Free-Standing Bilayer Silicene: The Effect of Stacking Order on the

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Free-Standing Bilayers Silicene: The Effect of Stacking Order on the Structural, Electronic and Transport Properties Jose Eduardo Padilha, and Renato B. Pontes J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 31 Jan 2015 Downloaded from http://pubs.acs.org on February 5, 2015

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The Journal of Physical Chemistry

Free-Standing Bilayers Silicene: The Effect of Stacking Order on the Structural, Electronic and Transport Properties José E. Padilha∗,† and Renato B. Pontes∗,‡ Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil., and Instituto de Física, Universidade Federal de Goiás, CP 131, 74001-970, Goiânia, GO, Brazil. E-mail: [email protected]; [email protected]

Abstract We theoretically investigate the structural, electronic and transport properties of bilayers silicene. Due to the large numbers of degrees of freedom permitted by the buckled structure of the silicene, its bilayer structure can present several possible stacking configurations. We show that in the lowest energy conformation, named AAp , the bilayer silicene looses its buckled structure becoming planar. This structural conformation is established since there is an energy gain if the system loses its π cloud to create extra (σ-like) chemical bonds between the two layers. Simulated STM images show excellent agreement with experimental STM images of bilayers silicene. We also analyze the 2D and 3D features of the band structure of the bilayers silicene. In particular, we show that the analysis of the 3D band structure is fundamental to a complete understanding ∗

To whom correspondence should be addressed Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil. ‡ Instituto de Física, Universidade Federal de Goiás, CP 131, 74001-970, Goiânia, GO, Brazil. †

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of the electronic and transport properties in this material. Moreover, we show that different structures present distinct electronic and transport properties (Ids × Vds ), where for some stacks, we verify an anisotropic behavior of the current as a function of the direction of the applied bias.

Introduction Silicene, a new elemental hexagonal material from Group IV, predicted and synthesized in 2009, 1–7 has attracted much attention due to its electronic properties that resembles graphene. 8–11 Its unique crystal lattice, similar to a buckled graphene lattice, also presents a linear energy-momentum dispersion relation, resulting in massless Dirac fermions around the Fermi level at the K and K ′ points. 7,12–14 In addition, as this material presents almost all graphene striking properties, such as high electron mobility, it could allow the scientists and engineers to bring together the graphene like technology to the silicon one. 12 From the experimental point of view, most of the works has been devoted to the single layer silicene. 12,15–18 Nevertheless, some experimental realizations reported the obtention of a second layer in some samples. 13,18 Kawai et al. 19 presented a well succeeded synthesis of a bilayer silicene on a (111) Ag surface. From the theoretical point of view, a large number of investigations has been done to understand the physics behind the single layer silicene. 20–30 However, only few theoretical investigations have dealt with the bilayer silicene. 31–34 Thus, a comprehensive study of the electronic and transport properties of the free-standing bilayer silicene as function of the stacking order is still lacking. In this work, by performing the state-of-the-art in solid-state simulations, we investigate the structural, electronic and transport properties of free-standing bilayers silicene. We show that in the lowest energy configuration the system loses its buckled structure, becoming planar. In this configuration, there is an energy gain if the system loses its π cloud to create extra (σ-like) chemical bond between the two layers. We also show that there are other possible stable structures, having a total energy slightly higher than the planar, where 2


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their obtention would be possible depending on the constraints imposed by the substrate or strain applied. We present STM-simulated images of the bilayers silicene, and these images can be used to identify the stacking sequences for some structures. We also analyze the 2D and 3D plots of the band structures, where we verify that the electronic structure of the bilayers silicene are highly sensitive to the stacking sequence presenting both metallic or semiconducting behavior. Finally, for some structures, given a strong anisotropy in the electronic structure, we verify that the transport properties present a directional dependence.

Computational Details In order to obtain the energetically most stable structure and investigate the electronic and transport properties of the bilayer silicene, we perform ab initio total energy calculations, based on density functional theory 35,36 (DFT), as implemented in SIESTA code. 37 For the exchange-correlation functional we use the LDA approximation. 38 To describe the interactions of the valence and core electrons norm-conserved pseudopotentials were used, as proposed by Troullier-Martins. 39 A double-zeta basis set plus a polarization function (DZP) and an energy cutoff of 400 Ry were used to expand the Kohn-Sham orbitals and to represent the charge density on the grid. The structures were considered relaxed when the forces on the atoms were smaller than 0.01 eV/Å. Additional calculations considering van der Waals interactions were performed, however no difference were observed. The STM images were simulated by using the procedure proposed by Tersoff-Hamann. 40 The electronic transport calculations were done with TRANSAMPA code, 41,42 which is based on Non-Equilibrium Green’s Function (NEGF) method combined with DFT (NEGF-DFT). To correctly describe the 2D structure of the bilayer silicene and to take into account all the anisotropy in its electronic structure, we considered a set of 1000 k-points in the xˆ[ˆ y ] direction, covering all k-points in the 2D Brillouin zone, for the calculations of the transport properties in the yˆ[ˆ x] direction (See Padilha et al. 43 for a complete description of the method used in these

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calculations).

Results and Discussion a1

(a)

z

x

D

A

y

(b)

(d)

(f)

Top layer

B

a2

y

Botton layer

x

AA

(c)

AA’

(e)

AB’

AB

A’B’

Figure 1: (a) Ball-and-stick representation of the structure of a single layer of silicene. The atoms occupying the A and B sites are on a different plane, separated by a distance ∆ ≈ 0.5Å. The possible stacking configurations of the bilayer are: (b) AA; (c) AA’; (d) AB; (e) AB’ and (f) A’B’. The different colors used in the atoms are used to represent the buckled structure of the system. A single layer of silicene consist of silicon atoms placed on the A and B sub-lattice of the honeycomb structure, as in graphene, with an additional feature that the structure is buckled. The two sublattices planes are separated by a distance ∆ ≈ 0.5Å, as presented in Figure 1(a). The bilayer silicene can be constructed by stacking two silicene sheets, as shown schematically in Figure 1(a)(right panel). Due to its buckled structure, there are five possible stacking modes between the two layers, whereas for graphene there are only two. These additional stacking modes come from the fact that the top layer has the A site on the top and the B site on the bottom (in the same same layer) and the bottom layer could have 4


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the same buckling order as the top, or the contrary, for example, the A site is on the bottom and the B site is on the top (when the bottom layer has a buckled inverted with respect to the top layer we represent the A and B sites with a comma: A’ and B’). In Figure 1(b-g), we show the five possible stacking modes. In Figure 1(b,c) all silicon atoms of the two layers are on the top of each other, whereas in Figure 1(d-g) we show the Bernal possible stacks. All layers were initially separated by a distance of 4.0 Å and the initial lattice constant we used the equilibrium one of the monolayer of silicene (≈ 3.86 Å). All systems were free to relax - positions of the atoms and lattice constant. In Figure 2(a-f) we show the final structure of each stacking with an additional one, AAb , that will be discussed in details later. Table 1, summarizes the energetics and lattice constant of each final structure (the total energy values are displayed relative to the lowest-energy structure). Table 1: Total energy difference(in eV) between the most stable structure(named AAp ) and the other considered stacks on the DFT calculations. Stacking AAp AAb AB AB′ AA′ A′ B′

∆Etotal [eV ] 0.00 0.16 0.17 0.24 0.33 0.73

Lattice Constant [Å] 4.12 3.74 3.84 3.84 3.84 3.82

Final Structure Figure 2(b) Figure 2(c) Figure 2(e) Figure 2(f) Figure 2(d) Figure 2(g)

From Table 1, the lattice constant for the AB, AB’ and AA’ is around 3.84Å and for the A’B’ is around 3.82Å . All of this stacks resembles both the lattice constant as well as the buckling parameter of the single layer silicene, but they are all higher in energy. The AAp stacking has a lattice constant that is 6% bigger than the silicene monolayer and 7.3% higher than the other possible stacks. Moreover, this system presents the lowest total energy, ≈ 0.16 eV/UC, smaller than the AAb , that is another possible stacking obtained from the compression of the AAp . A remarkable feature, is that this configuration (AAp ) has a planar surface [Figure2(a)]. One interesting point, is that the system with the largest total energy with respect to the others, is the one whose layers are not chemically bonded each other, 5



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AB’. This indicates that when the layers are covalently bonded one to another, the energy of the system is lowered, a behavior that is quite distinct of graphene, whose atomic layers are held together by van der Waals forces.

Figure 2: DFT-optimized structures of each system: (a) AAp , (b)AAb , (c) AA’, (d) AB, (e) AB’, (f) A’B’. (g) Total energy, in eV, as function of the lattice constant for the considered stacks. The lowest calculated total energy (in this case, the total energy associated to the AAp structure) was set to zero and the others were calculated with respect to this one. From the latter results we see that the energy of the system highly depends on its lattice constant. To a better understanding of this dependency and to determine if those stacks obtained from the free relaxation of the system are energy minimum rather than a local minima. For each system, we study the evolution of the total energy as function of the lattice constant. We vary the lattice parameter around the equilibrium position of each configuration and let all atoms to relax with this constraint. These results are shown in Figure 2(g) and is it possible to see that all stacks has a minimum in energy, being locally stable, around a specific lattice parameter. We also verify that phase transitions can occur varying the lattice parameter to higher values. 32 For the A’B’ stacking, when the lattice parameter is varied to values smaller than 3.78Å this system falls into another phase, named AB’ - Figure 2(e), where the layers are strongly bonded to each other and the energy of the system diminish by ≈ 0.5 eV . For 6


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all other systems, except for the AAp case, when the lattice parameter is diminished, the systems remains on the same phase, increasing its energy, whereas the AAp system falls in another phase, named AAb - Figure 2(b), with an increase on the energy of approximately 0.2 eV . Moreover, for all systems when the lattice constant is increased to values higher than 4.0Å all of them falls down to the AAp phase. This behavior indicates that in its freestanding form, all possible stacks will prefer to be on the AAp phase with a planar structure. This behavior was also observed by Lian et al. 32 Additionally, is important to mention that we studied other two possible structures for the bilayers silicene. These structures could be obtained by cutting two layers of a reconstructed Si surface, Si(111)-2×2 as discussed by T. Morishita et al. 44 Since in this work we are dealing with structures that can be obtained by stacking two single layers of silicene, the results associated to the other two structures are presented in the Supporting Information, Figure S1. The STM images for all of the six possible stacks are shown in Figure 3. Through the STM images we can observe that two systems, AAp and AAb , present a clear distinct pattern from the others. For the planar AAp structure we can see that all atoms remains on the plane of each layer, whereas for the AAb structure due to an increase of the buckling height there is a high spot followed by a neighbor low spot corresponding to the other atom in the lattice. The others stacks presents a similar STM image even with completely different structures, so that additional experimental measurements are needed to differentiate those structures. Regarding the lowest energy structure one question has to be addressed: Why does the lowest energy configuration present a planar structure? Initially, we can make a parallel with graphene, where the single layer has a strong π cloud and it is planar. For graphene, when two layers are brought together, to maximize the interaction between the layers and to preserve its π cloud, the arrangement of the bilayer graphene is such that half of the atoms in one layer lies on the top of half of the atoms in the other layer. This minimizes the energy of the system, whose atomic layers interact via van der Waals forces. Differently

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Figure 3: (a-f) STM-simulated images for the six structures of the free standing bilayer silicene. All STM images were simulated by using a voltage between the tip and the sample of 0.5V . The scale bar in the STM images is given in Å. of graphene, the single layer of silicene has a buckled structure with a separation within the planes of ∆ = 0.5Å, with a weak π cloud. If we contact two layers without relax the lattice of the system, the layers will bond together and the system acquires and extra buckling, with the planes of each layer separated by ∆ = 0.85Å, presented schematically in Figure 4(a-2)(Middle panel). This reconstruction creates an extra overlap between two atoms in the unit cell, as depicted schematically in Figure 4(a-2)(Right panel). As this new interaction is forbidden, a repulsion between those atoms is created, and to minimize this interaction, the system prefers to increase its lattice constant, making the system planar. In summary, in order to minimize the total energy, the system prefers to lose its π cloud creating an σ-bond between the layers, as we can see in the volume slice of the charge density of the system, passing through all bonds of the system, presented in Figure 4(b). We can see, from the plot, that the intensity of the chemical bonds is nearly the same for all bonds(characteristics of a covalently bonded system). This point highlights the fact that the atoms of different layers are strongly attached to each other as the atoms on the same layer are.

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Figure 4: (a) Schematic representation of: (1) Single layer of silicene. (2) Relaxed bilayer silicene on the buckled phase. (3) Full relaxed bilayer silicene on planar phase. All bond lengths were extracted from the first-principles calculations. (b) Volume slice of the charge density of the AAp bilayer, passing through the bonds of the system. (c) Atomic structure and STM image of a superstructure containing a single and a bilayer silicene. In regions (I), (II) and (III) we show the single layer of silicene, the transition region between the single and the bilayer structure, respectively. The applied voltage to obtain the STM image was 0.5V . The black and white circles represent the buckled structure of the single layer of silicene, whereas the two black circles represent the planar structure of the bilayer silicene. In a experimental realization, a bilayer silicene will appear when a second layer of silicene grows up on the top of a single layer silicene. 18,19 This would generate a step between single layer and bilayer region. To investigate this structure, we performed an additional calculation with a supercell containing a single layer and on the top of it a finite second layer. The system, after relaxation, and its resulting STM image is presented in Figure 4(c). We highlight three 9



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regions of the system: (I) The region containing only the single layer of silicene; (II) The region that contains the transition between the single layer and the bilayer; (III) The bilayer silicene. We clearly see that in region (I) the system preserves its buckled structure, and in the transition region (II), after structural relaxation, the system shows a strong distortion on the lattice of the single layer, keeping the bilayer almost unaffected. In region (III), we observe the perfect reconstruction of the layers on the planar structure of the bilayer silicene. In Figure 4(c)(bottom panel), we show a magnification of the STM images presented in the top panel of (c). This shows a clearly distinction on the images of the buckled structure and the planar one, passing though the transition region. These simulated STM images show excellent agreement with the experimental STM images. 18

Figure 5: (a-f) Ball-and-stick views (upper left panels) of the bilayers silicene, electronic band structure(lower left panels) and a three-dimensional view of the electronic band structure(right panels). In each structure, the dashed line delimits the unit cell. 10


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In Figure 5(a-f), we present schematic views (upper left panels) of the bilayers silicene in the possible stacks, two-dimensional(2D) plots of the band structures (lower left panels) and also three-dimensional (3D) view of the electronic band structures (right panels). Although all systems present a hexagonal symmetry, we choose to calculate the band structures in a rectangular unit cell. The same unit cell was used in the electronic transport calculations. Analyzing the overall picture of the electronic band structures we can see that depending on the structural arrangement, the bilayers silicene can present a metallic [Figure 5 a-d and f] or a semiconducting [Figure 5(e)] behavior. In the 2D plots of the band structures, the dashed lines are associated to valence and conduction bands in the X-Γ direction whereas the solid lines are associated to the bands in the Γ-Y direction. Besides the 2D band structures, we present 3D plots of the valence and conduction bands for each configuration. The 3D band structure is important to a complete understand of the transport properties in this material. Initially, we will focus in the AA’ stacking [Figure 5(c)]. Solely analyzing the 2D plot, we are led to conclude that this structure presents two Dirac cones (one slightly n-doped and another slightly p-doped). However, looking deeply in the 3D band structure, we can clearly see that do not exist a Dirac cone. The valence and conduction bands touch each other not only at one isolated point, but in well-defined lines (the solid blue lines, in the 3D plot)[See also the Supporting Information Figure S2 for the band structure in the hexagonal symmetry]. The same interpretation could be extended to the others stacks. In the 3D plots, we also highlight the solid red lines, that are states that will contribute to the electronic transport, but are not displayed in the conventional 2D plots of the band structure. 45 Moreover, as can be seen[Figure 5(b)] the bilayer silicene in the AAp stacking, is a semi-metal due to the small overlap between the top of the valence band and the bottom of the conduction band. In Figure [5(e)], it is also possible to see that the AB’ stacking, is a indirect band-gap semiconductor, with a gap of approximately 0.29 eV. Given the previous band structures results, in the rectangular symmetry [ Figure 5], we

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Figure 6: (a-f) Transmission coefficients(Tx and Ty ) as a function of energy, in eV, for the six investigated structures. (g) Schematic view of a bilayer silicene, indicating the xˆ and yˆ directions considered for the transport calculations. see that the electronic structure around the Fermi level is strongly dependent to the stacking order, and in most systems is strongly anisotropic depending on the direction in the Brillouin zone. This behavior could lead to a direction dependent electronic transport properties. To understand the intrinsic electronic transport properties of the bilayers silicene, we present in Figure 6(a-f), the direction dependent transmission coefficients (Tx and Ty ), for the two considered directions, illustrated in the ball-and-stick representation in Figure 6(g), where we show the xˆ and yˆ directions considered for the electronic transport calculations. The transmission coefficient, as can be seen, is highly dependent on the structure of the bilayer silicene. However, only the AAb structure(Figure 6(a) presents a strong direction dependency on the transmission function, being the transmittance along the zigzag direction (direction xˆ) higher than in the armchair direction (direction yˆ). The directional anisotropy in the electronic structure of the AAb stacking order can also be verified considering the Fermi velocity(vf ) of the electrons, and consequently in the mobility of the charge carriers, as the mobility µ is proportional to the Fermi velocity vf . For the bilayer silicene ( in the AAb stacking), in the xˆ and yˆ direction, we obtained: vfx = 1.05×105 m/s and vfy = 1.05×106 m/s. 12


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The Fermi velocity, in the xˆ direction, is in the same order of magnitude than the single layer silicene (4.2 × 105 m/s) whereas in the yˆ direction is around the same order than graphene (1.8 × 106 m/s). 46 More important, is that this structure will also present different charge mobility, depending on the transport direction. Additionally, in the transmittance plot for the structure AB’(Figure 6e), as a direct consequence of the electronic band structure, it is possible to see a gap around the Fermi energy (set as zero energy). Stressing again, 2D plots of the band structures are not enough to provide a complete understand of the electronic properties of the bilayers silicene. For instance, in the AA’ system, the 2D band structure presents two Dirac cones, one in the X-Γ direction and another one in the Γ-Y, that is not presented in the transmission function. In this case, the transmission function, that is integrated over the entire Brillouin zone, gives an approximately constant value between ±0.5eV, and this can be only understood through the 3D plot of the band structure, where we clearly can see the set of states in the same energy (solid blue lines in Figure 5(c)). This result is in contrast to that obtained to other 2D systems that present two direction-dependent Dirac cones in the 2D band structure. As an example, we can highlight the 6, 6, 12−graphyne, that presents two Dirac cones in the band structure and these Dirac cones are also present in the transmission coefficient plots. 43 To complete the study of the transport properties of the bilayers silicene, we present in Figure 7 the current (Ids ) as a function of the applied bias voltage (Vds ), along the xˆ and yˆ direction, for the six considered structures. As we have previously observed for the transmission function, the current for the AAb structure [Figure 7(a)], presents a different transport depending on the direction. The current in the yˆ direction that is along the zigzag configuration of the system, presents a current that is three times bigger than in the xˆ direction. For the AAp structure, the current in the xˆ direction slightly bigger than the yˆ between 0.1V and 0.4V, and for bias voltages bigger than 0.4V the current is degenerated and presents a saturation as function of the bias voltage. For the AB and A’B’ the current for the yˆ direction is always bigger than the xˆ, and does not present any tendency to saturate and to

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Figure 7: Current (Ids ) × Voltage (Vds ) along the xˆ and yˆ direction, for the six considered structures of the free standing bilayer silicene. became degenerate again. Finally, the current for the AB’ structure, presents a characteristic behavior of a semiconductor system, where the current starts to increase for voltages higher than 0.4V. Also, in the bias voltages range considered in our calculations, they are always degenerate with respect to the direction. In conclusion, based on first-principles electronic structure calculations, we show that in the lowest energy configuration the bilayer silicene looses its buckled structure, becoming planar. This conformation is settled since there is an energy gain if the system loses its π cloud to create extra (σ-like) chemical bonds between the two layers. The bilayer silicene on this planar configuration is a metal. The simulated STM images, for a region where there is a transition between single layer and bilayer silicene, are in excellent agreement with experimental STM images. In particular, we show that the analysis of the 3D band structure is fundamental to a complete understanding of the electronic and transport properties of the bilayer silicene. We verify that the transmission coefficient is highly dependent of the structure and in some cases we obtained an anisotropic behavior of the current as a function of the direction of the applied bias. These results opens up new routes to design bilayer 14


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silicene-based devices, since their intrinsic properties, which are highly dependent of the stacking order, can present a directional dependence as well.

Acknowledgments The authors thank the Brazilian agencies CAPES, FAPESP and INCT/CNPq for financial support. We acknowledge the use of computational facilities of CENAPAD-SP. We also thank A. Fazzio and Antônio J. R. da Silva for insightful discussions.

Supporting Information Available Additional information and figures of: (i) Band structures and STM images for the bilayers silicene obtained from the Si(111)-2×2 surface. (ii) Band structures for the bilayers silicene in the hexagonal symmetry. This information is available free of charge via the Internet at http://pubs.acs.org.

References (1) Kara, A.; Leandri, C.; Davila, M.; Padova, P.; Ealet, B.; Oughaddou, H.; Aufray, B.; Le Lay, G. Physics of Silicene Stripes. J. of Superconductivity and Novel Magnetism 2009, 22, 259-263. (2) Le Lay, G.; Aufray, B.; Leandri, C.; Oughaddou, H.; Biberian, J. P.; De Padova, P.; Davila, M. E.; Ealet, B.; Kara, A. Physics and Chemistry of Silicene Nano-Ribbons. Appl. Surf. Sci. 2009, 256, 524-529. (3) Sahin, H.; Cahangirov, S.; Topsakal, M.; Bekaroglu, E.; Akturk, E.; Senger, R. T.; Ciraci, S. Monolayer Honeycomb Structures of Group-IV Elements and III-V Binary Compounds: First-Principles Calculations. Phys. Rev. B 2009, 80, 155453.

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(4) Lebegue, S.; Eriksson, O. Electronic Structure of Two-Dimensional Crystals from Ab Initio Theory. Phys. Rev. B 2009, 79, 115409. (5) Aufray, B; Kara, A.; Vizzini, S.; Oughaddou, H.; Leandri,C.; Ealet, B.; Le Lay, G. Graphene-Like Silicon Nanoribbons on Ag(110): A Possible Formation of Silicene. Appl. Phys. Lett. 2010, 96, 183102. (6) Lalmi, B.; Oughaddou, H.; Enriquez, H.; Kara, A.; Vizzini, S.; Ealet, B.; Aufray, B. Epitaxial Growth of a Silicene Sheet. Appl. Phys. Lett. 2010, 97, 223109. (7) De Padova, P.; Quaresima, C.; Ottaviani, C.; Sheverdyaeva, P. M.; Moras, P.; Carbone, C.; Topwal, D.; Olivieri, B.; Kara, A.; Oughaddou, H.; et al. Evidence of Graphene-Like Electronic Signature in Silicene Nanoribbons. Appl. Phys. Lett. 2010, 96, 261905. (8) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666-669. (9) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature 2005, 438, 197-200. (10) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6, 183-191. (11) Novoselov, K. S.; Morozov, S. V.; Mohinddin, T. M. G.; Ponomarenko, L. A.; Elias, D. C.; Yang, R.; Barbolina, I. I.; Blake, P.; Booth, T. J.; Jiang, D.; et al. Electronic Properties of Graphene. Phys. Status Solid B 2007, 244, 4106-4111. (12) Kara, A.; Enriquez, H.; Seitsonen, A. P.; Lew Yan Voon, L. C.; Vizzini, S.; Aufray, B.; Oughaddou, H.; A Review on Silicene - New Candidate for Electronics. Surf. Sci. Rep. 2012, 67, 1-18.

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Page 16 of 21

Page 17 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(13) Chen, L.; Liu, C. C.; Feng, B. J.; He, X. Y.; Cheng, P.; Ding, Z. J.; Meng, S.; Yao, Y. G.; Wu, K. H. Evidence for Dirac Fermions in a Honeycomb Lattice Based on Silicon. Phys. Rev. Lett. 2012, 109 056804. (14) Houssa, M.; Pourtois, G.; Afanas’ev, V. V.; Stesmans, A. Can Silicon Behave Like Graphene? A First-Principles Study. Appl. Phys. Lett. 2010, 97, 112106. (15) Jamgotchian, H.; Colignon, Y.; Hamzaoui, N.; Ealet, B.; Hoarau, J. Y.; Aufray, B.; Biberian, J. P. Growth of Silicene Layers on Ag(111): Unexpected Effect of the Substrate Temperature. J. Phys.: Cond. Matt. 2012, 24 172001. (16) Lin, C. L.; Arafune, R.; Kawahara, K.; Tsukahara, N.; Minamitani, E.; Kim, Y.; Takagi, N.; Kawai, M. Structure of Silicene Grown on Ag(111). Appl. Phys. Expr. 2012, 5, 045802. (17) Fleurence, A.; Friedlein, R.; Ozaki, T.; Kawai, H.; Wang, Y.; Yamada-Takamura, Y. Experimental Evidence for Epitaxial Silicene on Diboride Thin Films. Phys. Rev. Lett. 2012, 108 245501. (18) Feng, B. J.; Ding, Z. J.; Meng, S.; Yao, Y. G.; He, X. Y.; Cheng, P.; Chen, L.; Wu, K. H. Evidence of Silicene in Honeycomb Structures of Silicon on Ag(111). Nano Lett. 2012, 12 3507-3511. (19) Arafune, R.; Lin, C.-L.; Kawahara, K.; Tsukahara, N.; Minamitani, E.; Kim, Y.; Takagi, N.; Kawai, M. Structural Transition of Silicene on Ag(111). Surface Science 2013, 608, 297-300. (20) Quhe, R.; Fei, R.; Liu, Q.; Zheng, J.; Li, H.; Xu, C.; Ni, Z.; Wang, Y.; Yu, D.; Gao, Z.; et al. Tunable and Sizable Band Gap in Silicene by Surface Adsorption. Scientific Reports 2012, 2 853-858.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(21) Wang, Y.; Zheng, J.; Ni, Z.; Fei, R.; Liu, Q.; Quhe, R.; Xu, C.; Zhou, J.; Gao, Z.; Lu, J. Half-Metallic Silicene and Germanene Nanoribbons: Towards High-Performance Spintronics Device. Nano 2012 7 1250037- 1250045. (22) Ni, Z.; Zhong, H.; Jiang, X.; Quhe, R.; Luo, G.; Wang, Y.; Ye, M.; Yang, J.; Shi, J.; Lu, J. Tunable Band Gap and Doping Type in Silicene by Surface Adsorption: Towards Tunneling Transistors. Nanoscale 2014 6, 7609-7618. (23) Quhe, R.; Yuan, Y.; Zheng, J.; Wang, Y.; Ni, Z.; Shi, J.; Yu, D.; Yang, J.; Lu, J. Does the Dirac Cone Exist in Silicene on Metal Substrates? Scientific Reports 2014, 4 5476-5484. (24) Liu, C. C.; Feng, W. X.; Yao, Y. G. Quantum Spin Hall Effect in Silicene and TwoDimensional Germanium. Phys. Rev. Lett. 2011, 107, 076802. (25) Ezawa, M. A. Topological Insulator Helical Zero Mode in Silicene Under an Inhomogeneous Electric Field. New J. Phys. 2012, 14, 033003. (26) Ezawa, M. Quantum Hall Effects in Silicene. J. Phys. Soc. Japan 2012, 81, 064705. (27) Dyrdal, A.; Barnas, J. Intrinsic Spin Hall Effect in Silicene: Transition from Spin Hall to Normal Insulator. Phys. Stat. Sol. Rap. Res. Lett. 2012, 6, 340-342. (28) Ezawa, M. Valley-Polarized Metals Quantum Anomalous Hall Effect in Silicene. Phys. Rev. Lett. 2012, 109, 055502. (29) Drummond, N. D.; Zolyomi, V.; Fal’ko, V. I. Electrically Tunable Band Gap in Silicene. Phys. Rev. B 2012, 85, 075423. (30) Ni, Z. Y.; Liu, Q. H.; Tang, K. C.; Zheng, J. X.; Zhou, J.; Qin, R.; Gao, Z. X.; Yu, D. P.; Lu, J. Tunable Bandgap in Silicene and Germanene. Nano Lett. 2012, 12, 113-118. (31) Ezawa, M. Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene. J. Phys. Soc. Japan 2012, 81, 104713. 18


Page 18 of 21

Page 19 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(32) Lian, C.; Ni, J. Strain Induced Phase Transitions in Silicene Bilayers: a First Principles and Tight-Binding Study. AIP Advances 2013, 3, 052102. (33) Huang, B.; Deng, H.-X.; Lee, H.; Yoon, M.; Sumpter, B. G.; Liu, F.; Smith, S. C.; Wei, S.-H. Exceptional Optoelectronic Properties of Hydrogenated Bilayer Silicene. Phys. Rev. X 2014, 4, 021029. (34) Liu, F.; Liu, C.; Wu, K.; Yang, F.; Yao, Y. d + id Chiral Superconductivity in Bilayer Silicene. Phys. Rev. Lett. 2013, 111, 066804. (35) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864. (36) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133. (37) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejòn, P.; SánchezPortal, D. Linear-Scaling Ab-Initio Calculations for Large and Complex Systems. J. Phys.: Cond. Matt. 2002, 14, 809-817. (38) Perdew, J. P.; Zunger, A. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Phys. Rev. B 1981, 23, 5048. (39) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993. (40) Tersoff, J.; Hamann, D. R. Theory of the Scanning Tunneling Microscope. Phys. Rev. B 1985, 31, 805. (41) Padilha, J. E.; Lima, M. P.; da Silva, A. J. R.; Fazzio, A. Bilayer Graphene Dual-Gate Nanodevice: An Ab Initio Simulation. Phys. Rev. B 2011, 84 113412. (42) Padilha, J. E.; Pontes, R. B.; da Silva, A. J. R.; Fazzio, A. IxV Curves of Boron and Nitrogen Doping Zigzag Graphene Nanoribbons. Int. J. Quant. Chem. 2011, 111, 1379-1386. 19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(43) Padilha, J. E.; Fazzio, A.; da Silva, A. J. R. Directional Control of the Electronic and Transport Properties of Graphynes. J. Phys. Chem. C 2014 118, 18793-18798. (44) Morishita, T.; Spencer, M. J. S.; Russo, S. P.; Snooka, I. K.; Mikami M. Surface Reconstruction of Ultrathin Silicon Nanosheets. Chemical Physics Letters 2011 506, 221-225. (45) Craster, R. V.; Antonakakis, T.; Makwana, M.; Guenneau, S. Dangers of Using the Edges of the Brillouin Zone. Phys. Rev. B 2012 86, 115130. (46) Trivedi, S.; Srivastava, A.; and Kurchania, R. Silicene and Germanene: A First Principle Study of Electronic Structure and Effect of Hydrogenation-Passivation. JCTN, 2014, 11, 1-8.

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