Transition-Metal-Atom-Embedded Graphane and Its Spintronic Device

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Transition-Metal-Atom-Embedded Graphane and Its Spintronic Device Applications Haixia Da,*,† Yuan Ping Feng,‡ and Gengchaiu Liang*,† †

Department of Electrical and Computer Engineering, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Republic of Singapore ‡ Department of Physics, 2 Science Drive 3, National University of Singapore, Singapore 117542, Republic of Singapore ABSTRACT: First-principles calculations are implemented to investigate the electronic and magnetic properties of transition-metal (TM)-atom-embedded graphanes. We find that most of the configurations possess magnetic ground states that have larger magnetic moments compared to embedding TM atoms in graphenes. Furthermore, the various magnetic moments can be generated by tailoring the different dopants. We also design a heterojunction structure with nickel- and vanadium-embedded graphanes in order to manipulate the spin currents. Due to the materials’ unique characteristics, the spin-down current can be totally suppressed while the spin-up current appears under a negative bias voltage, resulting in a perfect spin filter and spin current diode. Such properties imply promising potential applications in graphane-based nanodevices and spintronics.

1. INTRODUCTION Graphane, a fully prehydrogenated graphene, has attracted extensive interest along with recent experimental progress in preparing a single layer of graphane.1,2 Unlike semimetallic graphene3 and chiral-dependent graphene nanoribbons,4 graphane is an insulator with a band gap of about 5.4 eV.5 Graphane nanoribbons also exhibit semiconducting properties regardless of their edge orientations.6,7 Recently, theoretical studies have also shown the possible existence of an excitonic Bose
Einstein condensate in graphane.8 Graphane nanoribbons also show promising thermoelectric properties.9 Furthermore, the large ON-state currents and the high ratio of ON-state to OFF-state currents in graphane-based field effect transistors have been theoretically predicted.10 These outstanding characteristics lead graphane as a remarkable platform for electronic, thermal, optical studies, and applications.5
12 On the other hand, the magnetic properties of graphane-based structures and the possible applications in manipulating the spin degree of freedom for spintronic devices are still not fully understood. Stimulated by the recent reports on graphene decorated with transition metals (TMs), it is shown that hybridized graphene systems possess the magnetic properties necessary for potential applications in spintronics and other fields such as nanocatalysis13 and room-temperature hydrogen storage.14 It will be interesting to investigate whether similar properties appear in TM-atom-embedded graphane due to its unique sp3bonded monolayer structure. Although a recent theoretical work has presented magnetic properties of graphane having defects or TM impurities, the study only considered TM atoms replacing the hydrogen (H) atoms that are above the carbon (C) atoms.15 It has been recently shown theoretically that graphane sheets with foreign atoms have rich magnetic behaviors.16,17 The fundamental understanding of magnetic and transport properties in r 2011 American Chemical Society

graphane embedded with TM atoms, where the C atom, along with its attached H atom, is substituted by TM atoms still remains incomplete. In this work, therefore, we comprehensively investigate and provide physical insights to structural, electronic, and magnetic properties of TM-atom-embedded graphane structures, as well as explore their possible applications in spintronic devices. Our results show that the interaction between the TM atoms and graphane manifests via the bond lengths and binding energies. First-principles calculations on the electronic band structures further reveal that the hybridization of the TM and C atoms causes distinct changes in electronic and magnetic properties of these materials, leading to the splitting between the spin-up and spin-down channels. In addition, possible device application on spin current diodes is demonstrated by using the specific TM atoms, such as V and Ni atoms as dopants, in graphane. By investigating the spin transport characteristics of the heterojunction structure, we observe the different behaviors between spin-up and spin-down electrons. The spin-up current dramatically increases upon the application of negative bias voltage. In contrast, the spin-down current is totally suppressed. This distinction between spin-up and spin-down behaviors indicates possible practical applications of TM-embedded graphane in spintronic devices.

2. COMPUTATIONAL DETAILS Numerical calculations of total energies and electronic properties of TM-atom-embedded graphane systems are performed using the Vienna ab initio simulation package (VASP).18
20 The Received: April 15, 2011 Revised: October 16, 2011 Published: October 17, 2011 22701

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Figure 1. Schematics of optimized TM-atom-embedded graphane configurations, two upper panels are (a) side view and (b) top view, where yellow, white and gray balls stand for carbon, hydrogen and TM atoms, respectively. (c) Equilibrium heights (red-solid line) and bond lengths (blue-dasheddotted line), and (d) energy difference, ΔE = ENM
EFM, (red-solid line) and binding energies Eb (blue-dashed-dotted line), for various configurations.

ion-electron interactions are treated based on the projector augmented wave (PAW) approximation.21,22 The Perdew, Burke, and Ernzerh (PBE) functional under the spin-polarized generalized gradient approximation (GGA) is used to describe the exchange and correlation interaction.23 TM-atom-embedded graphane systems are considered as a C atom, along with its attached H atom, substituted by a TM atom in a 4  4 hexagonal graphane supercell, cf., Figure 1, a and b. Periodic boundary condition is set with the vacuum region between two neighboring images larger than 15 Å, which is enough to avoid the interactions between graphane images. The plane wave cutoff energy is set at 500 eV. Reciprocal space integrations are carried out at 9  9  1 Monkhorst
Pack k-point meshes. Symmetry-unrestricted optimizations for all configurations are performed by using the conjugate gradient scheme until the force acting on every atom is less than 0.01 eV/Å. The binding energy Eb is determined by Eb = Etotal
Es‑graphane
Eatom, where Etotal is the total energy of the TMatom-embedded graphane, Es‑graphane is the energy of the pristine graphane with single C and H vacancy, and Eatom is the energy of the single TM atom in a large cell (a cube of 15  16  17 Å3) surrounded by vacuum and periodic boundary conditions.

3. RESULTS AND DISCUSSION We first study the behaviors of two-dimensional (2D) pristine graphane, where H atoms are perpendicular to the graphane plane, and the bond lengths of C
C and C
H are 1.54 and 1.11 Å, respectively. The simulated band structure shows insulating properties with a direct band gap of value 3.52 eV. This is in good agreement with previous theoretical results.5,12,24 However, this result is smaller than experimental results (5.4 eV)1 due to the band gap underestimation by DFT calculations within GGA. Band gap closer to experimental values can be achieved using ab initio calculation with GW0 approximation.25 Next, we investigate the optimized structures of TM-atom-embedded graphane

systems. It is observed that the original configurations keep almost unvaried except that the TM atoms move out of the plane due to their large atom sizes. This induces a local curvature characterized by a height h, as shown in Figure 1a. Figure 1c shows the heights and bond lengths of TM-C in various configurations. It can be found that the Ti
C bond length is the largest whereas Co
C is the shortest among all structures due to their different electron affinities. Furthermore, three nearest-neighbor hydrogen atoms around each TM atom slightly shift away from the original perpendicular orientation due to the changed coordination numbers around the H atoms. This leads to the slightly distortion from the pristine graphane. To identify the ground states of the TM-atom-embedded graphane systems, we study both spin-unpolarized and spinpolarized configurations and calculate the energy differences (ΔE) between the nonmagnetic (NM) and ferromagnetic (FM) states as well as the binding energies per unit cell. As illustrated in Figure 1d, all the binding energies of the TM-atom-embedded graphanes are negative except for the Zn-embedded graphane where a positive binding energy indicates a repulsive interaction between the Zn atom and graphane. This results in an endothermic adsorption process. On the contrary, the negative binding energy indicates an attractive interaction between the single TM atom and graphane. This indicates an exothermic adsorption process. Specifically, it is found that the total energies of most systems under the FM states are much lower than those under the paramagnetic states, confirming that most configurations investigated are magnetic ground states. Unlike pristine graphane which has the nonmagnetic ground state, the TM-atom-embedded graphane systems exhibit diverse electric and magnetic properties. The spin-resolved band structures are presented in Figure 2 for all investigated configurations. The red and blue lines in the figure are the spin-up and spin-down subbands, respectively. Table 1 summarizes the band gaps of the spin-up and spin-down bandstructures. We observe that the substitution of different TM atoms into 22702

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Figure 2. Spin-polarized band structures in all TM-atom-embedded graphane configurations, where red and blue lines show the dispersion relationship in spin-up and spin-down channels, respectively. The Fermi level is set to be zero.

Table 1. Band Gaps (EG) for Different TM-Atom-Embedded Graphane in the Spin-up and -down Channels atom

EG/eV (spin up)

EG/eV (spin down)

Sc

1.10

1.10

Ti

1.33

2.44

V Cr

0 1.20

2.48 2.40

Mn

0

0

Fe

0.41

1.60

Co

1.89

1.90

Ni

0

2.68

Cu

0.51

3.00

Zn

0.74

0

graphanes leads to a large change in electronic properties. For example, the Cr-embedded graphane exhibits semiconducting properties with a band gap of 1.20 eV in the spin-up channel and 2.40 eV in the spin-down channel. Moreover, the density of states around Fermi level manifests in the spin-up channel, but not in the spin-down channel in the V and Niembedded graphane. Furthermore, it is found that except for the Sc/Co-embedded graphane, spin splitting in the spin-up and the spin-down channels indicates the capability of achieving spontaneous magnetism in other TM-atom-embedded graphanes.

The physical mechanism of magnetic moment formation in TM-atom-embedded graphanes can be attributed to the unsaturated electrons of the TM atoms inducing the polarization of the electrons around the metal atoms and the nearby C atoms.26 The effect can be illustrated by the difference between the total charge density of TM-atom-embedded graphane and atomic charge densities, i.e., the charge density difference (CDD).27 To elucidate the above mechanism, an example of the CDD in V-embedded graphane is shown in Figure 3a, where isosurfaces of the CDD in red (light) and in blue (dark) stand for the charge accumulation and depletion regions, respectively. Similarly, the contour plot shown in Figure 3b illustrates spatial spin distribution per a unit cell in the whole space, where the red and blue color represent the dominance of spin-up (the majority spin) and spin-down (the minority spin) electrons, respectively. It shows that the positive magnetic moment is localized at the V atom and there is a small negative magnetic moment redistributed over the three C atoms. The magnetic moments of TM-atom-embedded graphanes are shown in Figure 3c. For comparisons, we also calculate the magnetic moments of TM-atom-embedded graphene systems, and their values (dot-dashed line) are in good agreement with the reported study11 as shown in Figure 3c. We observe that the magnetic moments of TM-atom-embedded graphanes, except for Co-embedded graphane, are larger than those of TM-atomembedded graphenes. This implies that TM-atom-embedded graphanes could be promising for practical implementations in 22703

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Table 2. Total Magnetic Moments (μB) for TM-Atom-Embedded Graphane under Different Unit Cell Sizes

Figure 3. (a) Isosurfaces of the difference charge density in V-embedded graphane with red (light) and blue (dark) isosurfaces indicating charge accumulation and charge depletion regions. Isosurface charge density is taken to be 0.005 electrons/Å3. (b) Spatial spin distribution is defined as the difference between spin-up and spin-down electron densities for V-embedded graphene, where red color corresponds to positive values (majority spin states) of the spin density, blue to the negative values (minority spin states). (c) Total magnetic moments per unit cell in TM-atom-embedded graphene (red-solid line) and TMembedded graphane (blue-dashed-dotted line) configurations. The curves exhibit a significant difference between two cases. The total magnetic moments in most of TM-atom-embedded graphane configurations are larger than those in TM-atom-embedded graphene, which can be ascribed to their intrinsic different electrons skeleton.

high-density information storage. The enhancement in magnetic moments of TM-atom-embedded graphanes arises from the intrinsic structural properties of graphane. Compared to graphene which is a monolayer of carbon atoms with sp2 hexagonal network, graphane consists of a sp3 C
H network which changes the local charge distribution around the TM atoms directly. For example, in Ti-embedded graphene, three electrons of Ti are involved in forming covalent σ bonds with neighboring C atoms and the fourth electron yields a π bond.9 In Ti-embedded graphane, however, the three neighbor C atoms are hydrogen saturated, indicating that three electrons of Ti involve the formation of Ti
C bond which leaves one unpaired electron as well as 1 μB, where μB = ep/(2mc) is the Bohr magneton. Consequently, it is expected that the trends of magnetic moments in TM-atom-embedded graphane will be changed due to the unique sp3 skeleton in graphane. Furthermore, it is observed that the smallest magnetic moments are zero in Sc- and Co-embedded graphanes. These materials therefore have nonmagnetic ground states. The calculations on a 6  6 supercell including two Co atoms with Co
Co distance of 2.597 and 5.139 Å show that the starting configurations with different magnetic states converged to the same nonmagnetic state. In principle, the localized nonbonding dorbitals of TMs determine the magnetic moment of TMembedded graphane.13 In the case of Co-embedded graphane, three electrons of Co participate in the formation of Co
C bonding and two nonbonding orbitals are filled with four electrons. Therefore, it leads to zero magnetic moment in Coembedded graphane. On the other hand, the maximum magnetic

size of unit cell

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

22

0

0.82

2

3

2

1

0

1

0

1

44 66

0 0

1 1

2 2

3 3

3.5 3.1

1 1

0 0

1 1

2 2

1 1

moment appears in Mn-embedded graphane due to the largest unpaired d electrons. This is similar to results shown in the electron band structures in Figure 2. Next, the magnetic moments of the hybridized configurations with Ti, Fe, Ni, and Zn atoms are 1 μB. For the Ti- and Fe-embedded systems, as shown in Figure 2, their dyz and dxz orbitals stay away from the Fermi level and remain occupied for both spin channels. This means that they have no contribution to the net magnetic moments. For the dxy, dx2
y2, and dz2 orbitals, the dxy and dx2
y2 orbitals locate above (below) the Fermi level and are empty (occupied) in both of the spin channels. While the spin splitting of the dz2 orbital is large, one of them is below (above) the Fermi level in the spin-up channel and the other is above (below) the Fermi level in the spin-down channel, giving rise to one unpaired electron and resulting in 1 μB magnetic moment. On the other hand, in the case of Ni-embedded graphane, the pz orbital from the C atoms and dyz orbital from the Ni atoms cross through the Fermi level in the spin-up channel but no orbitals are aligned around the Fermi level in the spin-down channel. This system is metallic for spinup electrons but semiconducting for spin-down electrons. Furthermore, it can be observed that the magnetic moments of both V- and Cu-embedded graphanes are 2 μB. The band structure of V-embedded graphane is similar to that of Niembedded graphane but unlike Ni-embedded graphane the pz orbital from the C atoms in the former does not contribute to the electronic bands near the Fermi level. Its dxy and dx2 orbitals partially occupied (unoccupied), and the dz2 orbital is fully occupied (unoccupied) in the spin-up (spin-down) channel, leading to 2 μB magnetic moment. On the other hand, the 2 μB magnetic moment originates from the unpaired electrons in the dyz and dxz orbitals of the spin-up channel in Cu-embedded graphane. Finally, the magnetic moment of Cr-embedded graphane is 3 μB. The reason is the similar mechanism as that for Ti/Fe-embedded graphane, where dz2, dxy, and dx2 orbitals are fully occupied in the spin-up channel and unoccupied in the spin-down channel. Our theoretical findings have shown that the single TM atom substitution in 4  4 graphane unit cell offers rich magnetic properties. The coupling between the TM atoms and their neighbor metal atoms may affect the localization of impurity states and determine the stability of the induced magnetism. Therefore, we modify the unit cell size to clarify the doping concentration influence on the magnetic moments in TM-graphanes. The structures with different unit cell sizes are fully relaxed and then the magnetic moments of all cases are examined as shown in Table 2. It is observed that except for Cu- and Mn-embedded graphanes in a 2  2 supercell, the magnetic moments of other cases are similar for different unit cell size due to their localized characteristics, indicating that the magnetic moment of TM
graphane is not sensitive to the doping concentrations. The change of magnetic moments in Cu- and Mn-embedded graphane within a 2  2 supercell can be attributed to the large structure distortions of small unit cell. 22704

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Figure 4. (a) Calculated spin currents as a function of the bias voltage, where the red (solid line with square symbol) and black (dash line with circle symbol) lines represent the spin-up and spin-down currents, respectively. The inset is the schematic illustration of heterojunction structure based on Ni-embedded graphane and V-embedded graphane, where gray, white, and color balls are carbon, hydrogen, and two different TM atoms, respectively. The electrodes are infinitely extending along x and z directions as a 2D sheet. (b) The spin-resolved transmission curves (schematic figures describe the mechanism in the insets, where white arrows stand for spin-up electrons of two electrodes) are shown as a function of the energy for spin-up and spin-down electrons at three specified bias points Vb = 0 V, (0.08 V, respectively. The conduction window is indicated by dotted line and the Fermi level is set as zero.

To evaluate their possible applications of Ni/V-embedded graphane in spintronic devices, a heterogeneous junction composed of two configurations with different metal elements, as shown in the inset of Figure 4a is implemented. The system infinitely extends along the x and z directions. We calculate the transport properties of the system using the fully self-consistent nonequilibrium Green’s function method combined with DFT, which is implemented in Atomistix Toolkit (ATK).28
30 The cutoff energy is 150 Ry and a Monkhorst
Pack k-mesh along the x and y directions is sampled as 9  1. A single-ξ polarized basis set is used. The room temperature current
voltage characterare calculated using the Landauer formula, Iσ = (e/h)Ristics ∞
∞Tσ(E,Vb)[f(E
μL,σ)
f(E
μR,σ)] dE, where Tσ(E,Vb) is the transmission function for the different spin electrons (σ = v, V), E is the injection energy of the tunneling electrons, f(E
μL(R),σ) is the Fermi
Dirac distribution function with chemical potentials μL(R),σ = EF + ΔL(R),σ ( eV/2, ΔL(R),σ is the spin splitting energy in the left (right) electrodes, and Vb is the applied bias voltage. As shown in Figure 4a, the calculated current
voltage curves present the clear spin-dependent transport behaviors between the spin-up and spin-down electrons. It can be found that the spin-down current completely vanishes for both positive and negative bias voltage. This is due to their zero

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density of states (DOSs) around the Fermi level in both Ni- and V-embedded graphanes, as shown in Figure 2. However, the spin-up current shows a different behavior. Under a positive bias voltage, the spin-up current increases slightly and then is suppressed, while under the negative bias voltage, it increases monotonically. As a result, Is(Vb) 6¼ Is(
Vb), where Is = Iv
IV. This exhibits a spin current diode application using TM-atomembedded graphane heterojunction.31 To further understand the physical insights of transport behaviors of spin-up electrons, we show the schematics of DOSs in Ni/V-embedded graphane and investigate their transmission spectra at different bias voltage (Vb) of
0.08, 0, and 0.08 V, for the X, Y, and Z points, respectively, shown in Figure 4b. Based on dispersion relations of Ni- and V-embedded graphanes in Figure 2, the spin-up DOSs of these two systems have an overlap around the Fermi level in equilibrium, resulting in a peak around the Fermi level in spin-up transmission spectrum at the zero bias voltage as the Y point of Figure 4b. When the positive bias voltage is applied, the DOSs of Ni-embedded graphane are shifted upward but the DOSs of V-embedded graphane are pushed toward the lower energy. Therefore, the overlap area in the conduction window between μ1 and μ2 decreases, leading to the transmission decreasing at the Z point as shown in Figure 4b. Furthermore, this effect competes with the effect of the conductance increase as the conduction window increases, resulting in the negative differential resistance effect observed around 40 mV. Nevertheless, the case for the negative bias voltage is different. Considering the Vb =
0.08 V for the X point shown in Figure 4b, the DOSs of Ni
embedded graphane and V-embedded graphane are moving downward and upward, respectively, resulting in an increase in the overlap of the DOSs of two leads. This enhances the transmission. Correspondingly, the spin-up currents will increase as the negative bias voltage increases. With the results of the spin-down current, this heterojunction structure with different TM atoms in graphanes not only shows the spin current diode behaviors but also demonstrates that high spin filter efficiency can be achieved by carefully tailoring the embedded TM atoms in graphanes. It indicates the potential applications of TM-atom-embedded graphane structures in the fields of carbon nanoelectronics and spintronics. In additional to TM atoms replacing C
H atoms to be embedded in graphane, there are still other possible processes when the systems are exposed in hydrogen plasma surroundings. These possible processes might vary electronic and magnetic properties of graphane-based systems, resulting in different transport properties. It would be interesting to investigate the details and their alternative device application in future works.

4. CONCLUSIONS In this work, the electronic and magnetic properties of a graphane sheet decorated with TM atoms are investigated comprehensively using first-principles calculations. We find that, compared to pristine graphane, TM-embedded graphanes show promising various magnetic moments and that maximum magnetic moment can reach up to 3.5 μB by embedding Mn in the graphane. Finally, a heterojunction structure with different TM atoms embedded in graphane is implemented to manipulate the spin currents. It is found that the spin-down current can be totally blocked due to the unique behaviors of V/Ni-embedded graphane systems while the spin-up current appears at the negative 22705

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (H.D.); [email protected] (G.L.).

’ ACKNOWLEDGMENT H.X.D. is deeply indebted to Dr. Eduardo Cuansing, Mr. Kaitai Lam, and Mr. Y. Qian for their valuable assistance and discussions. This work was funded by the Agency for Science, Technology and Research (A*STAR), Singapore, under grant number 082-101-0023, and the Singapore National Research Foundation Competitive Research Programme Fund. Computational resources are provided by Department of Physics and the Computational Nanoelectronics and Nanodevice Lab, Department of Electrical and Computer Engineering, National University of Singapore.

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(27) Chan, K. T.; Neaton, J. B.; Cohen, M. L. Phys. Rev. B 2008, 77, 235430. (28) Brandbyge, M.; Mozos, J. L.; Ordejo’n, P.; Taylor, J.; Stokbro, K. Phys. Rev. B 2002, 65, 165401. (29) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (30) Taylor, J.; Guo, H.; Wang, J. Phys. Rev. B 2001, 63, 245407. (31) Mina, Y.; Yaoa, K. L.; Liua, Z. L.; Chenga, H. G.; Zhua, S. C.; Gao, G. Y. J. Magn. Magn. Mater. 2009, 321, 312–315.

’ REFERENCES (1) Elias, D. C.; Nair, R. R.; Mohiuddin, T. M. G.; Morozov, S. V.; Blake, P.; Halsall, M. P.; Ferrari, A. C.; Boukhvalov, D. W.; Katsnelson, M. I.; Geim, A. K.; et al. Science 2009, 323, 610–613. (2) Ryu, S.; Han, M. Y.; Maultzsch, J.; Heinz, T. F.; Kim, P.; Steigerwald, M. L.; Brus, L. E. Nano Lett. 2008, 8, 4597–4602. (3) Konstantinova, E.; Dantas, S. O.; Barone, P. M. V. B. Phys. Rev. B 2006, 74, 035417. (4) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (5) Leb
egue, S.; Klintenberg, M.; Eriksson, O.; Katsnelson, M. I. Phys. Rev. B 2009, 79, 245117. (6) Li, Y. F.; Zhou, Z.; Shen, P. W.; Chen, Z. F. J. Phys. Chem. C 2009, 113, 15043–15045. (7) S-ahin, H.; Ataca, C.; Ciraci, S. Phys. Rev. B 2010, 81, 205417. (8) Cudazzo, P.; Attaccalite, C.; Tokatly, I. V.; Rubio, A. Phys. Rev. Lett. 2010, 104, 226804. (9) Ni, X.; Liang, G. C.; Wang, J. S.; Li, B. W. Appl. Phys. Lett. 2009, 95, 192114. (10) Fiori, G.; Leb
egue, S.; Betti, A.; Michetti, P.; Klintenberg, M.; Eriksson, O.; Iannaccone, G. Phys. Rev. B 2010, 82, 153404. (11) Boukhvalov, D. W.; Katsnelson, M. I.; Lichtenstein, A. I. Phys. Rev. B 2008, 77, 035427. (12) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Phys. Rev. B 2007, 75, 153401. (13) Krasheninnikov, A. V.; Lehtinen, P. O.; Foster, A. S.; Pyykko, P.; Nieminen, R. M. Phys. Rev. Lett. 2009, 102, 126807. (14) Kim, G.; Jhi, S.-H.; Lim, S.; Park, N. Appl. Phys. Lett. 2009, 94, 173102. (15) Yang, C. K. Carbon 2010, 48, 3901–3905. (16) Wang, Y. L.; Ding, Y.; Shi, S. Q.; Tang, W. H. Appl. Phys. Lett. 2011, 98, 163104. (17) Medeiros, P. V. C.; BritoMota, F. D.; Mascarenhas, A. J. S.; Castilho, C. M. C. D. Nanotechnology 2010, 21, 115701. (18) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (19) Kresse, G.; Hafner, J. Comput. Mater. Sci. 1996, 6, 15. (20) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169. (21) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. (22) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (24) Samarakoon, D. K.; Wang, X. Q. ACS Nano 2009, 3, 4017. (25) S-ahin, H.; Ataca, C.; Ciraci, S. Appl. Phys. Lett. 2009, 95, 222510. (26) Wu, M.; Liu, E.-Z.; Jiang, J. Z. Appl. Phys. Lett. 2008, 93, 082504. 22706

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