Electronic structure, imaging contrast and chemical reactivity of graphene moir\'e on metals

Realization of graphene moir\'e superstructures on the surface of 4d and 5d transition metals offers templates with periodically modulated electron density, which is responsible for a number of fascinating effects, including the formation of quantum dots and the site selective adsorption of organic molecules or metal clusters on graphene. Here, applying the combination of scanning probe microscopy/spectroscopy and the density functional theory calculations, we gain a profound insight into the electronic and topographic contributions to the imaging contrast of the epitaxial graphene/Ir(111) system. We show directly that in STM imaging the electronic contribution is prevailing compared to the topographic one. In the force microscopy and spectroscopy experiments we observe a variation of the interaction strength between the tip and high-symmetry places within the graphene moir\'e supercell, which determine the adsorption cites for molecules or metal clusters on graphene/Ir(111).

Graphene layers on metal surfaces have been attracting the attention of scientists since several decades, starting from middle of the 60s, when the catalytic properties of the closepacked surfaces of transition metals were in the focus of the surface science research [1][2][3][4].
The demonstration of the fascinating electronic properties of the free-standing graphene [5,6], renewed the interest in the graphene/metal systems, which are considered as the main and the most perspective way for the large-scale preparation of high-quality graphene layers with controllable properties [7][8][9][10]. For this purpose single-crystalline as well as polycrystalline substrates of 3d − 5d metals can be used.
One of the particularly exciting questions concerning the graphene/metal interface is the origin of the bonding mechanism in such systems [2][3][4]11]. This graphene-metal puzzle is valid for both cases: graphene adsorption on metallic surfaces as well as for the opposite situation of the metal deposition on the free-standing or substrate-supported graphene. In the latter case the close-packed surfaces of 4d and 5d metals are often used as substrates [12,13].
A graphene layer prepared on such surfaces, i. e. Ru(0001) [14][15][16], Rh(111) [13,17,18], Ir(111) [19,20], or Pt(111) [21,22], forms so-called moiré structures due to the relatively large lattice mismatch between graphene and metal substrates. As a consequence of the lattice mismatch the interaction strength between graphene and the metallic substrate is spatially modulated leading to the spatially periodic electronic structure. Such lateral graphene superlattices are known to exhibit selective absorption for organic molecules [23] or metal clusters [24]. Especially, the adsorption of different metals -Ir, Ru, Au, or Pt -on graphene/Ir(111) has been intensively studied showing a preferential nucleation around the so-called F CC or HCP high-symmetry positions within the moiré unit cell [12,25]. In the subsequent works [25,26] this site-selective adsorption was explained via local sp 2 to sp 3 rehybridization of carbon atoms with the bond formation between graphene and the cluster.
However, a fully consistent description of the local electronic structure of graphene/Ir(111), the observed imaging contrast in scanning probe experiments and the bonding mechanism of molecules or clusters on it is still lacking, motivating the present research.
Here we present the systematic studies of the graphene/Ir(111) system by means of density functional theory (DFT) calculations and scanning tunnelling and atomic force microscopy (STM and AFM) performed in constant current / constant frequency shift (CC / CFS) and constant height (CH) modes. The obtained results for the graphene/Ir(111) system allow to separate the topographic and electronic contributions in the imaging contrast in 2 STM and AFM as well as to shed light on the spatially modulated interaction between graphene/Ir(111) and the metallic STM/AFM tip, which is of paramount importance for the understanding of absorption of metals on top of graphene/Ir(111) as well as of similar graphene-metal systems.

Results
The unit cell of graphene on Ir(111) is shown in Fig. 1(a) with the corresponding highsymmetry local arrangements of carbon atoms above Ir layers marked in the figure: AT OP (circles), F CC (squares), HCP (down-triangles), and BRIDGE (stars). The DFT-D2 optimized local distances between graphene and Ir(111) are 3.27Å (HCP ), 3.28Å (F CC), 3.315Å (BRIDGE), 3.58Å (AT OP ). This result is very close to the recently published equilibrium structure for this system [20]. The similar distances for HCP , F CC, and BRIDGE positions can be related to the fact that in all these cases one of the carbon atoms in the graphene unit cell is placed above Ir(S) atom defining the local interaction strength for the particular high-symmetry position. The obtained distances are very close to those between carbon layers in pure graphite and this was explained by a binding interaction dominated by van der Waals effects between graphene and Ir(111) that is modulated by weak bonding interactions at the F CC and HCP places and anti-bonding chemical interaction around AT OP positions [20]. As a result a small charge transfer from the graphene π states on Ir empty valence band states is detected in calculations and the Dirac point is shifted by ≈ 100 meV above the Fermi level (E F ) that is close to the data obtained by photoelectron spectroscopy [34] [see Fig. 2(c) and discussion below].
The graphene/Ir(111) system is a nice example of the moiré structure, which is easily recognisable in LEED and on the large scale STM images shown in Fig. 1(b). The extracted lattice parameter of this structure from LEED and STM is 25.5Å and 25.2Å, respectively, that is in good agreement with previously published data [33]. In most cases, for the typical bias voltages used in STM imaging, the graphene/Ir(111) structure is imaged in the so-called inverted contrast [ Fig. 1(c,d)] [33], when topographically highest AT OP places are imaged as dark and topographically lowest F CC and HCP as bright regions. This assignment was initially done in Ref. [33], where the STM topography of neighbouring regions of the clean and graphene-covered Ir(111) surface were imaged. In our studies we perform the "on-the-fly" switching between CC STM and CFS AFM imaging during scanning [ Fig. 1 where we observe the inversion of the topographic contrast z(x, y) (see also Fig. S1 of the supplementary material [35]). This becomes clearly evident around areas marked by arrows in Fig. 1(d) where the darkest contrast in CC STM becomes the brightest one in CFS AFM for the AT OP position. In the latter case the darkest areas correspond to HCP sites that correlates with the calculated height changes between lowest and highest carbon positions.
The pronounced difference between the F CC and HCP areas can be explained by fact that additional bias voltage was applied in order to increase the atomically-resolved contrast.
The inversion of the imaging contrast was also detected in CC STM images when the bias voltage is changed from −0.5 V to −1.8 V during scanning [ Fig. 2 In order to prove this assertion we have performed the force microscopy and spectroscopy experiments on graphene/Ir(111). Fig. 3 shows (a,b) the frequency shift of an oscillating scanning sensor as a function of a distance from the sample, ∆f (d), and (c) the corresponding tunnelling current, I(d), measured in the unit cell of graphene/Ir(111) along the path marked in the CC STM image shown as an inset of (a). During these measurements the tunnelling current was used for the stabilisation of the feedback loop, allowing to determine the relative z-position of the ∆f and I curves. Following the sequence:  Fig. 4). Taking into account that during CH imaging at +50 meV in Fig. 4 the imaging contrast for I(x, y) is inverted due to the higher DOS for the F CC and HCP positions and that variation of the distance for CH imaging and CC STM imaging (when U T is changed from −0.5 V to −1.8 V) is nearly the same, one can separate the topographic and electronic contributions into imaging at different biases and distances.
Here we would also like to note that the change of the bias voltage during CH AFM imaging does not lead to any changes in the imaging contrast for ∆f (Fig. 5). The first row shows the two small-scanning range atomically resolved ∆f (x, y) images acquired on the same place of the graphene/Ir(111) sample with opposite signs for the bias voltage: the imaging contrast is the same with the slight variation of the imaging scale that can be explained by the small drift of the oscillating tip. The first look on the I(x, y) map (lower row) might give an impression that the contrast is fully inverted. However, the absolute value of the tunnelling current is the same and only more negative values of the tunnelling current are shown as darker areas in the image for current.

Discussion
The graphene/Ir(111) system was studied with DFT methods in oder to deeply understand the effects of the electronic structure on the adsorption properties of this system. Here we present the comparison between experimental and theoretical STM data. The STM images are calculated using the Tersoff-Hamann formalism [36], in its most basic formulation, approximating the STM tip by an infinitely small point source [18,37,38]. In these simulations the constant current condition was fulfilled that leads to the increasing of the distance between the sample and a tip from 2.50Å for U T = −0.5 V to 3.21Å for U T = −1.8 V  Fig. 2(c)] explain the fact that these places become brighter for higher bias voltages in experimental and simulated CC STM images [ Fig. 2(a,b)].
The calculated LDOS for graphene/Ir(111) compared with DOS for the free-standing graphene [(10 × 10) unit cell] is shown in Fig. 2(c)  to note, that one can also consider the increased LDOS around E F for F CC, HCP , and BRIDGE positions as a hint indicating that these places can be a nucleation centers for adsorbed atoms.
In oder to get better insight in the results obtained during AFM experiments we performed simulations of these data in the framework of DFT formalism (we would like to note that a qualitative description of the buckled graphene systems was performed in Ref. [39], where the model Lennard-Jones potential was used to model tip-sample interaction). Due to the large size of the unit cell of the graphene/Ir(111) system we selected two approaches. In the first one, which requires less computational resources, the tip-sample force is expressed as a function of the potential V ts (r) on the tip due to the sample: However, this method does not take into account the geometrical and electronic structure of the scanning tip and thereby does not allow to get absolute values for the force or frequency shift and the correct distance between the tip and the sample, and only qualitative result for the attractive region of the interaction can be obtained. The result of such simulations for graphene/Ir(111) is shown in Fig. 6(a), which is in rather good agreement with experimental data: the regions around AT OP positions are imaged as dark compared to other high-symmetry cites imaged as brighter contrast. Unfortunately, the information about repulsive region of the forces can not be obtained from such calculations. However, if the model corrugation-dependent repulsive potential is added, then the resulting simulated ∆f 7 curve reproduces qualitatively the experimentally obtained results.
For the purpose to reproduce our data in a more quantitative way, the interaction between the tip and the graphene/Ir(111) system was simulated within the second approach, where W-tip is approximated by the 5-atom pyramid as shown in Fig. 6(b). The results of these calculations are compiled in Fig. 6(c-e). The interaction energy (system was rigid without allowing to relax) between model W-tip and the surface was calculated for two limiting places of graphene/Ir(111), AT OP and F CC. The calculated points are shown by filled rectangles and circles in Fig. 6(c) for the F CC and AT OP positions, respectively. The Morse potential was used to fit the calculated data as the most suitable for the graphenemetal systems [41,42] Fig. 1(a) was used in DFT calculations, which were carried out using the projector augmented plane wave method [27], a plane wave basis set with a maximum kinetic energy of 400 eV and the PBE exchange-correlation potential [28], as implemented in the VASP program [29]. The long-range van der Waals interactions were accounted for by means of a semiempirical DFT-D2 approach proposed by Grimme [30]. The studied system is modelled using supercell, which has a (9 × 9) lateral periodicity and contains one layer of (10 × 10) graphene on a four-layer slab of metal atoms. Metallic slab replicas are separated by ca. 20Å in the surface normal direction. To avoid interactions between periodic images of the slab, a dipole correction is applied [31]. The surface Brillouin zone is sampled with a (3 × 3 × 1) k-point mesh centered the Γ point. In such experiments I T (x, y) and ∆f (x, y) are measured for different z-coordinates. The 9 STM/AFM images were collected with Aarhus SPM 150 equipped with KolibriSensor TM from SPECS [18,32] with Nanonis Control system. In all measurements the sharp Wtip was used which was cleaned in situ via Ar + -sputtering. In presented STM images the tunnelling bias voltage, U T , is referenced to the sample and the tunnelling current, I T , is collected by the tip, which is virtually grounded. During the AFM measurements the sensor was oscillating with the resonance frequency of f 0 = 999161 Hz and the quality factor of Q = 45249. The oscillation amplitude was set to A = 100 pm or A = 300 pm.
Preparation of graphene/Ir(111). The graphene/Ir(111) system was prepared in ultrahigh vacuum station for STM/AFM studies according to the recipe described in details in Ref. [33]