Article pubs.acs.org/JPCC
Self-Assembled Ti Quantum Wire on Zigzag Graphene Nanoribbons with One Edge Saturated Chong Li,† Fengmin Wu,‡ Jingbo Li,*,†,‡ and Lin-Wang Wang*,§ †
State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O.Box 912, Beijing 100083, China ‡ Zhejiang Normal University, Jinhua 321004, Zhejiang Province, China § Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ABSTRACT: Using first-principles calculations, we study on the energetics, kinetics, and electronic properties of transition metal atoms Ti, Mn, and Au on zigzag graphene nanoribbons (ZGNRs) with one edge saturated by two H atoms C(2H), while the other one by one H atom C(H). Because of the larger magnetic bearded edge states on the C(2H) edge, all these three adatoms prefer adsorbing on the C(2H) edge, but Ti binds stronger to ZGNRs on the C(2H) edge than both Mn and Au atoms. The saturated C(2H) edge not only dramatically enhances the Ti mobility from the center to C(2H) edge but also weakens the diffusion isotropy; thus, Ti quantum wire is formed readily along the C(2H) edge. Along Ti atomic wire there is a spin-up conducting channel contributed by pure Ti 3d state, indicating spin-dependent charge transport properties. This may open new avenues in fabricating metal quantum wires. large,24 leading to form 3D island structures on graphene. Excitingly, experiment found Ti or Ni atom coating on suspended carbon nanotubes forms a continuous nanowire due to curvature-induced rehybridization of carbon sp2 orbitals but pure sp2 orbitals.25 Motivated by this phenomenon and inspired by the localized edge states of ZGNRs that greatly enhance the binding energy of adatoms,16 we thus choose ZGNRs with one edge saturated by two hydrogen atoms C(2H), while the other edge by one hydrogen atom C(H) as substrate, named H2-ZGNRs-H. This is because the C atom is sp3 hybridization on the C(2H) edge and has stronger bearded edge states, which are clearly different from on the C(H) edge where the C atom is pure sp2 hybridization.2,26−28 We anticipate that the localized bearded edge states on the C(2H) edge further enhance the binding energy of 3d transition metals to ZGNRs and facilitate fabrication of 1D 3d transition metal quantum wires. To test this idea and indentify the physical origin of this potential behavior, we have performed first-principles calculations to comprehensively study on the energetics and kinetics of typical Ti, Mn, and Au adsorbed on H2-ZGNRs-H. These metals can be divided into three types. (1) The binding energy of Ti to graphene is relatively large, and the 3d shell is less than half-filled. (2) The binding energy of Mn to graphene is relatively small, and the 3d shell is exactly half-filled. (3) The binding energy of Au to graphene is extremely small, and the d shell is fully filled. We find that all these three adatoms prefer adsorbing on the C(2H) edge where there exists larger magnetic bearded edge states. Especially Ti atom binds quite
1. INTRODUCTION As a promising candidate for electronics and spintronics, graphene-based nanostructures have drawn an unprecedented attention due to their interesting electronic and transport properties,1−7 also boosted by the recent advances in production technique.6−13 Particularly for zigzag graphene nanoribbons (ZGNRs) with one H atom on each zigzag edge, there are quite localized edge states near the Fermi energy level on both edges.3 Such localized edge states have an important effect on atomic adsorption properties. Indeed, recent investigations show that different metal adatoms adsorbed on ZGNRs can lead to spin-polarized current;14−16 this is a practical routine to magnetize graphene. More interestingly, alkali metal adsorbed on ZGNRs spontaneously form onedimensional (1D) atomic chains16 driven by the edge states, although Na adatoms form three-dimensional (3D) island structures on graphene.17,18 Likewise, 3d transition metals are also formed 3D island structures on graphene.19 This indicates that by choosing proper ZGNRs as substrate, fabrication of 3d transition metal atomic chain is highly possible. More importantly, transition metals easily magnetize graphene nanostructures20−23 and provide the required ferromagnetism, dimensionality, and facile manipulation. Thereby, it is necessary to study on the effect of localized edge states on the 3d transition metal adsorption, diffusion, and subsequent electronic properties. However, as we know, the binding energy of 3d transition metal to graphene is relatively small. The maximal case is around 1.80 eV for the Ti atom;20,21 the resulting ratio ΔE/EC is only 0.37, which is far smaller than the case of alkali metal adsorbed on graphene. Here ΔE is the binding energy between adatoms and substrate, and EC is cohesive energy per atom of the bulk metal. Also, the activation energy barrier is relatively © 2012 American Chemical Society
Received: September 5, 2012 Revised: October 28, 2012 Published: October 30, 2012 24824
dx.doi.org/10.1021/jp3088034 | J. Phys. Chem. C 2012, 116, 24824−24828
The Journal of Physical Chemistry C
Article
magnetic moments on the C(2H) edge are larger than on the C(H) edge, corresponding to 0.32 and 0.21 μB, respectively, which agree well with previous calculations.28 More interesting, the two localized edge states simultaneously decay into the center from their respective edges with different decay profile. This decay depends on their decaying factors D. Under the condition of one-orbital tight-bonding approach,2 the decaying factors D can be written as
strong to ZGNRs on the C(2H) edge, and it diffuses faster from the center to C(2H) edge than to the C(H) edge due to the less localized bearded edge states on the C(H) edge; thus, Ti quantum wire is formed along the C(2H) edge. Moreover, spin-dependent charge transport properties can be identified along the Ti quantum wire. This provides us another strategy to fabricate 1D metal quantum wires by saturating different atoms on both ZGNRs edges to change the edge chemical potential.
2. CALCULATION METHOD All calculations are based on density functional theory using the Perdew−Burke−Ernzerhof exchange-correlation functional.29 The projector augmented wave method is used as implemented in Vienna ab initio simulation package (VASP).30 H2-ZGNRsH has a width of 14.5 Ǻ and contains four unit cells along the ribbon direction. To eliminate the coupling between adjacent nanoribbons, 12.0 and 15.0 Ǻ vacuums are added to edge-toedge and layer-to-layer, respectively, The cutoff energy of the plane-wave basis is 500 eV, and 5 × 1 × 1 k-point meshes are used for the Brillouin zone integration.31 The atomic relaxation is carried out until forces are less than 0.02 eV/Ǻ . We employ the “nudged elastic band” (NEB) method32 to locate the transition state geometries.
D(2H) =
D(H) =
1 2[1 + cos(kdz)]
⎛ kd ⎞ 2 cos⎜ Z ⎟ ⎝ 2 ⎠
⎛ 2π ⎞ ⎜0 ≤ kd ≤ ⎟ Z ⎝ 3 ⎠
⎛ 2π ⎞ ⎜ ≤ kdZ ≤ π ⎟ ⎝ 3 ⎠
(1)
(2)
where dZ is the unit cell length shown in Figure 1a. D(2H) and D(H) are different decaying factors for the C(2H) and C(H) edge, respectively, which represent the geometrical progression factors between the amplitude of wave functions in the same sublattice. From eqs 1 and 2, we find that the decaying factor of localized bearded edge states near the Fermi energy level on the C(2H) edge ranges 0.5 ≤ D(2H) ≤ 1.0, while on the C(H) edge it ranges 0.0 ≤ D(H) ≤ 1.0; this means that the bearded edge states on the C(2H) edge are less localized than the distribution of localized edge states on the C(H) edge because the minimum of D(2H) and D(H) is equal to 0.5 and 0.0, respectively. The above-mentioned localized edge profiles can also be confirmed by plotted band structures, as shown in Figure 1c. The two sub-bands near Fermi energy level exhibit different dispersion along the ribbon direction. Especially for spin-up sub-band, in the window of 0 ≤ kdZ ≤ 2π/3, it has a small dispersion, but for 2π/3 ≤ kdZ ≤ π, there is almost no dispersion. These states are mainly contributed by edge C atoms pZ orbitals with antibonding π* states, shown in Figures 1b and 1d, respectively. The antibonding π* states on interedge C atoms of the C(2H) edge are relatively extended, while on outmost edge C atoms of the C(H) edge they are extremely sharp; thus, when the bearded edge states decay into the center of ribbon from the C(2H) edge, they undergo a small fluctuation. Such profiles facilitate the adatoms diffusion to the C(2H) edge from the center (see below). It should be noted that due to the outmost edge C atoms on the C(2H) edge bonding to two H atoms, this changes π electrons into σ states, thus no π electrons contribution to the states near the Fermi energy level. 3.2. Adsorption Properties. We next investigate on the adsorption profiles involving different metals Ti, Mn, and Au atoms. The binding energy is defined as
3. RESULTS AND DISCUSSION 3.1. Electronic Structure. Let us first study on localized edge states near Fermi energy level on both sides of H2ZGNRs-H, as represented in Figure 1a. It is seen clearly that the charge density is mainly localized on the C(2H) edge interedge C atoms, while for the C(H) edge, it is mainly distributed on the outmost edge C atoms. However, the bearded edge states on the C(2H) edge are stronger than the localized edge states on the C(H) edge. This is because the
ΔEad = (Etotal − NEadatom − EZGRNs)/N
(3)
where Etotal, Eadatom, and EZGRNs are the total energies of the adsorbed system, isolated adatoms, and H2-ZGNRs-H, respectively. The results are summarized in Table 1. On the whole, due to the stronger magnetic charge density on the C(2H) edge, all these three adatoms prefer adsorbing on the C(2H) edge, while the C(H) edge is a metastable adsorption site. However, the most stable adsorption sites are quite different for respective adatoms; i.e., for Ti and Mn, both of them favor hollow adsorption site, whereas for Au, it favors the top adsorption site, as shown in Figure 2a, but due to the edge effect, the Ti atom slides slightly away from the center of hollow site. Basically, this adsorption behavior can be
Figure 1. (a) Charge density plot of ρ↑ − ρ↓ near Fermi energy level ranging from −1.0 to 1.0 eV. This energy window contains one spinup and one spin-down state near the Fermi energy level shown in (c). (b) and (d) are the local density of states of C(2H) and C(H) edges, respectively. The states of C(2H) correspond to 0 ≤ kdZ ≤ 2π/3, while the states of C(H) correspond to 2π/3 ≤ kdZ ≤ π shown in (c). Arrows in (a) represent the decaying properties of the localized (bearded) edge states from edge to center of H2-ZGNRs-H. 24825
dx.doi.org/10.1021/jp3088034 | J. Phys. Chem. C 2012, 116, 24824−24828
The Journal of Physical Chemistry C
Article
From Table 1, we can also see that the magnetization μag does not change for Ti adatom, while μag increases for the Mn adatom, but it decreases for Au adatom. Such variable magnetic profiles obey the following rules. For less half-filled d orbitals (Ti), there is strong hybridization between metal d orbitals and ribbon p states, thus lower the energy of d orbitals. Usually, the outmost metal s electrons transfer to unoccupied d orbitals and lead the magnetic moments increase, but in fact the outmost metal s electrons couple with the localized bearded edge states, instead of transferring to unoccupied d orbitals. Consequently, d orbitals remain less half-filled. According to Hund’s rule, all the d electrons can own the same spin direction, so for the Ti atom, the system increases an extra 2 μB, but at the same time two Ti s electrons saturate two electrons of H2-ZGNRs-H (decreasing 2 μB); thus, overall the magnetic moments do not change for Ti adsorption. Likewise, for the Mn adatom, the system increases by 3 μB; thus, the total magnetic moments are 7 μB. For the Au adatom, it is different from both cases of Ti and Mn, the full filled d orbitals have no contribution to the system, but Au has one s electron and saturates one electron of H2-ZGNRs-H; thus the total magnetic moments is 3 μB. 3.3. Diffusion and Stability Properties. We now study of the diffusion profiles of adatoms on H2-ZGNRs-H to check the mobility of adatoms. Two diffusion directions are focused, also shown in Figure 2a. One is along both edges of H2-ZGNRs-H (x direction); the other is near perpendicular ribbon (y direction). For Ti and Mn adatoms, x directions are H1−H1 and H5−H5 on C(2H) and C(H) edges, respectively, while y directions are H3−H2−H1 from the center to C(2H) edge and H3−H4−H5 from the center to C(H) edge, respectively. The results are presented in Figures 2b and 2c for Ti and Mn adatoms, respectively. It is seen clearly that along both directions for Ti and Mn atoms the activation energy barriers are lowered compared with the case on graphene.24 Especially from center to C(2H) edge (y direction), the activation energy barriers are greatly reduced to 0.33 and 0.20 eV, respectively, indicating that the saturated C(2H) edge dramatically enhances the Ti mobility from center to C(2H) edge. Thereby Ti and Mn atoms diffuse much faster from the center to the C(2H) edge. In other words, they arrive quite easily on the C(2H) edge, but along the C(2H) edge in x direction, the energy barrier is relatively larger (0.61 and 0.68 eV for Ti and Mn atoms, respectively), meaning that the saturated C(2H) edge also weakens the diffusion isotropy for Ti and Mn atoms. Basically, this can be understood by the smaller fluctuation of localized charge density from the C(2H) edge to the center. When Ti and Mn atoms arrive at the C(2H) edge, then they hop in along the x direction, forming 1D atomic wire. Taken together, by saturating different H atoms on both edges to change the ZGNRs edges chemical potential, 1D metal quantum wires are formed on the lower potential energy edge; this strategy is clearly different from ref 16 by using a transverse electronic field. Unlike the cases of Ti and Mn atoms, Au atom diffuses along top sites as y direction,34 but the activation energy barrier is quite high (0.70 eV) from the center to C(2H) edge, as shown in Figure 2d; thus, it is not easy to reach at the C(2H) edge forming quantum wire. On the other hand, the lower binding energy of Au to H2-ZGNRs-H again makes the forming quantum wire unstable. In fact, at higher coverage, we find that Au triangle trimer is more stable than atomic wire structure on H2-ZGNRs-H. Collectively, from energetics and kinetics point
Table 1. Energetic and Structural Properties of Transition Metals on H2-ZGNRs-Ha atom
site
h
ΔE
EC
ΔE/EC
μag
Ti
H1 H5 H1 T11 T2 T12
1.75 1.77 1.80 2.09 2.42 2.43
−3.24 −2.63 −1.61 −0.87 −1.56 −1.24
−4.85
0.668 0.542 0.551 0.297 0.409 0.320
4.00 4.00 7.00 9.00 3.00 3.00
Mn Au
−2.92 −3.81
a
The properties listed below include the favored adsorption sites, distance of adatom H2-ZGNRs-H h(Å), adsorption energy ΔE (eV/ atom), and the magnetization of the adsorption systems μag (μB). For reference, we also list the experimental cohesive energy per atom of the bulk metal EC (eV) from ref 33 and the ratio of the adsorption energy to the bulk cohesive energy ΔE/EC.
Figure 2. (a) Ball and stick model of H2-ZGNRs-H. The possible adsorption sites, both diffusion paths and directions, are presented. The dashed line represents the center of nanoribbon. (b−d) Diffusion profiles of Ti, Mn, and Au adatoms on H2-ZGNRs-H, respectively. The dotted lines represent the different diffusion directions on nanoribbon. (e) Adsorption energy (averaged) of adatoms on H2ZGRs-H as a function of number of adatoms.
understood by the less half-filled or half-filled d orbitals which like multicoordinate sites. For full filled d orbitals, s electrons are highly free; thus, the Au atom adsorbs on the top site where the localized edge states are maximum. Among three adatoms, Ti has the largest binding energy, while Au has the smallest binding energy. This well consists with the case of adatoms on graphene.21 Also, the binding energies of metals to H2-ZGNRsH are in line with their adsorption high h, namely h(Ti) < h(Mn) < h(Au), again indicating that Ti binds strongest to ribbon. Compared with the C(H) edge, the C(2H) edge greatly enhances the binding energy of Ti atom; the resulting ΔE/EC (0.668) approaches the case of alkali metal adsorbed on graphene.16,20 Thereby, the C(2H) edge can effectively suppress the growth of Ti 3D island structures and potentially facilitates growth of 1D quantum wire if Ti has superior mobility on H2-ZGNRs-H. 24826
dx.doi.org/10.1021/jp3088034 | J. Phys. Chem. C 2012, 116, 24824−24828
The Journal of Physical Chemistry C
Article
of view Au adatoms prefer cluster structure to quantum wire on H2-ZGNRs-H. Stability is another key factor controlling the formation of 1D quantum wire;35−37 thus, we need to check the stability of 1D atomic wire at higher coverage of adatoms. Here six unit cells along the ribbon direction are used to ignore the interaction between adjacent dimers or trimers at initial stages; the results are presented in Figure 2e. It is seen clearly that on the whole the binding energy increases as Ti atoms increase. Specifically, due to the strong binding between Ti atoms, the binding energy greatly increases from one to two Ti atoms. When the coverage reaches 100% (six Ti atoms), the binding energy again increases because of formation of closed 1D quantum wire. We also check the stability of other possible structures, i.e., different cluster structures, and find 1D quantum wire is the most stable one. The ground state of all the studied coverages is ferromagnetic, and the bond length of Ti−Ti is 2.46 Ǻ , which just corresponds to the length of graphene unit cell. On the contrary, for Mn at higher coverage, the binding energy first increases as shown in Figure 2e and then decreases because of strain induced by larger Mn−Mn bond length (averaged) of 2.57 Ǻ . Therefore, at high coverage (100%) Mn 1D quantum wire is unstable viewed from energetics. Since the previous study has shown that H2-ZGNRs-H is stable at room temperature,28 it is necessary to investigate the thermal stability of 1D quantum wire on H2-ZGNRs-H by using molecular dynamics (MD). The system keeps at 400 K and 5000 time steps (1 fs/step) in the moles−volume− temperature (NVT) ensemble. After 5 ps constant temperature process, Mn quantum wire separates away from H2-ZGNRs-H, suggesting that Mn quantum is unstable at high coverage and high temperature, agreeing well the calculations binding energy at higher coverage shown in Figure 2e. For Ti quantum wire, we define Ti−Ti bond length and quantum wire height to characterize the relative thermal stability, as plotted in Figure 3.
Figure 4. PDOS of Ti adatoms on nanoribbon (a, b) are one Ti atom adsorption and six Ti atoms adsorption (100%), respectively. (c, d) Spin-up and spin-down charge density of partially occupied states (within an energy interval EF−0.25 eV) of Ti nanowire on H2ZGNRs-H, respectively.
Figure 3. Bond length and distance of Ti nanowire on H2-ZGNRs-H during the MD simulation process. The final structure of system after 5 ps is presented in the inset.
orbitals. Because of the strong hybridization between Ti d orbitals C p states, the p state of C atom that binds to Ti disappears and has no contribution to the states near the Fermi energy level. On the basis of this result, we can arrive that when Ti atoms are 100% adsorption, the states near the Fermi energy level will be fully originated from pure spin-up Ti d orbitals. Figure 4b confirms our hypothesis. This means that a spin-up conducting channel emerges along 1D Ti quantum wire, as shown in Figure 4c,d, which present spin-up and spin-down charge density of partially occupied states (within an energy interval EF−0.25 eV), indicating spin-dependent charge transport properties. Finally, we comment on the fabrication of H2-ZGNRs-H because fabrication of H2-ZGNRs-H is a prerequisite condition for further Ti quantum wires growth. In the spirit of the shadow effect,38 it is highly possible to fabricate the H2-ZGNRs-H. First, prepare a ZGNRs with both edges saturated by one H atom and then mask off one edge by using nanomaterials such as Si nanowires.39 Finally irradiate protons from the top of the ZGNRs. Because of the shadow effect, only one edge is exposed to protons and can be saturated by two H atoms, while the other edge remains by one H atom, leading to a H2-ZGNRs-H.
The bond length does not change during constant temperature process. Although the height of Ti quantum wire has a small fluctuation, it still binds strong to H2-ZGNRs-H, as shown in the inset of Figure 3. The curling occurs at edges, but the local structure is nearly planar. So Ti quantum wire is stable at 400 K. The higher temperature 400 K facilitates Ti atoms hopping in the x direction along the C(2H) edge, forming uniform 1D quantum wire. 3.4. Magnetic Properties of Ti Quantum Wire. We here address the effect of Ti adsorption on the electronic properties of system. Figure 4a presents the partial density of states (PDOS) for one Ti adatoms, from which we can see clearly that the states near the Fermi energy level are contributed by C p orbitals (nonbonding to Ti) at both edges and spin-up Ti d
4. CONCLUSIONS In conclusion, we have studied on the energetics, kinetics, and electronic properties of transition metal atoms Ti, Mn, and Au on H2-ZGNRs-H and find that all the studied adatoms prefer adsorbing on the C(2H) edge, but only Ti atoms bind strong enough to ZGNRs on the C(2H) edge. The saturated C(2H) edge not only enhances the Ti mobility from center to C(2H) edge but also weakens the diffusion isotropy. These exotic properties help to form 1D Ti quantum wire on ZGNRs. Along Ti quantum wire a spin-up conducting channel resulting from the Ti 3d state is formed, indicating spin-dependent charge transport properties. This provides us an alternative strategy to fabricate 1D metal quantum wires by saturating different atoms on both ZGNRs edges to change the edge chemical potential. 24827
dx.doi.org/10.1021/jp3088034 | J. Phys. Chem. C 2012, 116, 24824−24828
The Journal of Physical Chemistry C
■
Article
(26) Kusakabe, K.; Maruyama, M. Phys. Rev. B 2003, 67, 092406. (27) Lee, G.; Cho, K. Phys. Rev. B 2009, 79, 165440. (28) Xu, B.; Yin, J.; Xia, Y. D.; Wan, X. G.; Jiang, K.; Liu, Z. G. Appl. Phys. Lett. 2010, 96, 163102. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (30) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (31) Monkhorst, H. J.; Ernzerhof, J. D. Phys. Rev. B 1976, 13, 5188− 5192. (32) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901−9904. (33) Kittel, C. Introduction to Solid Sate Physics, 8th ed.; Wiley: New York, 2005. (34) Brito, W. H.; Miwa, R. H. Phys. Rev. B 2010, 82, 045417. (35) Jia, Y.; Zhu, W. G.; Wang, E. G.; Huo, Y. P.; Zhang, Z. Y. Phys. Rev. Lett. 2005, 94, 086101. (36) Jia, G.. X.; Guo, C. S.; Zhang, R. Q.; Zhang, W. J.; Bello, I.; Fraueheim, T. J. Phys. Chem. C 2009, 113, 8829−8835. (37) Zanella, I.; Fagan, S. B.; Mota, R.; Fazzio, A. J. Phys. Chem. C 2008, 112, 9163−9167. (38) Ota, N.; Gorjizadeh, N.; Kawazoe, Y. J. Magn. Soc. Jpn. 2010, 34, 573−578. (39) Xu, G.; Bai, J.; Torres, C. M., Jr.; Song, E. B.; Tang, J.; Zhou, Y.; Duan, X.; Zhang, Y.; Wang, K. L. Appl. Phys. Lett. 2010, 97, 073107.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (J.L.);
[email protected] (L.-W.W.). Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS J. Li gratefully acknowledges financial support from National Science Fund for Distinguished Young Scholar (Grant No. 60925016) and the National Basic Research Program of China (Grant No. 2011CB921901). L. W. Wang’s work at LBNL is supported by DMS/BES/SC of the U.S. Department of Energy under Contract DE-AC02-05CH11231. The authors acknowledge the computing resources provided by the Supercomputing Center, CNIC, CAS.
■
REFERENCES
(1) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. J. Phys. Soc. Jpn. 1996, 65, 1920−1923. (2) Lee, H.; Son, Y.-W.; Park, N.; Han, S.; Yu, J. Phys. Rev. B 2005, 72, 174431. (3) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (4) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature (London) 2006, 444, 347−349. (5) Ritter, K. A.; Lyding, J. W. Nat. Mater. 2009, 8, 235−242. (6) Zhang, Y.; Tan, Y. W.; Stormer, H. L.; Kim, P. Nature (London) 2005, 438, 201−204. (7) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature (London) 2005, 438, 197−200. (8) Li, X.; Wang, X.; Zhang, L.; Lee, S.; Dai, H. Science 2008, 319, 1229−1232. (9) Hwang, E. H.; Adam, S.; Sarma, S. D. Phys. Rev. Lett. 2007, 98, 186806. (10) Berger, C.; Song, Z. M.; Li, X. B.; Wu, X. S.; Brown, N.; Naud, C.; Mayou, D.; Li, T. B.; Hass, J.; Marchenkov, A. N.; et al. Science 2006, 312, 1191−1196. (11) Yang, X.; Dou, X.; Rouhanipour, A.; Zhi, L.; Räder, H. J.; Müllen, K. J. Am. Chem. Soc. 2008, 130, 4216−4217. (12) Cano-Márquez, A. G.; Rodríguez-Macías, F. J.; CamposDelgado, J.; Espinosa-González, C. G.; Tristán-López, F.; RamírezGonzález, D.; Cullen, D. A.; Smith, D. J.; Terrones, M.; Vega-CantùY., I. Nano Lett. 2009, 9, 1527−1533. (13) Campos, L.; Manfrinato, V.; Sanchez-Yamagishi, J.; Kong, J.; Jarillo- Herrero, P. Nano Lett. 2009, 9, 2600−2604. (14) Gorjizadeh, N.; Farajian, A. A.; Esfarjani, K.; Kawazoe, Y. Phys. Rev. B 2008, 78, 155427. (15) Rigo, V. A.; Martins, T. B.; da Silva, A. J. R.; Fazzio, A.; Miwa, R. H. Phys. Rev. B 2009, 79, 075435. (16) Choi, S. M.; Jhi, S. H. Phys. Rev. Lett. 2008, 101, 266105. (17) Caragiu, M.; Finberg, S. J. Phys.: Condens. Matter 2005, 17, R995−R1024. (18) Breitholtz, M.; Kihlgren, T.; Lindgren, S. Å.; Walldén, L. Phys. Rev. B 2003, 67, 235416. (19) Ma, Q.; Rosenberg, R. A. Phys. Rev. B 1999, 60, 2827−2832. (20) Chan, K. T.; Neaton, J. B.; Cohen, M. L. Phys. Rev. B 2008, 77, 235430. (21) Ding, J.; Qiao, Z. H.; Feng, W. X.; Yao, Y. G.; Niu, Q. Phys. Rev. B 2011, 84, 195444. (22) Sevinçli, H.; Topsakal, M.; Durgun, E.; Ciraci, S. Phys. Rev. B 2008, 77, 195434. (23) Kan, E. J.; Xiang, H. J.; Yang, J.; Hou, J. G. J. Chem. Phys. 2007, 127, 164706. (24) Nakada, K.; Ishii, A. Solid State Commun. 2011, 151, 13−16. (25) Zhang, Y.; Franklin, N. W.; Chen, R. J.; Dai, H. Chem. Phys. Lett. 2000, 331, 35−41. 24828
dx.doi.org/10.1021/jp3088034 | J. Phys. Chem. C 2012, 116, 24824−24828
