Bilayer graphene films over Ru(0001) surface: Ab-initio calculations and STM images simulation

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Surface Science xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Surface Science journal homepage: www.elsevier.com/locate/susc

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D.A. Kroeger a, E. Cisternas b, J.D. Correa c a

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Keywords: Ru(0001) Bilayer graphene STM

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With the aim of better understanding recent experimental results, we performed density functional theory calculations (DFT), including van der Waals interactions, on bilayer graphene over a Ru(0001) surface. Two stacking sequences (AB and AA) for bilayer graphene were considered and compared with monolayer graphene. For each case relaxed atomic positions, calculated STM images and density of states were obtained and these are discussed in detail. Our results suggest that Moiré patterns of graphene over a Ru(0001) surface have a remarkable electronic influence, whose origin is the coupling of graphene layers and the Ru(0001) surface. Additionally, we found that atomic lattice observed by STM on such Moiré patterns is related with stacking sequence of bilayer graphene. © 2014 Elsevier B.V. All rights reserved.

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1. Introduction

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Two dimensional (2D) materials are currently attracting considerable scientific and technological interest [1]. From the scientific point of view, they bring the opportunity to test diverse theories on a distinct dimensionality [2–4], while their corresponding electronic structure properties suggest several technological applications [5–7]. Among two dimensional materials, the most widely studied to date has been a stable monolayer of graphite: graphene. Graphene can be obtained from highly oriented pyrolitic graphite (HOPG), resulting in a 2D structure formed exclusively by carbon atoms ordered in a honeycomb lattice. As HOPG is a very common sample in scanning tunneling microscopy (STM) and Raman spectroscopy laboratories, several of its electronic and phononic properties have been reported mainly from these experimental techniques [8–13]. At the same time, from a theoretical point of view, a single graphene layer and few graphene layers are tractable by means of computational methods involving tight binding and/or density functional theory (DFT) [2,14–16]. In the same context, graphitic structures adsorbed on metal surfaces have been reported [17,18], while further investigations have shown that these structures can consist of few graphene layers, or even monolayers [19]. Nowadays, it is well known that the electronic properties of graphene are strongly modified when it rests on another graphene layer [20] or on a Ru(0001) surface [18,21–23]. As a counterpart, graphene adsorbed on a boron nitride substrate showed electronic properties comparable to freestanding graphene [24]. Thus, as the substrate plays

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Departamento de Física, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54 D, Temuco, Chile Departamento de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia

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Bilayer graphene films over Ru(0001) surface: Ab-initio calculations and STM images simulation

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E-mail address: [email protected] (E. Cisternas).

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an important role in the electronic properties of graphene, the scientific interest for few graphene layers adsorbed on different surfaces has experienced a rapid increase in recent years [25–37]. In particular, the existence of two distinct phases of bilayer graphene (BLG) on Ru(0001) could be very interesting (due to their different electronic properties), and according to experimental results reported recently [31], the first layer could be used as a template to grow different phases of bilayer graphene. Motivated by experimental observations, this paper presents a theoretical study on the two stacking sequences (AB and AA) of bilayer graphene over the Ru(0001) surface. For greater clarity the paper has been organized as follows: details of DFT calculations are given in Section 2; comparison of calculated STM images for monolayer and bilayer grahene with experimental observations, as well the main theoretical results for BLG is presented in Section 3; main conclusions are summarized in Section 4.

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2. Calculation method

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In order to mimic the Ru(0001) surface, a three-layer unit cell was modeled. To model the Ru(0001) surface we fixed the Ru-bulk lattice constant and the atomic positions in the first Ru-bulk layer. As graphene on Ru forms a surprisingly large unit cell, 10 × 10 Ru units were necessary to accommodate 11 × 11 bilayer graphene units: graphene (11 × 11) on Ru (10 × 10). Therefore, the mismatch between Ru bulk and graphene lattice vectors is 0.02 Å. Two stacking sequences for graphene layers were considered: AA and AB, each with configuration having a corresponding unit supercell composed of 784 atoms. Monolayer graphene over Ru(0001) was also considered, so that we validated

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Fig. 1(a) and (b) shows the relaxed atomic positions of a monolayer graphene over the Ru(0001) surface. We found protrusions or mounds

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in the graphene layer forming a superstructure, periodicity of which is 27.45 Å. The maximum height difference among carbon atoms (or mound height) is 1.62 Å; nevertheless it reduces to 1.41 Å, by including vdW corrections (see Table 1). Thus, as stated by Wang and Bocquet [29], this result confirms the significant role played for dispersive forces. Mound heights calculated here are very close to those values calculated in Refs. [23] and [29] (1.5 Å and 1.31 Å respectively), and close to the value 1.16 Å, which was recently calculated in Ref. [33]. Moreover, the mound height calculated here presents a good agreement with experimental values reported elsewhere: 1.5 Å [34] and 1.2 Å [35]. A calculated STM image (Vbias = 1.5 V at constant height mode) for this system [Fig. 1(c)] shows the current maxima (bright zones) over protrusions. As reported from STM measurements [21,25,26,30,32,35, 36], calculated images reproduce the main experimental characteristics: on bright mounds all carbons are resolved; there are two inequivalent tunneling current minima, where only one of the two atoms in the graphene unit cell is resolved. According Wang and Bocquet [29], such current minima inequivalence can be explained by different symmetric registries of C pairs with respect the Ru surface. A line profile was performed along the highlighted segment in Fig. 1(c) (see inset), and it shows that tunneling current increases roughly 18 times when the STM tip goes from a minimum to a maximum. Such an increase may not be attributable exclusively to graphene layer deformation: considering that reference plane for a calculated STM image is 1 Å above the topmost carbon atom and 2.6 Å above the bottom one, it is expectable that tunneling current increases only 2.6 times. As occurs for graphene over different substrates [13,16], these results suggest that the STM tip also detects modifications in the electronic structure. To support this last statement we calculated STM images for several bias voltages and, by assuming that depressions in current lead to proportional approximation of the STM tip to the surface, we could have an estimation of the corrugation detected experimentally. Therefore, calculated corrugation amplitude for several bias voltages is summarized in Table 2. This fact agrees with experimental data obtained independently [26,27,44] which show a dependence on bias voltage applied during experiments. However, these calculations do not show a bright areas shifting as reported by Pan et al. [26]. On the other hand, lattice constant of calculated STM image (27.45 Å) differs from the value obtained experimentally (30 Å) [26, 35], because the unit cells which describe more precisely this parameter are graphene (12 × 12) on Ru (11 × 11) [18,21] or graphene (25 × 25) on Ru (23 × 23) [22,33]. Nevertheless, DFT calculations employing these enormous unit cells produce even lower mound heights (1.14 Å in Ref. [33]). Additionally, calculated STM images for a rigid graphene

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our results by comparing them with previous experimental reports. In this last case the unit supercell was composed of 542 atoms. For these models we performed DFT calculations using the SIESTA ab initio package [38], which employs norm-conserving pseudo-potentials and localized atomic orbitals as the basis set. Double-ζ plus polarization functions were used under the generalized gradient approximation (GGA) for the exchange correlation potential [39]. All structures were fully relaxed until the atomic forces are smaller than 0.05 eV/Å. We have considered super-cells with periodic boundary conditions. The Brillouin zone was sampled employing only the Γ point; however, we checked the convergence of total energy employing a Monkhorst– Pack mesh of 3 × 3 × 1. For both BLG stacking sequences we have performed calculations including van der Waals (vdW) interactions, using the exchange–correlation potential optB88-vdW [40] which has been successfully applied to graphene over Ni(111) [41]. For monolayer graphene we performed two additional calculations: (a) including vdW correction and (b) considering a rigid flat model for the graphene monolayer to elucidate the effects of atoms relaxation on STM image. Theoretical STM images were obtained using the code STM 1.0.1 (included in the SIESTA package). This code uses the wave functions generated by SIESTA on a reference plane and extrapolates the values of these wave functions into the vacuum. For the following results the reference plane is 1 Å above the top carbon atom so that it is sufficiently close to every carbon atom and the charge density is large and well described. As images were generated under the Tersoff–Hamann approximation [42], the states contributing to the tunneling current lay in the energy window [EF − eVbias, EF], with EF being the Fermi energy. Data visualization was possible using the WSxM 5.0 freeware [43], and Gaussian smoothing was applied to obtain the final STM images. Larger unit cells, graphene (12 × 12)/Ru(11 × 11) or graphene (25 × 25)/Ru(23 × 23), have been reported experimentally and theoretically [26,28,33,37]. However, with the aim of reducing the high computational costs required to include vdW corrections and due to the good agreement with experimental data, we have restricted to the graphene (11 × 11)/Ru(10 × 10) unit cell. This super cell has been employed in a previous work [44] to show that vdW interactions reduce by 25% the corrugation of moiré pattern.

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Fig. 1. (Color online) Side view (a) and top view (b) of relaxed atomic positions of monolayer graphene over the Ru(0001) surface. Ru atoms appear in gray, while C atoms are colored according to their height over the Ru surface. (c) Calculated STM image (constant height mode at Vbias = 1.5 V) and its corresponding line profile (inset).

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Height [Å]

Height [Å]

27.45 27.76 27.45 27.45 27.45 27.76 27.76 27.74 27.74 ~30.0 29.7 ± 0.3

1.62 1.41 0.00 1.42 1.43 1.09 1.10 1.09 1.13 1.20–1.50 ~1.00

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Table 2 Calculated corrugation amplitudes (in arbitrary units) for different bias voltages. Results correspond to monolayer and BLG over the Ru(0001) surface, where stacking sequences AB and AA were considered independently.

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monolayer present essentially the same characteristics as those calculated after relaxation. These facts indicate clearly that superstructures have a strong electronic origin.

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3.2.1. Relaxed atomic positions Relaxed configurations of BLG having AB and AA stacking sequences are presented in Fig. 2. For both configurations it is important to note that mounds appear on each graphene layer, although not as

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3.2.2. Calculated STM images Fig. 3 shows calculated STM images (constant height mode) for different bias voltages for BLG over the Ru(0001) surface: stacking sequences AB (left) and AA (right). These images show that both configurations present current maxima (bright regions) located over mounds, and forming a superstructure, the periodicity of which is D = 27.45 Å. Additionally, line profiles performed along the highlighted segments (see corresponding inset) show that current fluctuation cannot be explained exclusively by the relaxed atomic coordinates (see Table 2). Thus, and similar to what occurs for monolayer graphene, it is expectable an increase of tunneling current of ~ 1.9 times by passing from a minimum to a maximum due to relaxed atomic positions (vdW interactions included). However, calculated corrugation amplitudes present larger increases. As Table 2 shows, both stacking sequences of BLG present a bias voltage dependent corrugation. Furthermore, while BLG AA shows an

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remarkably on the top one (see Table 1). Such mounds form a superstructure, the periodicity of which is 27.45 Å. Moreover, depending on the layer position, mounds present similar heights, irrespective of the stacking sequence. Thus, the mound height is ~1.10 Å for the topmost layer, while for the bottom layer this value is ~1.43 Å. Previous results, including monolayer graphene, were obtained under GGA approximation. However as Table 1 shows, calculations including vdW interactions produce mounds with lower heights and larger lattice constants for each system. Thus, although for both stacking sequences the calculated height for bottom mound is ~ 1.10 Å, the calculated height for top mound results 0.90 Å for BLG-AA and 0.82 Å for BLG-AB. Top mound heights calculated here differ from previous theoretical calculations [29]; nevertheless it is necessary to mention that such previous calculations have included vdW interactions from a semi-empirical approach. Our DFT-vdW calculations also indicate that minimum vertical distances between bottom graphene layer and Ru surface increase by 5% in both configurations, while minimum vertical distance between graphene layers reduces by 11% and 13% for BLG AB and BLG AA respectively. Thus, BLG AB presents an interlayer distance of 3.32 Å in agreement with the literature value of 3.3 Å [25,31], while BLG AA presents an interlayer distance of 3.37 Å.

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Fig. 2. (Color online) Relaxed atomic positions of BLG over the Ru(0001) surface. Side and top views of stacking sequence AB are presented in (a) and (b), while the corresponding views for stacking AA appear in (c) and (d).

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atomically resolved honeycomb lattice for different bias voltages, BLG AB presents a lattice which changes from triangular to honeycomb at Vbias ∼ 1.0 V. These results agree with previous theoretical calculations at Vbias ∼ 0.6 V (including vdW interactions from a semi-empirical approach), which shows a triangular lattice for BLG AB and a honeycomb lattice for BLG AA [29]. On the other hand, experimental STM images of BLG over Ru(0001) have shown moiré patterns whose apparent corrugation is related to the atomically resolved lattice: a triangular lattice associated to an apparent corrugation of 1.10 Å, and a honeycomb lattice associated to an apparent corrugation of 0.05 Å [31]. These experimental findings agree qualitatively with our results for Vbias = 0.5 V: calculated corrugation amplitude for AB stacking (triangular lattice) is larger than the corresponding value for AA stacking (honeycomb lattice). Additionally, the same experimental report showed an apparent height of 3.3 ± 0.1 Å and 2.1 ± 0.1 Å between graphene layers in AB and AA stacking sequences respectively. Of course, apparent height for BLG AA is considerably

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Fig. 3. (Color online) Calculated STM images at different bias voltages Vbias for BLG over Ru(0001) surface. Stacking sequence AB (AA) is presented to the left (right). Bright (dark) regions correspond to high (low) tunneling current. Highlighted segments show where line profiles were performed (see corresponding inset).

smaller than the theoretical value calculated here (3.37 Å). However, according to these authors, the apparent height can be significantly different because distinct BLG stacking sequences present different charge transfer to the bottom layer, as indicated by angle-resolved photoemission spectroscopy (ARPES) [31]. Furthermore, Que et al. [37] have reported experimental STM images showing triangular and honeycomb lattices co-existing on moiré patterns of large-area BLG on Ru(0001). As proposed by these authors, such observations can be explained by a continuous variation from AA to AB stacking sequence due to a lattice mismatch between the two graphene layers. Thus, as our results show for Vbias b 1.0 V and according to interpretation of authors of Ref. [37], honeycomb lattices are revealed over AA stacked regions, while triangular lattices are revealed over AB stacked regions. Moreover, according to our theoretical results, corrugation amplitude depends on BLG stacking sequence (see Table 2); hence one can explain the co-existence of two moiré patterns with different periodicities [37].

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This work was partially supported by Universidad de La Frontera, Project DI14-0037 and the Research Office of the Universidad de Medellín through Project No. 684. D.A.K. acknowledges full funding support from Dirección General de Investigación y Postgrado and Programa de Incentivo a la Iniciación Científica (PIIC) of Universidad Técnica Federico Santa María. E.C. thanks financial support from Anillo Project ACT1117. DFT calculations were performed on the supercomputing infrastructure of the NLHPC (ECM-02) at CMCC-UFRO.

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By employing DFT methods we theoretically studied mono- and bilayer graphene over the Ru(0001) surface. These systems were modeled using a large unit supercell composed of 10 × 10 Ru unit cells supporting 11 × 11 graphene unit cells. AB and AA stacking sequences were considered for bilayer graphene applying for each configuration GGA approximation and vdW corrections. For each configuration STM images and line profiles at different bias voltages were calculated as well the PDOS in the energy window − 4.0 eV b E − EF b 4.0 eV. For monolayer graphene we have reproduced the main characteristics revealed experimentally: superstructures in STM images, which also appear for a rigid monolayer graphene model, and corrugation dependence on bias voltage. In this way we showed that STM superstructures can be explained by the mounds induced on the graphene sheet due to their mismatch with the Ru lattice constant and by a strong electronic structure modification. In fact, electronic structure modifications induced by Ru surface were revealed by PDOS calculations. For bilayer graphene (BLG), we calculated STM images which present superstructures. For bias voltages larger than 1.0 V, these calculated STM images look very similar, irrespective of stacking sequence. Nevertheless, for bias voltage lower than 1.0 V, stacking sequences present different corrugation amplitudes, whose values are less than the corresponding value to monolayer graphene over Ru surface. Also for Vbias b 1.0 V, it was found that BLG AA presents an atomically resolved lattice with honeycomb symmetry, while BLG AB presents an atomically resolved lattice with triangular symmetry. These findings are in agreement with experimental data reported previously and allow to explain the experimental observation of atomically resolved lattices with triangular and honeycomb symmetry. Additionally we found that superstructures detected by STM on BLG present also a combined effect: electronic structure modification and mounds induced in upper graphene layer, this time by the mounds of bottom graphene layer. Finally, the calculated PDOS for bilayer graphene appeared fairly similar for each stacking sequence, and it is no possible to conclude whether they conduced to different phases. Nonetheless, it is important to emphasize that small differences between corresponding DOS explain the atomically resolved lattice during STM experiments at low bias voltages (Vbias b 1.0 V).

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3.2.3. Bias voltage dependence and density of states As Fig. 3 shows for BLG AB (left), calculated STM image at Vbias = 0.5 V show dark regions while a triangular lattice appears over the mound. For Vbias = 1.0 V, the surface turns completely visible, although atomically resolved lattice remains triangular. By increasing bias voltage (Vbias ≥ 1.5 V) all carbon atoms belonging to the top graphene layer are revealed (showing a honeycomb lattice), while the mound turns even brighter. Line profiles were performed along highlighted segments on each image, summarizing their corresponding corrugation amplitudes in Table 2. Clearly a bias voltage dependence is also revealed for STM images of BLG. To understand the bias voltage dependence of STM images, projected density of states (PDOS) of graphene layers over the Ru(0001) surface were also obtained. As Fig. 4(a) shows, monolayer graphene electronic structure (blue solid line) is strongly modified by Ru(0001) surface, so that the typical DOS graphene shape is lost. This effect can be explained by graphene atoms nearest to the Ru surface [29]: binding between C and Ru is covalent like, reducing the role of dispersive interaction. As a checkpoint, please note that for the energy range −

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1.5 b E − EF b 1.5 eV [see Fig. 4(b)], our results look similar to those calculated in a previous work for monolayer graphene [29], while the main differences come from distinct considerations of vdW interactions. The strong interaction with Ru surface can also explain the notorious modification on electronic structure of AA and AB stacking sequences of BLG for the energy range − 1.0 eV b E − EF b 0.5 eV. Outside this energy range, interaction between graphene layers dominates, recovering the BLG DOS. Nevertheless, there is also a remarkable contribution of Ru to the STM image formation for bias voltage larger than 0.5 V (E − EF b − 0.5 eV), according Tersoff–Hamann interpretation [42]). See total density of states (DOS) presented in Fig. 4(c) and (d).

It is also interesting to note that calculated STM images present two low tunneling current zones, which appear slightly brighter for the AA stacking sequence (see Fig. 3). This effect is due to a larger local density of states (LDOS) for AA as compared with AB stacking sequence [15]. Additionally, it is important to mention that, distinct to what occurs for monolayer graphene, all carbon atoms are revealed for BLG AA over Ru(0001) surface.

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Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.susc.2014.10.010.

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