graphene hybrid: Ab initio study

Materials Chemistry and Physics 183 (2016) 580e587

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Electronic and magnetic properties of modified silicene/graphene hybrid: Ab initio study Suman Chowdhury, Debnarayan Jana* Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, W.B., India

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Electronic and magnetic properties of two dimensional graphene/silicene hybrid have been explored.
There is no magnetism in the system for a single carbon atom vacancy.
A net magnetic moment of 4.0 Bohr magneton is observed for a single silicon atom vacancy.
Unpaired electrons introduce midgap states which is otherwise absent in the pure system.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 December 2015 Received in revised form 16 August 2016 Accepted 9 September 2016 Available online 10 September 2016

Among other two-dimensional (2D) novel materials, graphene and silicene both have drawn intense research interest among the researchers because they possess some unique intriguing properties which can change the scenario of the current electronic industry. In this work we have studied the electronic and the magnetic properties of a new kind of materials which is the hybrid of these two materials. Density functional theory (DFT) has been employed to calculate the relevant electronic and magnetic properties of this hybrid material. The pristine structure is modified by substitutional doping or by creating vacancy (Y-X, where one Y atom (Si or C) has been replaced by one X atom (B, N, Al, P or void)). The calculations have revealed that void systems are unstable while Si-B and Si-N are most stable ones. It has been noticed that some of these doped structures are magnetic in nature having induced mid-gap states in the system. In particular, Si-void structure is unstable yet it possess the highest magnetic moment of the order of 4 mB (mB being the Bohr magneton). The estimated band gaps of modified silicene/ graphene hybrid from spin polarized partial density of states (PDOS) vary between 1.43e2.38 eV and 1.58 e2.50 eV for spin-up and spin-down channel respectively. The implication of midgap states has been critically analysed in the light of magnetic nature. This study may be useful to build hybrid spintronic devices with controllable gap for spin up and spin down states. © 2016 Elsevier B.V. All rights reserved.

Keywords: Semiconductors Magnetic properties Electronic structure Computer modelling and simulation

1. Introduction Two dimensional (2D) materials possess thickness of several

* Corresponding author. E-mail address: [email protected] (D. Jana). http://dx.doi.org/10.1016/j.matchemphys.2016.09.018 0254-0584/© 2016 Elsevier B.V. All rights reserved.

atomic layers and are extended periodically in the other two dimensions. After the experimental discovery of graphene by Novoselov et al. [1,2], it has received considerable attention from the scientific community. Graphene has led to many new research ideas. It possesses some unique properties which has been found to have great potential for use in future nanoelectronic devices [1e6]. But the main drawback of graphene is that the band gap of

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graphene is zero. For this reason graphene is not suitable for nanoelectronic devices. So it is always desirable to have a finite bandgap. There are several ways of opening up of band-gap in graphene: (a) by B-N doping [7e10], (b) by applying strain [11], (c) by chemical functionalization [12]. Opening up of band-gap in graphene has been seen to be quite uncontrollable. This makes it incompatible for making practical devices. In this situation, researchers have focussed towards silicon (Si), the next element in the same group of C. This new 2D material having honeycomb structure is known as silicene [13]. Experimentally, silicene has been synthesized by Vogt et al. [14]. Silicene nanoribbons grown on a silver (110) substrate have been studied experimentally by Padova et al. [15]. We have studied the magnetic properties of planar silicene by using DFT [16,17] and reported that di-vacancy induced silicene exhibits large magnetic moment (~0.5 mB per pair of vacancies). However, it remains non-magnetic in the case of monovacancy. From first principles calculations, optical properties of Al and P doped buckled silicene have also been studied by us [16,18]. In that work, the signature of buckling has been noted in the optical spectra for perpendicular polarization. The magnetic and anisotropic optical properties of four differently shaped silicene nanodisks have also been explored by us. Zigzag-trigonal nanodisk has been found to possess maximum magnetic moment among all the other nanodisks. The origin of the non-zero magnetic moment has been argued in the light of zero energy states and edge atoms [16,19]. The advantage of this new 2D material is that it can easily be interfaced with the modern Si based industry. Keeping in mind the exoticness of these 2D materials, several approaches have been proposed to design novel nanostructures suitable for device applications. One of them is to combine Si and C atoms to make various nano-structures. As a bi-product of this combination Si-C nanotubes [20,21] and Si-C nanowires [22] have been proposed which have been proven to be a promising candidate for hydrogen storage. Theoretically, proposed Si-C zigzag nanoribbons have been found to be half-metal without any application of external electric field [23,24]. Experimentally Si-C nanorods have been synthesized through a reaction between carbon nanotubes and SiO [25]. Ciraci et al. [26] also have thoroughly explored 22 different honeycomb structures of group-IV elements and III-V binary compounds. In that work they have also explored the stability of Si-C nanosheet by employing DFT calculation. Drissi et al. [27] have examined the hydrogenation effect of this silicene/graphene hybrid system by using DFT. They have pointed out that full hydrogenation increases the band-gap (~1.0 eV). However, half chemical modification with hydrogen reduces the gap. Drissi et al. [28] have also calculated the electronic and optical properties of silicene/graphene hybrid by incorporating the many-body effect. From their phonon mode analysis, it has been found that the structure is stable. The phenomena of ferromagnetic ordering observed at reasonably high temperatures in some compounds containing no atoms with open d or f shells is known as d0 ferromagnetism [29,30] e.g. in HfO2 [31], ZnO [32e34] with vacancies and so on. It should be worthy to mention here that d0 ferromagnetism in ZnO has been explained via oxygen vacancy, defect complex on Zn, vacancy and H [33] and Zn interstitial defect states [34] and in ZnS by VZn along with S dangling bonds on the nanoparticle surface [30]. In most of the situations, ferromagnetism does not appear in the bulk when they are defect free and pure. Thus, lattice defect seems to be a genuine necessary factor for the occurrence of d0 ferromagnetism. They may be point defects, atomic vacancies or interstitials e induced by irradiation or thermal treatments (annealing) or by lattice mismatch. Surface, grain boundaries and dislocations also can participate to generate this d0 ferromagnetism. In other words, the defect states can give rise to an appreciable magnetic moment in connection with the molecular orbitals localized very close to the

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defect site [30]. The utility of d0 ferromagnetism lies in the fact that large magnetization like Fe, Co, Ni can be achieved in a nanomaterial having an active defect. Thus, one can visualize magnetism in a non-magnetic pristine semiconducting matrices with some appropriate impurities/voids of non-magnetic sp atoms. Hence, d0 magnetism can take an important key role in designing novel materials in spintronics at room temperature. The nanoparticle surface area in 2D systems seems to be an integral part in triggering this d0 ferromagnetism in contrast to bulk one. Recently Ju et al. [35] have studied the d0 ferromagnetism in hydrogenated silicene sheet by employing DFT. Here, it is to be noted that, in some alkaline-earth metal nitrides XN (X ¼ Ca, Sr, Ba), half-metallic d0 ferromagnetism has been predicted without any defects [36,37]. Motivated by the prospect of d0 ferromagnetism in 2D nanomaterial and the important characteristic features of silicene/graphene hybrid, here, we have explored the electronic and magnetic properties of modified silicene/graphene hybrid where the modification has been done through doping and vacancy. This study will enable one to choose the appropriate hybrid materials having suitable band gaps and significant magnetic moments for device application. 2. Computational details The whole calculations have been performed within the framework of DFT [38e40], using the generalized gradient approximation (GGA) according to Perdew, Burke, Ernzerhof (PBE) [41] parameterization implemented in SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) [42,43] code. Well tested Troullier Martin [44], norm conserving pseudopotentials in fully separable Kleinman and Bylander form have been employed for all the elements. The double z plus polarized basis set is used throughout the whole range of systems. A 300 Ry mesh cutoff has been used for the reciprocal space expansion of the total charge density. Brillouin zone (BZ) has been sampled by using 10101 mesh of k points within Monkhorst-Pack (MP) [45] scheme. But for partial density of states (PDOS) calculation, 80801 mesh of k points have been used. All the structures are optimized by minimizing the forces on individual atoms below 0.02 eV/Å using the standard conjugate-gradients (CG) technique. The convergence criteria for energy of the self-consistent field (SCF) cycle is chosen to be 105 eV. Interlayer gap separation along the z direction between two successive silicene/graphene hybrid layers has been set at 20 Å to avoid artificial interaction among the layers. 3. Results and discussions Both graphene and silicene have two atoms in its unit cell. In this hybrid structure, among the two atoms, one is C and the other is Si. 44 supercell (32 atoms) have been considered for study. Two types of modification have been done in the 44 supercell: (a) substitutional doping where either C or Si atoms have been replaced by other atoms, (b) void or vacancy where C or Si atoms have been removed from the system. We have also sub-divided the doping and the void case as (i) carbon replacement, where one of the C atoms has been replaced by other atom for doping or removed to create vacancy, (ii) silicon replacement, where one of the Si atoms has been replaced by other atom for doping or removed to create vacancy. As dopant atoms we have used, boron (B), nitrogen (N), aluminium (Al) and phosphorus (P) which are neighbors of C and Si in the periodic table because of their close atomic radii [46e48]. If a C atom is replaced by B, N, Al or P, we shall call the structure C-X (where X ¼ B, N, Al or P). Similarly, when a Si atom is replaced by B, N, Al or P, we shall call the structure Si-X (where X ¼ B, N, Al or P). On the other hand, if a C or a Si atom is completely

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endothermic and exothermic process. From the formation energy data, it can be stated that void systems are the most unstable system. C-Al is also unstable as they all have positive formation energy. However, Si-B and Si-N system are the most stable system as they have the lowest defect formation energy. 3.1. Density of states (DOS) While discussing the electronic structure of planar silicene/ graphene hybrid, Density of states(DOS) analysis is very important. DOS for a given band n can be defined as,

Nn ðEÞ ¼ Fig. 1. Top view of the 44 supercell of planar pristine graphene/silicene hybrid. The red and blue balls respectively denote the C and Si atoms. Unit cell of the pristine structure is shown by green lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

removed from the system, we shall call the structure C-void and Sivoid respectively. In Fig. 1 we have illustrated the top view of the pristine structure. Whereas, in Figs. 2 and 3 we have shown the modified structures used in this work. The Si-C bond length (dSiC) in the pristine relaxed structure has been found to be 1.79 Å which is close to the value that obtained by Ciraci et al. [26] and bond angle of 120 clearly indicates that the system is fully sp2 hybridized. The defect formation energy of the full supercell of the geometrically relaxed doped silicene/graphene hybrid systems has been estimated by the following relation,

i h Edf ¼ Ed þ Erep  Epr  Edoped

(1)

where, Edf, Ed, Erep, Epr and Edoped are respectively the defect formation energy, total energy of the doped structure, total energy of a single atom which has been replaced from the pristine structure, total energy of the pristine structure and total energy of a single atom which has been doped. However, for the void structure we have adopted the first approach described in Ref. [49] for the formation energy calculation. In such a case, the expression in (1) can be used with Edoped ¼ 0. Bond length, bond angle, formation and Fermi energy of all the modified structures have been illustrated in Table 1. Positive and negative values of formation energy respectively denote

1

UBZ

Z

d3 k dðE  En ðkÞÞ 4p3

(2)

where UBZ is volume of the BZ in k space and En(k) describes the dispersion of the given band and the integral is defined over BZ. PDOS resolves the contributions of electronic states of each atom to the energy spectrum according to the angular momentum of the states. This study is of importance for qualitative understanding of electron hybridization in the system. In Fig. 4 we have plotted the orbital projected partial density of states (PDOS) of the pristine structure. From the DOS, we have obtained the band gap of the pristine system as 1.342 eV. Unlike graphene and silicene, which have zero band gap, it is semiconductor in nature [27,28]. The band gap of the buckled silicene/graphene hybrid has been found to be 2.4 eV by Drissi et al. [27,28] by using both LDA and GGA functional. These functionals however, are known to underestimate the band gap. So, to match more closely with the experimental results, the authors have taken into account quasiparticle corrections by using GW approximation. They have found that by using GW approximation, the obtained band gap (3.48 eV) is higher than that of LDA and GGA band gap. It is also interesting to note that the buckled structures possess higher band gap than its planar counterpart. The origin of this band gap can be traced from the tight-binding model. The two non-equivalent sub-lattices of the silicene/graphene hybrid break the sub-lattice symmetry. This symmetry remains intact in pure graphene and silicene. Drissi et al. [27,50,51] have demonstrated the existence of this band-gap due to sublattice symmetry breaking from tight-binding model. If we carefully observe the PDOS of different modified systems, we can note that for several structures, there appear mid-gap states which are absent in the pristine structure. Although there exist reports of midgap states in graphene [52e57] and silicene [58], but to our knowledge, this paper clearly demonstrates the existence of

Fig. 2. (a) Represents all the modified structures where one of the carbon atoms has been replaced by another dopant atom. The black ball denotes the dopant atom (Al, B, N or P). (b) The modified C-void system, where the empty box denotes the position of the void.

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Fig. 3. (a) Represents all the modified structures where one of the silicon atom has been replaced by another dopant atom. The black ball denotes the dopant atom (Al, B, N or P). (b) The modified Si-void system, where the empty box denotes the position of the void.

Table 1 Different structural parameters, Fermi energy and defect formation energy (in eV) of different modified structures. System

Bond-length (in Å)

Bond angle

Fermi energy (in eV)

C-Al

dSiAl ¼ 2.19

3.71

6.08

C-B

dSiB ¼ 1.89

b ¼ 120 Si AlSi b Si BSi ¼ 120

4.38

0.20

C-N

dSiN ¼ 1.80

3.00

dSiP ¼ 2.11

b ¼ 120 Si NSi b ¼ 120 Si PSi

2.39

C-P

2.54

1.99

Si-Al

dCAl ¼ 1.89

4.87

0.91

Si-B

dCB ¼ 1.60

b ¼ 120 C AlC b ¼ 120 C BC

4.83

4.66

Si-N

dCN ¼ 1.47

3.48

4.08

Si-P

dCP ¼ 1.75

b ¼ 120 C NC b ¼ 120 C PC

2.84

2.75

4.03 4.81

9.22 11.31

C-void Si-void

midgap states in some of the modified silicene/graphene hybrid systems. From an electronic structure point of view, a pz vacancy in bipartite lattice causes due to either a vacancy or due to some bond formation with other atoms. Through bond formation, the pz orbital detaches itself from the p band. This causes an imbalance between number of sites in two sublattices. The term imbalance means sublattice symmetry breaking. As we have seen, in the pristine form the graphene/silicene hybrid system is made up of two triangular interpenetrating perfect sublattices. One is made up with Si atoms and the other is with C atoms. In the modified structure when one or more atoms are replaced by other dopant atoms, or completely removed by creating vacancy then this sublattice symmetry is broken. The states near the Fermi energy are strongly affected due to this sublattice symmetry breaking. It also breaks the electronhole symmetry in the system. For the appearance of midgap states, sublattice symmetry breaking is a necessary condition [57,59]. But not all sublattice symmetry breaking lead to midgap states in the energy spectrum. It can be seen from Figs. 5 and 6 that C-N, C-P, Si-Al, Si-B systems do not possess midgap states in its DOS spectrum though sublattice symmetry is broken in these systems. Now we shall try to analyze the mid-gap states that appear in modified silicene/graphene hybrid. In seven structures i.e. C-Al, CB, C-void, Si-N, Si-P and Si-void we have observed mid-gap states. Generally, mid-gap states appear because of the presence of unpaired electrons in the system [60]. In order to examine whether these mid-gap states are localized or extended, we have plotted the isosurface charge density within the energy range of the mid-gap states of some of the structures in Fig. 7. As it can be seen (see Fig. 7 (b)) the carbon-related mid gap states are localized, however, it is clear from DOS (see Fig. 5 (e)) that they form the partially filled

Defect formation energy (in eV)

band, contributing non-zero DOS at EF, hence they do participate in the conduction process. In the C-void system, after the removal of the C atom, the three under coordinated Si atoms form bonds with each other. So, the charge densities are not localized on some particular atoms, rather extended over some region. But in all other cases, it is localized on some particular atoms. So the presence of mid-gap states in all other cases arises due to unsaturated bonds or the presence of unpaired electrons. But Si-void system possesses the impurity mid-gap states which can be observed from its DOS. It is evident from the Figs. 7d and 6e that charge density distribution

Fig. 4. Partial density of states of the pristine structure. The Fermi energy (EF) is indicated by the vertical solid line.

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Fig. 5. Partial density of states (PDOS) of different modified systems where a single C atom has been replaced. (a) C-Al, (b) C-B, (c) C-N, (d) C-P, (e) C-void (inset is the zoomed portion near the Fermi level).

related to the carbon-related mid-gap states are in fact localized, but from DOS (Fig. 6e) that they form the partially filled band, contributing non-zero DOS at EF. Therefore, these states indeed do participate in the conduction process, despite the related contribution in charge density is of localized character.

In Table 1 we have provided the Fermi energy for each of the modified structure. For comparison it is to be noted that the Fermi energy of pristine silicene/graphene hybrid is 3.14 eV. If we further examine the shifts of the Fermi energy (EF) from the PDOS plot (Figs. 5 and 6) with respect to the pristine system (see

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Fig. 6. Partial density of states (PDOS) of different modified systems where a single Si atom has been replaced. (a) Si-Al, (b) Si-B, (c) Si-N, (d) Si-P, (e) Si-void.

Fig. 4), we can observe shifts in both towards conduction band (CB) and valence band (VB). When the system is doped with B, Al and also with voids, EF is shifted towards VB, because B, Al and void doping are equivalent to p or hole doping in the system. Whereas, for N and P doped system, it is shifted more towards

the conduction band because N and P doping introduce n or electrons in the system. In future it will be interesting to study the stability of these structures by employing molecular dynamics. Among all the modified structures, the most stable structures have been found to be Si-B and Si-N.

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Fig. 7. Isosurface charge density of (a) C-Al, (b) C-void, (c) Si-N and (d) Si-void. The blue, red, pink and black balls respectively denote Si, C, Al and N atoms (isosurface value: 0.003 e/ Å3). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Spin-up band-gap (in eV), spin-down band-gap (in eV) and net magnetic moment (in mB) of different modified systems. System

Spin-up band gap (in eV)

Spin-down band gap (in eV)

Magnetic moment (in mB)

C-Al C-B C-N C-P Si-Al Si-B Si-N Si-P C-void Si-void

1.957 2.023 2.334 2.379 2.011 1.964 2.104 1.435 1.733 2.042

1.901 2.102 2.505 2.379 2.011 1.964 2.104 1.73 1.733 1.589

1.0 0.06 1.0 1.0 0 0 1.0 1.0 0 4.0

3.2. Magnetic property In Figs. 5 and 6 we have plotted the spin-polarized PDOS of C and Si replacement modified systems respectively. Also in Table 2 we have reported the spin-up and spin-down band-gap along with the net magnetic moment of the system. Magnetism occurs in a system if there is an asymmetry between spin-up and spin-down DOS. Among all the modified structures, the most asymmetric DOS is seen to exist in the Si-void system [17,49]. It can be seen from the charge density plot (see Fig. 7 (d)) that, after the complete removal of the Si atoms, the under coordinated three C atoms however do not form any bonding to saturate the bonds. As a result, it introduces a net non-zero magnetic moment in the system [17,49]. Also, the Si-void system exhibits mid-gap states contributed by the down-spins. Apart from the C-B system, where the net magnetic

moment is quite low, all the other structures are seen to be magnetic (from Table 2) and show mid-gap states. We have mentioned earlier that the appearance of the mid-gap states is due to the presence of unpaired electrons in the system and these unpaired electrons are responsible for the existence of the magnetic moment. Pujari and Kanhere [60] also observed similar kind of behavior in hydrogenated graphene (known as graphane) with mono and di-vacancy. But the C-void system is non-magnetic as mentioned earlier because of the absence of unpaired electrons [49] in the system. If we carefully study the spin-up and down band gap of the systems, it is easy to notice that for all the non-magnetic systems, the spin-up and the spin-down band-gap is exactly same. But in some of the magnetic systems, they are not equal. From Table 1, it is clear that the range of the band gaps are also different for different spin channel for different modified systems. The values

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of band gaps lie between 1.43 - 2.38 and 1.58e2.50 eV for spin up and spin down channel respectively. The data given in Table 2 also indicate that magnetism can be switched on and off by choosing the appropriate adatoms in silicene/graphene hybrid. 3.3. Conclusions Electronic properties of modified silicene/graphene hybrid systems have been investigated by employing DFT calculation in GGA formalism. Formation energy analysis revealed that both the void systems are unstable. However, Si-B and Si-N are noticed to be stable. The range of the band gaps are found to be different for different spin channels ranging between 1.43e2.38 eV and 1.58e2.50 eV for up and down spin channel respectively. It has been found that Si-void system exhibits maximum magnetic moment (4 mB) because of the presence of unpaired electrons. In contrast, C-void system is non-magnetic in nature because of the absence of unpaired electrons. The presence of unpaired electrons also introduces the mid-gap states which is otherwise absent in the pristine structure. We hope this work will shed some light to the experimentalists to build appropriate spintronic devices by using silicene/graphene hybrid. Acknowledgements This work is partially supported by DST-FIST, DST-PURSE, Government of India. One of the authors (SC) gratefully acknowledges DST, Govt. of India for providing financial assistance through DSTINSPIRE fellowship scheme. The authors would like to acknowledge the computational facility provided by University of Calcutta, Department of Physics. The authors also would like to thank Prof. B. Pujari and Prof. D. Kanhere for fruitful discussions. References [1] A. Neto, F. Guinea, N. Peres, K. Novoselov, A. Geim, Rev. Mod. Phys. 81 (2008) 109. [2] K. Novoselov, A. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, Science 306 (2004) 666. [3] A.K. Geim, Rev. Mod. Phys. 83 (2011) 851. [4] A.K. Geim, K.S. Novoselov, Nat. Mater 6 (2007) 183. [5] A.H.C. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81 (2009) 109. [6] D.S.L. Abergel, V. Apalkov, et al., Adv. Phys. 59 (2010) 261. [7] P. Nath, S. Chowdhury, D. Sanyal, D. Jana, Carbon 73 (2014) 275. [8] P. Nath, D. Sanyal, D. Jana, Phys. E 56 (2014) 64. [9] D. Jana, P. Nath, D. Sanyal, in: M. Aliofkhazraei, et al. (Eds.), Modification of Electronic Structure of Graphene by Boron and Nitrogen Doping, Graphene Science Handbook, Nanostructure and Atomic Arrangements, vol. 2, CRC Press, New York, 2016, ISBN 978-1-46-659131-8, pp. 231e246. Ch 15. [10] S. Chowdhury, R. Das, P. Nath, D. Jana, D. Sanyal, in: V.K. Thakur, M.K. Thakur (Eds.), Electronic and Optical Properties of Boron- and Nitrogenfunctionalized Graphene Nanosheet, Chemical Functionalization of Carbon Nanomaterials: Chemistry and Applications, CRC Press, New York, 2015, ISBN 978-1-48-225394-8, pp. 949e957. Ch-42. [11] Z.H. Ni, T. Xu, Y.H. Lu, Y.Y. Wang, et al., ACS Nano 2 (2008) 230. [12] T. Kuila, S. Bose, A.K. Mishra, P. Khanra, N.H. Kim, J.H. Lee, Prog. Mater. Sci. 57 (2012) 1061. [13] S. Cahangirov, M. Topsakal, E. Aktrk, H. Sahin, S. Ciraci, Phys. Rev. Lett. 102

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