Ab Initio Investigation about the Possibility of Ferromagnetism Induced

Feb 23, 2010 - We study structural deformation, electronic states, and intrinsic magnetism induced by the cation vacancy (VB) in boron nitride nanotub...
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J. Phys. Chem. C 2010, 114, 4357–4361

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Ab Initio Investigation about the Possibility of Ferromagnetism Induced by Boron Vacancy in BN Nanotubes Rui Liu,† Jia Li,†,‡ and Gang Zhou*,† Department of Physics, Tsinghua UniVersity, Beijing 100084, People’s Republic of China, and Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany ReceiVed: December 7, 2009; ReVised Manuscript ReceiVed: February 11, 2010

We study structural deformation, electronic states, and intrinsic magnetism induced by the cation vacancy (VB) in boron nitride nanotubes (BNNTs), in comparison with the BN sheet, using spin-polarized density functional theory. Two types of vacancy configurations are observed in tubes, depending on the nature of the vacancy and the local stress. The underlying formation mechanisms are discussed from the viewpoint of the electronic and geometrical (or stress-induced) effects. Under additional stress, the VB prefers the open configuration to the closed 5-1DB configuration, showing different properties and potential applications. Due to the strong localization, the magnetic interaction between the VB-induced moments is short-range along either the axis or the circumference, meaning the ferromagnetism is difficult to be present. The simulation of negative charge injection implies VB-defective BNNTs might be promising candidates for spin-transport devices. In addition, the effects of surrounding H and F atoms on the spin-polarized states and magnetism of defective BNNTs are also explored. I. Introduction In recent years, the intrinsic magnetism induced by native defects in sp-electron systems has attracted increasing attention for potential applications in spintronics,1 because the conventionally magnetic impurity doping2 can be completely skipped in the fabrication procedure. It was theoretically shown that cation vacancies in bulk wide-gap nitrides result in the appearance of local moments, and may induce the ferromagnetism in some cases.3 In contrast to the bulk, low-dimensional nanostructures (e.g., nanotube and nanoribbon) are more appropriate candidates for microelectronic devices, catering to the ongoing miniaturization. Boron nitride nanotubes (BNNTs) have high thermal and chemical stabilities and thus are expected to be used as high-temperature nanodevices or protective shields of nanodevices in specific circumstances.4 It is meaningful to study what kind of conditions can induce ferromagnetism of BNNTs all the while. Similar to dopants5 or adatoms,6,7 the vacancies in BNNTs, native8 or created by electron irradiation,9 can also generate new spin-polarized states in the gap10 and induce local moments.8 This is not unexpected because any localized sp states in solids have the possibility to form local moments in essence.5-7,11,12 This, however, does not ensure the existence of ferromagnetism in systems, which is crucial for spintronic devices.7 To the best of our knowledge, this critical issue whether local moments induced by the defect states can lead to a collective magnetism by the long-range coupling, as well as its implications for practical spintronic applications, was not basically involved in previous reports on vacancy-induced intrinsic ferromagnetism of BNNTs. Consequently it is not explicitly addressed whether BNNTs containing vacancies or what kind of defective BNNTs could be used as nanospintronic devices. * Corresponding author. E-mail: [email protected]. † Tsinghua University. ‡ Fritz-Haber-Institut der Max-Planck-Gesellschaft.

Noting the theoretical prediction of cation vacancies-induced ferromagnetism in wide-gap nitrides3 and experimental observations of B monovacancies in the BN sheet,13 in this article, we studied the dependencies of geometry and stability of the cation vacancy (VB), as well as the spin-polarized electronic structure, in BNNTs on ambient conditions using spin-polarized density functional theory. First, we confirmed that the vacancy configuration, as well as the spin-polarized states, is related to the nature of the vacancy and the local stress. Successively, we discussed the formation mechanisms of different configurations from the interaction between the nearest-neighbor (NN) atoms of the vacancy (i.e., electronic effects) and the induced stress distribution (i.e., geometrical effects). In particular, we focused on the open configuration of the VB, including formation or existence conditions, spin-polarized electronic structures, chemical activity and magnetism, and application prospects. Finally, for applications in spintronics, we proposed to inject negative charges into such sp-electron systems and studied the properties. II. Calculation Method and Model Since most of grown BNNTs prefer a zigzag orientation,14 here we focused on zigzag BNNTs [i.e., the (10,0) tube was considered]. All calculations were performed using the Vienna ab initio simulation package (VASP)15 within the framework of spin-polarized density functional theory (DFT). The generalized gradient approximation of PBE exchange correlation functional16 and the projector augmented wave potentials describing the electron-ion interaction17 were employed. A cutoff energy of 400 eV was used for the plane-wave basis set, and further increase in cutoff showed little difference in results. A tetragonal 1 × 1 × 3 supercell was adopted, with a vacuum region of 14 Å between tubes. Integration over the Brillouin zone was done using the Monkhorst-Pack scheme18 with 1 × 1 × 3 k-points for structural optimization and 1 × 1 × 7 k-points for electronic structure calculations. The vacancy was created by the removal of a B or N atom from the tube. The NN atoms of the vacancy were defined as 1, 2, and 3 as shown by image

10.1021/jp911623m  2010 American Chemical Society Published on Web 02/23/2010

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Figure 1. Minimum-energy path (MEP) of the transition from the open configuration to the 5-1DB configuration for the cation vacancy (VB) in the (10,0) BNNT by the NEB calculation. Dots indicate the calculated images and the line is a smooth interpolation with the spline function. (a-e) Structures corresponding to the calculated images in the minimum energy pathway of the structural transition. The images are shown by meshes with different colors in order to illustrate the differences of configurations more clearly. Among the three nearest neighbor atoms of the VB, two ones at the same circumference are labeled as N1 and N2, and the remaining one is labeled as N3. Numbers are the distance between the N1 and N2 atoms in angstrom. The activation barrier is about 163 meV.

(a) in Figure 1. All atoms were fully relaxed until the Hellmann-Feynman force on each atom was less than 10 meV/ Å. Furthermore, the climbing image nudged elastic band (NEB) method19 was used to calculate the activation barrier for structural transition. III. Results and Discussion Since there are two types of constituents with different chemical characteristics in BNNTs, structural defects in BNNTs are more complicated than those in carbon nanotubes (CNTs). For example, a previous study indicated that the B-B or N-N bonds in curved BN nanostructures (e.g., NTs and fullerenes) are “frustrated” due to the higher energy cost as compared to the B-N bonds, and accordingly even-member rings are more stable than odd-member rings at the growing tube edge.20 Furthermore, our present calculations of BNNTs showed that the stable structures of vacancies are not as simple as mentioned in the previous report10 but essentially dependent on the nature of the vacancy, which reflects the interactions of the NN atoms, and the local stress corresponding to the curvature of the system. The free-relaxation of the VB structure leads to an open configuration (as shown by image (a) in Figure 1), arising from the outward movements of three NN N atoms of the VB. This is consistent with a recent simulation using the AM1 semiempirical method.21 Each of the three N atoms has one sp2-like dangling bond (DB). However, when the N1 and N2 atoms at the same circumference were intentionally moved (inward) closer at the beginning of the optimization, a weak N-N bond of 1.48 Å is formed after relaxation, and consequently, a 5-1DB (one pentagon and one DB located at the nonagon) configuration is present (as shown by image (e) in Figure 1). Such closed configuration was previously studied,10 whereas the open configuration was largely ignored. Our calculations showed that the total energy of the 5-1DB configuration is 1.56 eV lower than that of the open configuration. This result is consistent with previous DFT studies using periodical boundary condition,8,10

Liu et al.

Figure 2. Schematic illustrations of the formation of the VB and VN in BNNTs and the BN sheet, showing dangling bonds or unpaired electrons along the circumference (yellow) and pz electron pairs perpendicular to the tube (red), as well as the stress along the circumference or on the plane (green arrows). (a) VB, the open and closed 5-1DB configurations are on the left and right, respectively; (b) VN, the initial and final configurations are on the left and right, respectively; (c) VB + NB in the tube, the initial and final configurations are on the left and right, respectively; (d) VB in the sheet as an example.

but different from a recent work using cluster model.21 Such the discrepancy might be attributed to different calculation models and parameters used. Moreover, the NEB calculation yielded a barrier of 163 meV for the structural transition from the open to the 5-1DB configuration in the (10,0) BNNT (Figure 1). This indicates that the open configuration may stably exist at low temperature such as several tens of K, significant for low-temperature applications of defective BNNTs, but the structural transition to the 5-1DB configuration would take place at room temperature. The size and electronic structure of the VB vary in the transition process. As shown by images in Figure 1, the N1 and N2 atoms not only move closer to each other along the circumference but also inward along the radius, releasing the local stress. On the other hand, the hydrogenation reaction demonstrated that the N1-N2 bond of the 5-1DB configuration is very weak and can be easily broken by hydrogen molecules,8 whereas the case is different for the nitrogen vacancy (VN) in the (10,0) BNNT: only the 5-1DB configuration with the B-B bond of 1.82 Å is achieved, consistent with the previous report.10 In what follows, we would address the difference between the formation of VB and VN configurations from the electronic (interactions) and geometrical (stress) effects. When a vacancy is formed by breaking three σ bonds, every NN N atom of the VB has one DB (or one unpaired electron) and a pair of pz electrons perpendicular to the tube (Figure 2a), whereas every NN B atom of the VN only possesses one unpaired electron (Figure 2b). The unpaired electrons (the lone pz electron pairs) tend to enhance (weaken) the bonding between the NN atoms, as shown by yellow arrows in Figure 2a,b (red arrows in Figure 2a). On the other hand, the geometrical effects are reflected by the stress depending on the curvature of the tube (as shown by green arrows in Figure 2a,b), which results in a large force along the circumference on the N1 and N2 atoms. From the minimum-energy path of the structural transition and associated structures (Figure 1), we could see that apart from the repulsion due to the lone pz electron pairs, the (local) stress imposed on the atoms in the vicinity of the VB is a substantial obstacle for the bonding between the atoms with the unpaired electrons (Figure 2a,b). Our calculations showed that the structure at the barrier peak (image (b) in Figure 1) is more stable by 0.5 eV than that with the initial N1-N2 distance of 2.51 Å. So in the free-relaxation, under the tensile stress along the circumference the N1 and N2 atoms move away until the

Ferromagnetism in BN Nanotubes distance between them increases to 3.10 Å, exhibiting an open configuration (as shown on the left of Figure 2a), whereas the closed 5-1DB configuration is present only by intentionally presetting the initial configuration. Note that moving (inward) the N1 and N2 atoms closer will increase the overlap of electron clouds of unpaired electrons, overcoming the repulsion between the lone pz electron pairs (as shown on the right of Figure 2a), whereas in the case of the VN, due to the lack of localized pz electron pairs, the only force resisting the attraction between the NN B atoms is the tensile stress along the circumference (as shown on the left of Figure 2b). In the system, the electronic effects are superior to the geometrical effects, so the B1 and B2 atoms spontaneously move closer during the free-relaxation, facilitating the “head to head” overlap of electron clouds of unpaired electrons (as shown on the right of Figure 2b). As a result, a Jahn-Teller distortion occurs, reducing the total energy of the system. The same phenomenon was also observed at the B-rich-ended mouths of BNNTs12 and in the growth of BNNTs.20 From the above analysis and discussion, we could identify that the repulsion between the lone pz electron-pairs (i.e., electronic effects) and the (local) stress imposed on the NN atoms of the VB (i.e., geometrical effects) are responsible for the barrier of the structural transition from the open to 5-1DB configuration. That is, decreasing the two effects would promote the structural transition and then the open configuration may not be present. A typical example is the case of the VN vacancy mentioned above. On the contrary, increasing the two effects would effectively prevent the structural transition, and correspondingly the open configuration could be stable at higher temperature, such as room temperature. Typically, by introducing a nitrogen antisite (NB) defect near the NN N1 (or N2) atom, as shown in Figure 2c, we found the open configuration is more stable than the 5-1DB configuration. Indeed, the deformation induced by the NB defect generates an additional internal tensile stress on the neighbor N1 (or N2) atom (as shown on the left of Figure 2c) because of smaller radius of N than B. This determines that the two N atoms are difficult to move (inward) closer to each other (as shown on the right of Figure 2c). In addition to the substitutional doping with atoms smaller than constituents, applying a transverse force (or external stress) along some certain directions might also be a method to stabilize the open configuration of the vacancy in BNNTs. For better understanding of the role of stress in the formation of various vacancy configurations, as a comparison, we provided the stable vacancy configuration in the BN sheet which can be regarded as a BNNT with infinite radius. It was found that in the BN sheet, either VB or VN remains the open configuration (Figure 2d), well consistent with the recent experimental observation.13 This reflects that the stress in the BN plane, rather than the electronic effects, plays a predominant role. It was known that the plane stress can restrain the NN B (or N) atoms of the VN (or VB) from moving out of the sheet, as shown by green arrows in Figure 2d. This hinders the interaction of the NN atoms (see Figure 2d). Furthermore, strictly speaking, the perfect two-dimensional crystals cannot exist in the free state.22 Recent study by transmission electron microscopy revealed that the freely suspended graphene is not perfectly flat, and exhibits intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations.23 We could anticipate that the same roughening should exist in the practical BN sheet, and the same vacancy configurations as those in BNNTs might be present under the same conditions accordingly. On the other hand, it was experimentally and theoretically

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Figure 3. Spin-polarized local density of states (LDOS) and spin densities of (10,0) BNNTs with different vacancies. (a) The 5-1DB configuration of the VB, (b) the open configuration of the VB, and (c) the 5-1DB configuration of the VN. The N1 and N2 atoms are identical due to the same conditions encountered, and both different from the N3 atom. Red solid, blue dashed, and black solid lines represent the LDOS of the N1 (or B1), N2 (or B2), and N3 (or B3), respectively. The Fermi level is set to zero. The spin density isosurfaces in the values of +0.08 and -0.08 au are depicted in red and yellow, respectively.

shown that due to high transverse softness, large NTs in bundles tend to be polygonized at the ground state, instead of being circular, to release the internal stress.24 A polygonized NT, in general, has a number of flat lateral surfaces. In this case, the vacancy would possibly be formed on the lateral surfaces of large NTs, so the formation mechanism like that in the sheet is still effective. From the above analysis of geometrical and electronic effects on the formation of vacancies, we could suggest that with increasing tube radius, the open configuration is more possible than the 5-1DB one, which is compatible with early prediction by virtue of the size-dependent formation energy of the VB in BNNTs.25 For example, the energy difference between the open and 5-1DB configurations for the (16,0) BNNT is 0.31 eV less than that for the (10,0) BNNT mentioned above, and simultaneously, the N1-N2 bond length of the 5-1DB configuration is 1.51 Å, larger than that in the (10,0) tube. As a result, the open configuration of the vacancy in larger BNNTs gradually becomes stable in a larger temperature range. Different vacancy configurations should correspond to different electronic states and physical and chemical properties. It was found that BNNTs and the BN sheet containing one vacancy are spin-polarized, with a local moment of 1 µB, regardless of the tube size or shape and the vacancy configuration. However, the detailed spin configurations (e.g., the spin-splitting of the states in the different spin components) are dominated by the atomic configuration and the vacancy nature. Figure 3 shows the spin-polarized local density of states (LDOS) and spin densities of (10,0) BNNTs with different vacancies. It can be seen that for the VB vacancy in the 5-1DB configuration, one unoccupied state of minority-spin appears in the gap because the unpaired electron of the N3 atom occupies the deep state with majority-spin (Figure 3a and the inset). Whereas, in the open configuration, three unpaired electrons of the NN N atoms occupy the deep states (two with majority-spin and one with minority-spin as shown in Figure 3b). Correspondingly, the two kinds of NN atoms, i.e., N1 (N2) and N3, exhibit opposite spin (see the inset of Figure 3b). The unpaired electrons of the N1 and N2 atoms are spin-parallel, following the Hund’s rule, like in the cases of open N-rich-ended BNNTs,12 whereas the unpaired electron of the N3 atom has the opposite spin orientation. Comparatively, the state that the unpaired electrons of the N1 and N2 atoms are spin-antiparallel is only 56 meV higher in energy. It could be expected that at room or elevated temperature, the spin orientations of the unpaired electrons of the N1 and N2 atoms first change to antiparallel from parallel, and subsequently, a chemical bond is formed between N1 and

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Figure 4. Spin-polarized local density of states (LDOS) of the 5-1DB configuration of the vacancy with (a) one adsorbed F on the B3, (b) one adsorbed H on the N3, and of the open configuration of the VB with (c) one adsorbed H on the N1, and (d) two adsorbed H atoms on the N1 and N2. Red solid, blue dashed, black solid, cyan solid, and green solid lines represent the LDOS of the N1 (B1), N2 (B2), N3 (B3), and adsorbed F and H atoms, respectively. The Fermi level is set to zero. The corresponding adsorption structures are shown in the insets.

N2 when they approach each other along the reaction coordinate as shown in Figure 1. In the process, the calculated total moment of VB is always 1 µB. For the VN vacancy, not only the B3 atom but also the B1 and B2 atoms are responsible for the occupied gap state of majority-spin (see Figure 3c and the inset). Interestingly, the spin-polarized gap states of the VB and VN correspond to acceptor-like and donor-like states, respectively. This discrepancy of the gap states is attributed to the different local potentials in the vicinity of the cation and anion vacancies in BNNTs, compatible with the cases in bulk III-V semiconductors.26 Successively, as an example, we focused on the effects of vacancy configurations (open and 5-1DB) on the magnetic and adsorption properties of BNNTs. Obviously, the open configuration has three DBs, whereas the 5-1DB configuration has only one DB. The DB states are chemically active, facilitating the oxidation27 and adsorption.8,28 Here we considered two kinds of atoms, H and F atoms, which are frequently present in the experiments of BNNTs.29,30 As expected, the H and F atoms could steadily adsorb on the N3 (or B3) atom in the 5-1DB configuration, regardless of the type of vacancy (see the insets in Figure 4a,b), being highly exothermic. More precisely, the F atom is easily trapped by the VN vacancy with the donor-like states, whereas the H atom is easily bound by the VB vacancy with the acceptor-like states. The

Liu et al. adsorption energies31 are respectively 6.82 and 4.66 eV. Meanwhile, due to a complete electron transfer (i.e., nearly one electron per adsorbed-atom) between the adsorbed atom and the tube, the number of electrons of defective BNNTs becomes even. The local moment is contributed by sp2 states (see Figure 3), but not by pz states like in C-adsorbed BN nanosystems and graphitic nanosystems.7 Therefore, along with the saturation of only one DB in the adsorption, the spin-polarization disappears (Figure 4a,b), whereas in the open configuration, the H atom would preferably adsorb on the N1 (or N2) atoms due to curvature effects, and simultaneously, the remaining N2 (or N1) atom is bonded to the N3 atom (see the inset in Figure 4c). The system also becomes nonmagnetic (Figure 4c). We further took into account the adsorption of one more H atom (corresponding to higher H concentration), that is, two H atoms adsorbed on one VB. Since the vacancy generally promotes the dissociation of H2 molecules,32 this model appears reasonable. For the 5-1DB configuration, one H chemically adsorbs on the N3 atom, and the other H would physically adsorb on the N1-N2 bond, consistent with the cases of H on perfect BNNTs,33 whereas for the open configuration, a different result is obtained: two H atoms prefer to adsorb on the N1 and N2 atoms, saturating the DBs (see the inset in Figure 4d), and the unpaired electron of the N3 atom is completely preserved, contributing to the local moment of 1 µB (Figure 4d). As a result, the open vacancy configuration of BNNTs exhibits the unique magnetic response to H concentration (i.e., 1, 0, and 1 µB for 0, 1, and 2 hydrogen atoms per vacancy, respectively). In addition, the open configuration may have implications in the hydrogen storage of BNNTs via the hydrogenation reaction. Finally, we studied the magnetic coupling between VBinduced local moments (along the circumference and the axis) of such defective BNNTs for possible spintronic applications. Note that our calculations showed that the 5-1DB configuration of the VB is more stable than the open configuration, and might be a global minimum, so here we only focused on the former. In detail, two VB vacancies were arranged along (1) the circumference in the 1 × 1 × 3 supercell and (2) the axis in the 1 × 1 × 4 supercell. Depending on the initial conditions of the self-consistent calculations, stable ferromagnetic (FM), and antiferromagnetic (AFM) structures were obtained. In general, the magnetic coupling could be illustrated by the energy difference between the FM and AFM phases of systems. Our calculations showed that the AFM and FM states of defective BNNTs with the VB, either along the circumference or the axis, are nearly degenerate, indicating a very weak magnetic coupling. The reason is that the spin-polarized states induced by a neutral VB are very localized (see Figure 3). Due to the short-range coupling, unrealistically high defect concentration is needed to induce collective magnetism of systems. Since cation vacancies in the III-V systems are likely to be (partially) compensated and become charged defects,34 we also considered the negative charge effects on the magnetic coupling between local moments along the axis. When one electron is injected into one VB, the spin-polarization disappear (Figure 5a). When two electrons are injected into one VB, the spin-splitting of the conduction-band bottom of BNNTs is induced, and the FM-AFM energy difference is 32 meV. However, as compared to the case in the neutral vacancy, the spin-polarized states are delocalized (Figure 5b). This means that the intrinsic magnetism like cation vacancyinduced ferromagnetism in wide-gap nitrides3 is not present in such defective BNNTs, different from the earlier prediction deduced from the presence of the local moments.8 This discrepancy well validates that the ferromagnetism comes from

Ferromagnetism in BN Nanotubes

Figure 5. Spin-polarized density of states (DOS) for defective (10,0) BNNT under the negative charge injection. (a) One injected electron per VB and (b) two injected electrons per VB. The Fermi level is set to zero.

the long-range magnetic coupling of the local moments. Also, this may be the reason why the ferromagnetism of pristine defective BNNTs has not been observed experimentally up to now. Moreover, we also calculated the formation energies of the 5-1DB configuration of the VB in neutral and charged states and found that, as compared with the neutral state, the -2 charge state is not stable for all of the possible values of the electronic chemical potential, whereas the -1 charge state can exist in the range of allowable electronic chemical potential. This is consistent with the previous results by Piquini et al.35 Comparatively, we suggest that the doping or adsorption method may be practical for inducing the ferromagnetism of BN nanomaterials. IV. Conclusion The structure, stability, spin-polarized states, and magnetism of BNNTs with cation vacancies were systematically studied by ab initio calculations. Apart from the 5-1DB configuration, the VB vacancy in tubes was identified to have an open configuration, which is dependent on the interaction between the NN atoms of the vacancy and the local stress associated with the curvature. For example, under additional tensile stress, the open vacancy configuration would be preserved. Although a single vacancy induces a local moment of 1 µB regardless of the vacancy configuration and the tube curvature, the two kinds of vacancy configurations (open and 5-1DB) have different spinpolarized states. As compared to the 5-1DB configuration, the open one has more complex properties and application potential. The strong localization restricts the magnetic coupling between these local moments to be short-range, and thus such defective BNNTs are nonferromagnetic, which would be likely to be used as spin-transport channels, like CNTs.36 Moreover, it was found that the surrounding H atoms could steadily adsorb on the VB, and then affect the spin-polarization of systems. Acknowledgment. This work was supported by the Ministry of Science and Technology of China (Grant Nos. 2006CB605105 and 2009CB929400) and the National Natural Science Foundation of China (Grant No. 10774084). References and Notes (1) (a) Makarova, T. L.; Sundqvist, B.; Ho¨hne, R.; Esquinazi, P.; Kopelevich, Y.; Scharff, P.; Davydov, V. A.; Kashevarova, L. S.; Rakhmanina, A. V. Nature 2001, 413, 716. (b) Coey, J. M. D.;

J. Phys. Chem. C, Vol. 114, No. 10, 2010 4361 Venkatesan, M.; Fitzgerald, C. B.; Douvalis, A. P.; Sanders, I. S. Nature 2002, 420, 156. (c) Andriotis, A. N.; Menon, M.; Sheetz, R. M.; Chernozatonskii, L. Phys. ReV. Lett. 2003, 90, 026801. (d) Makarova, T. L. Semiconductors 2004, 38, 615. (2) Dietl, T.; Haury, A.; d’Aubigne´, Y. M. Phys. ReV. B 1997, 55, R3347. (3) Dev, P.; Xue, Y.; Zhang, P. Phys. ReV. Lett. 2008, 100, 117204. (4) (a) Rubio, A.; Corkill, J. L.; Cohen, M. L. Phys. ReV. B 1994, 49, 5081. (b) Blase, X.; Rubio, A.; Louie, S. G.; Cohen, M. L. Europhys. Lett. 1994, 28, 335. (c) Chen, Y.; Zou, J.; Campbell, S. J.; Caer, G. L. Appl. Phys. Lett. 2004, 84, 2430. (5) (a) Wu, R. Q.; Liu, L.; Peng, G. W.; Feng, Y. P. Appl. Phys. Lett. 2005, 86, 122510. (b) Si, M. S.; Xue, D. S. Europhys. Lett. 2006, 76, 664. (6) (a) Li, F.; Zhu, Z. H.; Yao, X. D.; Lu, G. Q.; Zhao, M. W.; Xia, Y. Y.; Chen, Y. Appl. Phys. Lett. 2008, 92, 102515. (b) Zhang, Z.; Guo, W. J. Am. Chem. Soc. 2009, 131, 6874. (7) Li, J.; Zhou, G.; Chen, Y.; Gu, B. -L.; Duan, W. H. J. Am. Chem. Soc. 2009, 131, 1796. (8) Kang, H. S. J. Phys. Chem. B 2006, 110, 4621. (9) (a) Zobelli, A.; Ewels, C. P.; Gloter, A.; Seifert, G.; Stephan, O.; Csillag, S.; Colliex, C. Nano Lett. 2006, 6, 1955. (b) Zobelli, A.; Gloter, A.; Ewels, C. P.; Colliex, C. Phys. ReV. B 2008, 77, 045410. (10) Schmidt, T. M.; Baierle, R. J.; Piquini, P.; Fazzio, A. Phys. ReV. B 2003, 67, 113407. (11) Lehtinen, P. O.; Foster, A. S.; Ayuela, A.; Vehvila¨inen, T. T.; Nieminen, R. M. Phys. ReV. B 2004, 69, 155422. (12) Hao, S. G.; Zhou, G.; Duan, W. H.; Wu, J.; Gu, B. -L. J. Am. Chem. Soc. 2006, 128, 8453. (13) Jin, C.; Lin, F.; Suenaga, K.; Iijima, S. Phy. ReV. Lett. 2009, 102, 195505. (14) (a) Golberg, D.; Han, W.; Bando, Y.; Bourgeois, L.; Kurashima, K.; Sato, T. J. Appl. Phys. 1999, 86, 2364. (b) Golberg, D.; Bando, Y.; Kurashima, K.; Sato, T. Chem. Phys. Lett. 2000, 323, 185. (15) Kresse, G.; Furthm ¨ uller, J. Comput. Mater. Sci. 1996, 6, 15. Phys. Rev. B 1996, 54, 011169. (16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (17) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (18) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (19) Henkelman, G.; Uberuaga, B. P.; Jo´nsson, H. J. Chem. Phys. 2000, 113, 9901. (20) Blase, X.; De Vita, A.; Charlier, J. -C.; Car, R. Phys. ReV. Lett. 1998, 80, 1666. (21) Li, X. M.; Tian, W. Q.; Huang, X. R.; Sun, C. C.; Jiang, L. J. Nanopart. Res. 2009, 11, 395. (22) (a) Peierls, R. E. HelV. Phys. Acta 1934, 7, 81. (b) Mermin, N. D. Phys. ReV. 1968, 176, 250. (c) 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, 102, 10451. (23) Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S. Nature 2007, 446, 60. (24) (a) Tersoff, J.; Ruoff, R. S. Phys. ReV. Lett. 1994, 73, 676. (b) Lo´pez, M. J.; Rubio, A.; Alonso, J. A.; Qin, L.-C.; Iijima, S. Phys. ReV. Lett. 2001, 86, 3056. (c) Hao, S. G.; Zhou, G.; Duan, W. H.; Wu, J.; Gu, B.-L. J. Am. Chem. Soc. 2008, 130, 5257. (25) Gou, G. Y.; Pan, B. C.; Shi, L. Phys. ReV. B 2007, 76, 155414. (26) Altarelli, M.; Bassani, F. in Handbook on semiconductors, Vol. 1, Band theory and transport properties; Moss, T. S., Paul, W., Eds.; North-Holland Publishing Company: Amsterdam, 1982; pp 269-300. Deep centers in semiconductors; Pantelides, S. T., Ed.; Gordon and Breach: New York, 1986. (27) Zhang, J.; Zou, H. L.; Qing, Q.; Yang, Y. L.; Li, Q. W.; Liu, Z. F.; Guo, X. Y.; Du, Z. L. J. Phys. Chem. B 2003, 107, 3712. (28) Wang, C. C.; Zhou, G.; Wu, J.; Gu, B. -L.; Duan, W. H. Appl. Phys. Lett. 2006, 89, 173130. (29) Tang, C. C.; Bando, Y.; Huang, Y.; Yue, S. L.; Gu, C. Z.; Xu, F. F.; Golberg, D. J. Am. Chem. Soc. 2005, 127, 6552. (30) Golberg, D.; Bando, Y.; Tang, C. C.; Zhi, C. Y. AdV. Mater. 2007, 19, 2413. (31) Adsorption energy is defined as Eads ) Et(NT) + Et(A)- Et(NT + A), where Et(A), Et(NT), and Et(NT + A) respectively denote the total energies of isolated H (or F) atom and the defective NT without and with H (or F). (32) Wu, X. J.; Yang, J. L.; Hou, J. G.; Zhu, Q. S. J. Chem. Phys. 2006, 124, 054706. (33) Zhou, Z.; Zhao, J.; Chen, Z.; Gao, X.; Yan, T.; Wen, B.; Schleyer, P. von R. J. Phys. Chem. B 2006, 110, 13363. (34) Saarinen, K.; Laine, T.; Kuisma, S.; Nissila, J.; Hautojarvi, P.; Dobrzynski, L.; Baranowski, J. M.; Pakula, K.; Stepniewski, R.; Wojdak, M.; Wysmolek, A.; Suski, T.; Leszczynski, M.; Grzegory, I.; Porowski, S. Phys. ReV. Lett. 1997, 79, 3030. (35) Piquini, P.; Baierle, R. J.; Schmidt, T. M.; Fazzio, A. Nanotech. 2005, 16, 827. (36) Tsukagoshi, K.; Alphenaar, B. W.; Ago, H. Nature 1999, 401, 572.

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