Restoring a free-standing character of graphene on Ru(0001)

Realization of a free-standing graphene is always a demanding task. Here we use scanning probe microscopy and spectroscopy to study the crystallographic structure and electronic properties of the uniform free-standing graphene layers obtained by intercalation of oxygen monolayer in the"strongly"bonded graphene/Ru(0001) interface. Spectroscopic data show that such graphene layer is heavily p-doped with the Dirac point located at 552 meV above the Fermi level. Experimental data are understood within DFT and the observed effects are in good agreement with the theoretical data.


INTRODUCTION
The physics and chemistry of graphene (gr) on metals is one of the exciting fields of surface science [1][2][3][4][5]. These extensive studies allowed to understand the main interaction mechanisms at the graphene-metal interfaces and connect them with the changes in the electronic structure of graphene [2,6,7]. Even in the earlier studies of the graphene/metal interfaces the aim was not only to obtain information about interface itself (its geometry, bonding mechanism, its electronic structure), but to try modifying the properties of interface and of graphene. The latter can be realized, e. g., via adsorption of different species on top of the system or via intercalation of different materials between a graphene layer and a metallic substrate [1]. For the intercalationlike systems the most exciting cases include the intercalation of big molecules, like C 60 [8,9], and molecules of gases, like CO [10,11] or oxygen [12][13][14][15]. Initial experiments on oxygen intercalation were performed for the nearly free-standing graphene on Ir(111) (islands or complete layer) [14,15] or for strongly-interacting graphene/Ru(0001) where graphene has an incomplete monolayer coverage that allows using a low partial pressure of oxygen gas [12,13,[16][17][18]. Recently, it was demonstrated that oxygen can be also intercalated under full layer of graphene on Ru(0001) at the partial pressure of oxygen less than 1 mbar and 150 • C [19]. Oxygen intercalation under graphene on Ir(111) or Ru(0001) leads to the electronic decoupling of graphene from substrate with the corresponding p-doping of graphene as was found by X-ray photoelectron spectroscopy (XPS) [14,15,19]. Angle-resolved photoelectron spectroscopy (ARPES) data give for graphene/O/Ir(111) the position of the Dirac point (E D ) at 0.64 eV above the Fermi level (E F ) [14]. For graphene/O/Ru(0001) situation is controversial: the first ARPES experiments with a rather poor energy resolution give a p-doping of graphene in this system with the position of E D at ≈ 0.5 eV above E F [13], whereas the local STM/STS results give this position at 0.48 eV below E F [18], that can be considered as an artefact, because the interpretation of STS data for the graphene/metal systems is not a straightforward task.
In the present work we demonstrate the possibility to form the graphene/O/Ru(0001) intercalation system at the relatively low partial oxygen gas pressure and the elevated temperature for the complete initial graphene coverage on Ru(0001). The formed system of very high quality demonstrate the weak moiré structure as clearly deduced in scanning tunnelling and atomic force microscopy (STM and AFM) experiments. These experiments combined with the respective density functional theory (DFT) results allow to discriminate between geometric and electronic contributions in the microscopy imaging of this system. Our spectroscopy (STS) and DFT results show that a graphene layer in the graphene/O/Ru(0001) system is electronically decoupled from the substrate and demonstrates the p-doping of the graphene-derived π states. Analysis of the electronic structure of graphene, which can be accessed in ARPES experiments, is performed via unfolding of the graphene-related bands to the primitive (1 × 1) Brillouine zone of graphene.

RESULTS AND DISCUSSION
Crystallographic and electronic structures of graphene/Ru(0001) and graphene/O/Ru (0001) were compared in local STM/STS and AFM experiments. Figure 1 shows a large and small scale STM images of a complete graphene layer on Ru(0001). This system was prepared via decomposition of ethylene gas at 1300 K (for details, see Sec. Methods). Such preparation leads to a graphene layer of very high quality with extremely small number of defects, which are mainly Ar atoms buried under interface Ru layer and they are marked by circles in Fig. 1(a). Hight quality of graphene is also confirmed by the atomically resolved STM images of the strongly corrugated graphene/Ru(0001) system where all high-symmetry positions of this system are clearly resolved: ATOP, HCP, and FCC [ Fig. 1(a,b)]. They are marked by the corresponding capital letter in the inset of Fig. 1(a). Graphene covers Ru steps in a carpet fashion demonstrating the mirroring of the ATOP positions on the adjacent monoatomic steps in STM images of graphene/Ru(0001) [Fig. 1(c)]. This effect is assigned to the change of the atom stacking of the hcp Ru(0001) substrate. Relatively strong interaction between graphene and Ru(0001) and the orbital intermixing of the graphene π and Ru 4d states at the graphene/Ru interface makes it very difficult to distinguish separate carbon rings or atoms at step edges. This important fact will be later discussed for the graphene/O/Ru(0001) system where graphene is electronically decoupled from the substrate. in the direct imaging contrast while the highest ATOP places are imaged as bright areas and the low FCC and HCP areas as darker places. Moreover, no image contrast inversion is observed between STM and AFM contrary to graphene/Ir(111) [20,21]. Comparing these combined data with those from Fig. 1 we can see that the imaging contrast and the relative areas for the high-symmetry places in STM depend on the tunnelling conditions (U T and I T ), but in AFM measurements the result is very close to the real geometry of the graphene/Ru(0001) system (relative areas of all places and the graphene corrugation). Strong corrugation of graphene in the present system gives a possibility to obtain clear atomic resolution in AFM only for the ATOP positions with a faint atomic contrast for the HCP and FCC places [ Fig. 2 The oxygen intercalation was performed for the full graphene monolayer on Ru(0001) at 200 • C and a partial pressure of 1.8 × 10 −4 mbar of oxygen measured by the ion-gauge placed in the UHV chamber. Oxygen was introduced via a stainless steel pipe, which end was placed 1 mm from the sample surface that allows to increase the local pressure drastically (approximately by two orders of magnitude). This preparation procedure was initially also verified by the indepen- was also confirmed by the recent micro-LEED (low energy electron diffraction) studies of this system [17].
Similar to gr/Ru(0001) we also employ the combined STM/AFM measurements to the gr/O/Ru (0001) system. This allows to trace the true crystallographic structure of the system via discrimination between electronic and structural contributions in STM and AFM imaging. Figure 4 shows the results of such experiments. Similar to previously shown results for gr/Ru(0001) the scanning mode in Fig. 4(a)   Our values for the E D energy position correlates with previously estimated position from ARPES data (∼ 0.5 eV above E F ) [13]. However, previous dI/dV measurements reports n-doping of graphene in gr/O/Ru(0001) with E D = −0.48 eV [18], that can be considered as an artefact or misinterpretation of the experimental data.
In order to justify our experimental findings we perform analysis of these data within the framework of DFT (for computational details, see Sec. Methods). Figure 6 shows ( between C and Ru of 2.24Å (that corresponds to a minimal interlayer distance between graphene and Ru(0001) of 2.10Å) [ Fig. 6(c)]. The original electronic structure of free-standing graphene is strongly modified after its adsorption on Ru due to the charge transfer from Ru to C and strong orbital overlap of the valence band states of graphene and Ru at the interface [ Fig. 6(e)]. This can be indicated by the formation of the covalent-like bonds at the graphene-Ru interface for the strongly interacting places of the structure. These results are in very good agreement with previous works [30][31][32][33].
According to the previous [13,17] and present findings (Fig. 3)  for the studied systems [ Fig. 7 (a,b)]. For graphene/Ru(0001) one can clearly see the result typical for the strongly interacting system with the formation of several interface states at the K-point of BZ as a result of hybridisation between graphene and valence band states leading to the complete destruction of the Dirac cone. Thus, as it was already postulated in Ref. [6], in spite of the coexistence of the weakly and strongly interacting regions within the graphene/Ru(0001) system, due to the metallic character of graphene in this system, the electronic structure of graphene in its original BZ is defined by the bonding strength and the electronic structure at the most perturbed graphene places. Upon the oxygen intercalation hybridisation between graphene and metal valence band states is absent (see Supplementary material: Fig. S4). The main π (as well as σ ) branches are clearly recognisable in the electronic structure of graphene/0.5 ML-O-(2 × 1)/Ru(0001) [ Fig. 7 (b)] and they almost reproduce the electronic structure of the free-standing graphene (except for a upwards shift due to the graphene doping). It is interesting to note the absence of the gap at the Dirac point that is in good agreement with the model describing the electronic structure of graphene modified by its interaction with a substrate [7].
In order to prove our results we also perform simulations of STM images in the framework of the Tersoff-Hamann formalism [34]. Figure 8 shows constant-current STM images of (a) DFT Calculations. The DFT calculations were carried out using the projector augmented wave (PAW) method [35], a plane wave basis set and the generalized gradient approximation as param-eterized by Perdew et al. [36], as implemented in the VASP program [37]. The plane wave kinetic energy cutoff was set to 400 eV. The long-range van der Waals interactions were accounted for by means of the DFT-D2 approach [38]. The corresponding structures of the graphene-metal based systems are shown in Fig. 6 (a,c) and they are discussed in details in the text. The supercell used to model the graphene-metal interface has a (12 × 12) lateral periodicity with respect to Ru(0001).  (0001)) are allowed to relax.
In the total energy calculations and during the structural relaxations the k-meshes for sampling the supercell Brillouin zone are chosen to be as dense as 6 × 6 and 3 × 3, respectively, and centred at the Γ-point. The STM images are calculated using the Tersoff-Hamann formalism [34]. The band structures calculated for the studied systems were unfolded to the graphene (1 × 1) primitive unit cell according to the procedure described in Refs. [39,40] with the code BandUP [40].

Supplementary material for manuscript:
Restoring a free-standing character of graphene on Ru(0001)