy of the BC2N sheet is -8.134 eV/atom, which is less than -7.897 eV/atom of BN sheet but larger than -8.842 eV/atom of graphene sheet. The optimized bond lengths of the C-C, B-C, B-N, and N-C in the BC2N sheet are dC-C = 1.41 Å, dB-C = 1.53 Å, dB-N = 1.44 Å, and dN-C = 1.39 Å, respectively. The band structure in Figure 1b shows that the BC2N sheet is a direct-gap semiconductor with a gap of 1.46 eV, in good agreement with previous studies.19-21,23 To understand the origin of the semiconducting property in the BC2N sheet, we plot the charge densities for valence band maximum (VBM) and conduction band minimum (CBM) in Figure 1c. The VBM is distributed on the joint C and B atoms, with more contribution from the C atom as well as a π bonding character between the C and B atoms; whereas the CBM is mainly located on the C and slightly less on the attached N atoms, with an antibonding π bonding character between them. As is well-known, B, C, and N atoms have different site potentials, and the potential hierarchy is B > C > N. According to the schematic energy level diagram among the interaction of B, C, and N atoms (see Figure 1d),31-36 the bonding state between C and B atoms (b-CB) forms the VBM while the antibonding state between the C and N atoms (a-CN) exists as the CBM. 3.2. Electronic and Magnetic Properties of z-BC2NNRs. We now address the atomic and electronic properties of
ARTICLE
BC2NNRs. First, we discuss the properties of z-BC2NNRs. The z-BC2NNRs can be divided into five groups according to the buildup of edge atoms: (i) The two edges are ended by B and C atoms, respectively (Figure 2a). (ii) The two edges are ended by N and C atoms, respectively (Figure 2b). (iii) One edge is ended by N and C atoms and the other is ended by B and C atoms (Figure 2c). (iv) The two edges are ended by B and N atoms, respectively (Figure 2d). (v) Both the two edges are ended by C atoms (Figure 2e). We label the five kinds of z-BC2NNRs as BBCC, NN-CC, CN-CB, BB-NN, and CC-CC, respectively. The zBC2NNRs with Nz zigzag chains across the ribbon width are denoted as Nz-z-BC2NNRs. On the basis of this donation, the BB-CC and NN-CC Nz-z-BC2NNRs only have even Nz, the CCCC and BB-NN Nz-z-BC2NNRs only have odd Nz, while the CNCB Nz-z-BC2NNRs have continuous change of width with Nz. The Nz-z-BC2NNRs belonging to the same group have similar character in electronic structure, even to vary Nz. So we only present the atomic and electronic structures of one z-BC2NNR for each group as shown in Figure 2. Most of the z-BC2NNRs show semiconducting properties, except for the metallic CC-CC 5-z-BC2NNR. The BB-CC and NN-CC 4-z-BC2NNRs have direct-gaps of 0.31 and 0.11 eV at the Brillouin boundary, respectively (parts a and b of Figure 2); while the CN-CB 4-zBC2NNR and BB-NN 5-z-BC2NNR have indirect gaps of 0.86 and 0.78 eV, respectively (parts c and d of Figure 2). The energy gap vs the width of different groups of Nz-z-BC2NNRs (Nz = 2-17) is shown in Figure 3a. Similar to the semiconducting GNRs, the energy gaps of the semiconducting z-BC2NNRs decrease with increasing the ribbon width. Interestingly, the semiconducting BB-CC and NN-CC Nz-z-BC2NNRs become metallic when the ribbon widths are larger than 13 Å (Nz = 6). In contrast, the energy gaps of the CN-CB and BB-NN Nz-zBC2NNRs can not be closed until the ribbon widths are larger than 25 Å (Nz = 12) and 37 Å (Nz = 17), respectively. The mechanism for different electronic properties in the five groups of z-BC2NNRs has been carefully examined by analyzing the molecule orbitals. For the BB-CC 4-z-BC2NNR (with energy gap of 0.31 eV), the CBM locates at the joint C and N atoms with antibonding character near the BB edge, while the VBM is occupied by the π orbital electrons of the outmost C atoms at CC edge (see Figure 4a). The energy arrangement of VBM and CBM in 4-z-BC2NNR is consistent with the energy schematic in Figure 1d. Similarly, the VBM and CBM in the NN-CC 4-zBC2NNR (with energy gap of 0.11 eV) are mainly contributed by the joint C and B atoms with bonding character at NN edge and the π orbitals of outmost C atoms at the CC edge, respectively (Figure 4b). From Figure 1d, we can find that the energy gap between the C π orbital and C-N antibonding states is slightly larger than the gap between the C π orbital and bonding C-B states. Therefore, the energy gap of the NN-CC z-BC2NNR is always smaller than the BB-CC kind of the same width (Figure 3). For the BB-NN 5-z-BC2NNR (with energy gap of 0.78 eV), the VBM is mainly contributed by the joint C and B atoms with bonding character at NN edge, and CBM by the joint C and N atoms with antibonding character on BB edge (Figure 4c). Therefore, according to the energy hierarchy between the b-CB, a-CN, and π orbital of C atom (Figure 1d), the band gap of the BB-NN z-BC2NNR can be always larger than those of the BB-CC and NN-CC kinds of similar ribbon width (Figure 3). For the CN-CB 4-z-BC2NNR (with energy gap of 0.86 eV), something different arises. As shown in Figure 4d, the VBM of this ribbon group is mainly contributed to by the π 3573
dx.doi.org/10.1021/jp110217t |J. Phys. Chem. C 2011, 115, 3572–3577
The Journal of Physical Chemistry C
ARTICLE
Figure 2. Atomic and electronic structures of (a) BB-CC 4-z-BC2NNR, (b) NN-CC 4-z-BC2NNR, (c) CN-CB 4-z-BC2NNR, (d) BB-NN 5-zBC2NNR, and (e) CC-CC 5-z-BC2NNR. The red rectangle represents the adopted supercell model in calculations.
Figure 3. Energy gap of Nz-z-BC2NNR as a function of the ribbon width.
Figure 4. Electronic structures and partial charge densities of the VBM and CBM for (a) BB-CC 4-z-BC2NNR, (b) NN-CC 4-z-BC2NNR, (c) BB-NN 5-z-BC2NNR, and (d) CN-CB 4-z-BC2NNR. Magenta (dark) and light blue (gray) colors represent VBM and CBM charge densities, respectively.
orbital of outmost C and N atoms on CN edge, while the CBM is mainly contributed by the π orbital of the outmost C and B atoms on CB edge. As the site energy in the CN edge is lower than the CB edge,15,31 an energy gap can be induced by the
electron transfer from the CB edge to CN edge. Generally, the different site potentials of B and N atoms endow different energy levels of their joint C atoms, especially for carbon atoms at ribbon edges. This gives rise to a potential difference between the opposite edges of z-BC2NNRs, accompanied by the energy gap opening in these ribbons. As the ribbon width increases, the lowered potential difference between the opposite edges reduces the energy gap of the semiconducting z-BC2NNRs. In addition, according to the energy hierarchy (Figure 1d), the gap between the Cπ and a-CN states is close to that between the Cπ and b-CB states. Thereby the BB-CC and NN-CC Nz-z-BC2NNRs transform metallic from semiconducting at the same width value of 13 Å (Nz = 6) while the semiconducting BB-NN z-BC2NNRs transform to metallic until reaching to a critical value of 37 Å (Nz = 17). With increasing the width of the CN-CB z-BC2NNRs, interestingly a flat band gradually emerges around the Fermi level (Figure 5a). Since the flat band at the Fermi level implies localized electronic states, local electron-electron interaction may trigger spontaneous magnetization according to the Stoner criterion. So we switch on spin polarization in the calculations and examine the magnetic property of all the z-BC2NNRs. It reveals that only the CN-CB Nz-z-BC2NNR shows magnetic ground state when the ribbon width is larger than 1.98 nm (Nz = 9). For the CN-CB 13-z-BC2NNR, the exchange splitting of the flat band around the Fermi level is 0.018 eV (Figure 5b). Local magnetic moments in the ribbon favor a ferromagnetic coupling along the ribbon edges and an antiferromagnetic coupling between the two edges (insert of Figure 6). For example, the antiferromagnetic (AFM) coupling between the two edges in CN-CB 13-z-BC2NNR can be 4.1 and 1 meV lower than that of the nonmagnetic (NM) and ferromagnetic states, respectively. The change of energy gaps in the spin-up band structure and the spin-down band structure of CN-CB Nz-z-BC2NNR (Nz = 9-24) is plotted in Figure 5c. As the ribbon width increases from 1.98 nm (Nz = 9) to 5.16 nm (Nz = 24), the band gap of spin-down increases and that of the spin-up decreases. The gap difference between spin-up and down band structures increases monotonically with the ribbon width and culminates at Nz = 16, whereby the system becomes half-metallic. The half-metallic property is maintained even when the ribbon width is up to 5.16 nm (Nz = 24) within our computational ability. In addition, the polarized spins are highly concentrated on the edge carbon atoms, and a less fraction on joint B or N atoms, as shown in the insert of Figure 6. The magnetic moment of each 3574
dx.doi.org/10.1021/jp110217t |J. Phys. Chem. C 2011, 115, 3572–3577
The Journal of Physical Chemistry C
Figure 5. Electronic structures of CN-CB 13-z-BC2NNR (a) spin unresolved and (b) spin resolved. (c) Energy gaps of spin-up and down band structures with respect to the ribbon width.
Figure 6. Variation of magnetic moment and energy difference between nonmagnetic and antiferromagnetic states with respect to the ribbon width for CN-CB z-BC2NNRs. Insert illustrates the magnetization density of CN-CB 13-z-BC2NNRs. Magenta (dark) and light blue (gray) colors represent spin-up and -down directions, respectively.
edge carbon atom can be enhanced by increasing the ribbon width, accompanied by the further stabilization of the AFM ground state. We plot the magnetic moment per edge C atom and energy difference between NM and AFM states with respect to the width of CN-CB z-BC2NNRs in Figure 6. It is found that both of them increase gradually with increasing the ribbon width, and converge to 0.2 μB and -6.7 meV (Nz = 24), respectively. We find that the magnetic ground state in the wider CN-CB zBC2NNRs is resulted from the stabilization mechanism competition between charge and spin polarization at the opposite edged carbon atoms.10,36,37 When the ribbon width Nz is less than 9, the stabilization mechanism favors the charge polarization between the opposite edges. With increasing the ribbon width, the Coulomb interaction between the opposite edges is alleviated
ARTICLE
gradually. This is reflected by the reduced energy gap in CN-CB z-BC2NNRs with increasing the ribbon width (Figure 3). Yet for Nz larger than 8, the spin polarization between the opposite edges is enhanced and becomes dominant over the charge polarization due to the localization of the edge states. As a result, the C atoms at the two opposite edges start to hold electrons with different spin directions. Further increasing the ribbon width will increase the edge magnetic moment (Figure 6), as the effect of spin polarization is more favorable. 3.3. Electronic Properties of a-BC2NNRs. Next, we turn to explore the electronic properties of a-BC2NNRs. Akin to the zBC2NNRs, the a-BC2NNRs can be divided into four groups according to the alignment of edge atoms. We label the four kinds of a-BC2NNRs as BC-BC, NC-NC, CCNB-NBCC, and NC-CB a-BC2NNRs, respectively. The a-BC2NNR with Na dimer lines across the ribbon width is denoted as Na-a-BC2NNR. The BCBC, NC-NC Na-a-BC2NNRs have odd Na, and the NC-CB Na-aBC2NNRs have even Na, whereas the CCNB-NBCC Na-aBC2NNRs have continuous change of width with Na. The atomic and electronic structures of different groups of aBC2NNRs are displayed in Figure 7. The NC-NC and BC-BC 7-a-BC2NNRs are all metals as shown in parts a and b of Figure 7, respectively; while the CCNB-NBCC 7-a-BC2NNR and NC-CB 8-a-BC2NNR have direct gaps of 0.95 and 1.43 eV at the Brillouin boundary, respectively (parts c and d of Figure 7). Extensive calculations show that the Na-a-BC2NNRs in the same group have similar electronic structures (Na = 3-21). By varying the ribbon width, the NC-NC and BC-BC Na-a-BC2NNRs can always keep metallic property, while the energy gaps of the CCNB-NBCC and NC-CB Na-a-BC2NNRs decrease monotonically as Na increases (Figure 8). Our previous works have revealed that the electronic properties of a-BC2NNRs are determined by the proportion of C, B, and N atoms.38 The BC-BC and NC-NC a-BC2NNRs contain uncoordinated B or N atoms and therefore show metallic nature with p-type and n-type doped electronic characters, respectively. Increasing the ribbon width even can give rise to a magnetic ground state in both the ribbon groups. In contrast, all the B and N atoms in the ribbons belonging to the CCNB-NBCC and NC-CB groups are coordinated, thereby offering semiconducting property in these ribbons. Although the CCNB-NBCC and NC-CB groups have the same atomic proportion and edge configuration, the energy gap of the CCNB-NBCC group is more robustly than that of the NCCB group to the ribbon width increasing. For example, the energy gap of NC-CB group decreases from 1.82 eV of Na = 4 to 0.11 eV of Na = 12, yet the energy gap of CCNB-NBCC group decreases only from 1.57 eV with Na = 4 to 0.98 eV with Na = 12. Then, it is interesting to see why the CCNB-NBCC and NCCB Na-a-BC2NNRs own distinctly different energy gap even when their ribbon widths are nearly the same. To classify this issue, we plot the charge densities of the VBM and CBM for CCBN-NBCC and NC-CB 8-a-BC2NNRs in Figure 9, respectively. In both the nanoribbons, the VBMs are mainly contributed by the edge states localized at the edge C atoms bonding with the B atoms (CB), while the CBMs are mainly contributed by the edge states localized at the opposite edged C atoms bonding with the N atoms (CN). Thereby, the energy gap is induced by the potential difference between the edged CB and CN, where most of the VBM and CBM are distributed, respectively. With increasing the distance between the CB and CN in semiconducting a-BC2NNRs, the attenuated Coulomb interaction lowers the potential difference between the edged CB and 3575
dx.doi.org/10.1021/jp110217t |J. Phys. Chem. C 2011, 115, 3572–3577
The Journal of Physical Chemistry C
ARTICLE
Figure 7. Atomic and electronic structures of (a) NC-NC 7-a-BC2NNR, (b) BC-BC 7-a-BC2NNR, (c) CCNB-NBCC 8-a-BC2NNR, and (d) NC-CB 8-a-BC2NNR. Red rectangle represents the adopted supercell model in calculations.
Figure 8. Energy gap of Na-a-BC2NNR as a function of the ribbon width. Figure 10. Partial charge densities of VBM and CBM for (a) NC-CB 4-a-BC2NNR, (b) NC-CB 10-a-BC2NNR, (c) CCNB-NBCC 4-aBC2NNR, and (d) CCNB-NBCC 10-a-BC2NNR. Magenta (dark) and light blue (gray) colors represent VBM and CBM charge densities, respectively.
Figure 9. Electronic structures and partial charge densities of VBM and CBM for (a) CCNB-NBCC 8-a-BC2NNR, (b) NC-CB 8-a-BC2NNR. Magenta (dark) and light blue (gray) colors represent VBM and CBM charge densities, respectively.
CN and leads to the energy gap decreasing. To confirm this point, we examine the distance between the edged CB and CN and see how it affects the energy gaps of CCBN-NBCC and NC-CB aBC2NNRs. It is found that once the Na is larger than 6, the distance between the edged CB and CN in the CCNB-NBCC group is always less than that of the NC-CB group with the same Na. This explains why the energy gap of CCNB-NBCC group is always larger than that of NC-CB group with the same Na (Na > 6) (see Figure 8). For example, the distance between the edged CB and CN in NC-CB 4-a-BC2NNR is less than that in CCNBNBCC 4-a-BC2NNR by 0.12 Å. In contrary, this distance
difference becomes -2.27 Å between the NC-CB and CCNBNBCC 10-a-BC2NNRs (parts c and d of Figure 10). 3.4. Stability of BC2NNRs. We finally examine the stability for the BC2NNRs of different groups. The binding energy per atom for the BC2NNRs is defined as Ef = (Etotal - nBEB - nNEN - nCEC - nHEH)/N, which has been applied successfully in other systems.39,40 Etotal is the total energy of BC2NNR. EB, EN, EC, and EH are the atomic energies of B, N, C, and H, respectively. ni is the atomic number of i element. N is the atomic number containing all the elements. As shown in Figure 11, the binding energies of all the BC2NNRs are higher than the value (-8.13 eV) of the type II BC2N sheet. The relative stability of BC2NNRs is directly proportional to the ribbon width. For zBC2NNRs with the same width, the ribbon belonging to CC-CC group possesses the most stable structure, whereas the BB-NN kind has the highest binding energy and therefore is energetically most unfavorable. At a given Nz, the difference between the binding energy per atom of CC-CC and BB-NN z-BC2NNRs can achieve 0.12 eV. However, the relative stabilities of the aBC2NNRs in different groups are almost the same at a given 3576
dx.doi.org/10.1021/jp110217t |J. Phys. Chem. C 2011, 115, 3572–3577
The Journal of Physical Chemistry C
Figure 11. Binding energy of per atom in (a) Nz-z-BC2NNR and (b) Na-a-BC2NNR as a function of the ribbon width. Red dot lines are the binding energy per atom of the BC2N sheet.
Na (Figure 11b), because the change of binding energy per atom in these a-BC2NNRs is within 0.04 eV. Generally, the zBC2NNRs are more stable than the a-BC2NNRs with the same width. Our results indicate that the configuration of edge atoms can remarkably affect the stabilities of z-BC2NNRs as well. Even so, we expect that all the discussed BC2NNRs can be synthesized in experiments by oxidization etching.
4. CONCLUSIONS In summary, we present the first-principles investigations on the electronic and magnetic properties as well as stability of H-terminated BC2N nanoribbons. Both the zigzag and armchair edged BC2NNRs can own semiconducting or metallic properties. When the two opposite edges show different atomic alignments, the z-BC2NNRs show semiconducting property and the energy gap decreases with increasing ribbon width. Interestingly, the CN-CB z-BC2NNRs can show inherent spin polarization and half-metal when the ribbon width is sufficiently large. For the a-BC2NNRs, the electronic properties are determined by their doping characters. Once the a-BC2NNRs contain uncoordinated B (N) atoms, they become p-type (n-type) doped and show metallic property; otherwise the a-BC2NNRs show semiconducting property. Because of the different atomic alignment in the whole ribbons, the energy gap of the CCNB-NBCC a-BC2NNRs is more robust than that of the NC-CB ones when against to the change in the ribbon width. Concerning the stability, zigzag nanoribbons are more stable than armchair nanoribbons and can stably exist in an ambient environment. These results demonstrate a rich variety of electronic and magnetic properties of BC2NNRs, which may find useful applications in designing nanoelectronic and spintronic devices. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work is supported by the 973 Program (2007CB936204), National NSF (10732040), and Jiangsu Province NSF (BK2008042) of China.
ARTICLE
(2) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (3) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347. (4) Kim, W. Y.; Kim, K. S. Nat. Nanotechnol. 2008, 3, 408. (5) Zhang, Z.; Chen, C.; Guo, W. Phys. Rev. Lett. 2009, 103, 187204. (6) Wu, M.; Wu, X.; Zeng, X, C. J. Phys. Chem. C 2010, 114, 3937– 3944. (7) Zhu, X.; Su, H. J. Phys. Chem. C 2010, 114, 17257–17262. (8) Zheng, X. H.; Wang, X. L.; Abtew, T. A.; Zeng, Z. J. Phys. Chem. C 2010, 114, 4190–4193. (9) Lu, Y. H.; Feng, Y. P. J. Phys. Chem. C 2009, 113, 20841–20844. (10) Pisani, L.; Chan, J. A.; Montanari, B.; Harrison, N. M. Phys. Rev. B 2007, 75, 064418. (11) Li, Y.; Zhou, Z.; Zhang, S.; Chen, Z. J. Am. Chem. Soc. 2008, 130, 16739. (12) Botello-Mendez, A. R.; Lopez-Urías, F.; Terrones, M.; Terrones, H. Nano Lett. 2008, 8, 1562. (13) Wu, X.; Pei, Y.; Zeng, X. C. Nano Lett. 2009, 8, 2210. (14) Du, A. J.; Zhu, Z. H.; Chen, Y.; Lu, G. Q.; Smith, Sean, C. Chem. Phys. Lett. 2009, 469, 183. (15) Zhang, Z.; Guo, W. Phys. Rev. B 2008, 77, 075403. (16) Barone, V.; Peralta, J. E. Nano Lett. 2008, 8, 2210. (17) Ding, Y.; Wang, Y.; Ni, J. Appl. Phys. Lett. 2009, 94, 233107. (18) Zheng, F.; Zhou, G.; Liu, Z.; Wu, J.; Duan, W.; Gu, B.-L.; Zhang, S. B. Phys. Rev. B 2008, 78, 205415. (19) Watanabe, M. O.; Itoh, S.; Mizushima, K.; Sasaki, T. J. Appl. Phys. 1995, 78, 2880. (20) Watanabe, M. O.; Itoh, S.; Mizushima, K.; Sasaki, T. Appl. Phys. Lett. 1996, 68, 2962. (21) Watanabe, M. O.; Itoh, S.; Sasaki, T.; Mizushima, K. Phys. Rev. Lett. 1996, 77, 187. Watanabe, M. O.; Itoh, S.; Sasaki, T.; Mizushima, K. Phys. Rev. Lett. 1996, 77, 2846. (22) Chen, Y.; Barnard, J. C.; Palmer, R. E.; Watanabe, M. O.; Sasaki, T. Phys. Rev. Lett. 1999, 83, 2406. (23) Liu, A. Y.; Wentzcovitch, R. M.; Cohen, M. L. Phys. Rev. B 1989, 39, 1760. (24) Hiura, H. Appl. Surf. Sci. 2004, 222, 374. (25) Berger, C.; Song, Z.; Li, X.; Wu, X. Science 2006, 312, 1191. (26) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Iijima, S. Nature 2004, 430, 870. (27) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558–561. (28) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251–14269. (29) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169–11186. (30) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892–7895. (31) Nakamura, J.; Nitta, T.; Natori, A. Phys. Rev. B 2005, 72, 205429. (32) Dutta, S.; Manna, A. K.; Pati, S. K. Phys. Rev. Lett. 2009, 102, 096601. (33) Ding, Y.; Wang, Y.; Ni, J. Appl. Phys. Lett. 2009, 95, 123105. (34) Okada, S.; Igami, M.; Nakada, K.; Oshiyama, A. Phys. Rev. B 2000, 62, 9896. (35) Okada, S.; Oshiyama, A. Phys. Rev. Lett. 2001, 87, 146803. (36) Kan, E.-J.; Wu, X.; Li, Z.; Zeng, C.; Yang, J.; Hou, J. G. J. Chem. Phys. 2008, 129, 084712. (37) Kan, E.-J.; Li, Z. Y.; Yang, J. L.; Hou, J. G. Appl. Phys. Lett. 2007, 91, 243116. (38) Lu, P.; Zhang, Z.; Guo, W. Appl. Phys. Lett. 2010, 96, 133103. (39) Li, J. L.; Yang, G. W. J. Phys. Chem. C 2009, 113, 18292–18295. (40) Li, J. L.; Yang, G. W. J. Appl. Phys. 2010, 107, 113702.
’ REFERENCES (1) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U.S.A. 2005, 120, 10451. 3577
dx.doi.org/10.1021/jp110217t |J. Phys. Chem. C 2011, 115, 3572–3577
