The formation of an energy gap in graphene on ruthenium by controlling the interface

In this work, we have investigated the spectral function of graphene on a monolayer of intercalated gold on Ru(0001) using angle-resolved photoemission spectroscopy (ARPES). The intercalation leads to a decoupling of the graphene film, as documented by emergence of the characteristic linear π-bands near the Fermi level. However, a band gap at the band crossing is observed. We relate this gap opening to the broken symmetry of the two carbon sublattices, induced by the special lattice mismatch of the graphene and the intercalated gold monolayer.

2 carriers [3,4] and the quantum Hall effect observed at room temperature [5], render graphene a promising candidate for future electronic devices [6]. These properties derive from the equivalence of the quasi-particles to massless Dirac fermions and the conical shape of the πand π * -bands that cross only at two points (K and K ) of the Brillouin zone.
The lack of an energy gap near these crossings (at the Dirac energy E D ) limits the potential applications of graphene, and preparing graphene-based systems with a gap is an important step towards future graphene engineering. The simplest mechanism for opening a gap is by breaking the symmetry of the two graphene sublattices that protect this gap [7], for example in armchair nanoribbons [8] and in biased graphene bilayers [9,10], or by breaking the sublattice symmetry by bonding graphene (or bilayer graphene) to a substrate [11].
Epitaxial graphene on SiC(0001) presents an anomalous bandstructure near E D , which has been interpreted as being due to either many-body renormalization (i.e. 'kinking') of the bands caused by electron-plasmon scattering [12]- [18], or to symmetry breaking caused by substrate bonding as outlined above [19,20]. These behaviors are distinguished by the presence or absence of an energy gap, though interpretation of the data has been controversial [21,22]. A gap-like spectrum in disordered graphene has recently been demonstrated [23], so it is important when comparing samples that the number of defects be minimized in order to observe the intrinsic spectral function.
Here, we show that in a single system-graphene grown on the Ru(0001) surface-the behavior of the graphene bands near E D can be selected between two extremes, (i) exhibiting specific many-body kinks and (ii) a situation where a gap appears, by controlling the structure of the graphene-Ru interface. When the first layer below graphene is a graphene-like 'buffer layer', the spectrum is kinked because of many-body interactions, but when this buffer layer is replaced with a layer of Au atoms, the spectrum changes to an unmistakably gapped one. This is the first direct observation of a gap at the Dirac point in a sample without the complications of small domain size or high defect density [21,22].

Experimental details
The angle-resolved photoemission spectroscopy (ARPES) experiments were performed at the Electronic Structure Factory at Beamline 7 of the Advanced Light Source of Lawrence Berkeley National Laboratory by using a photon energy of 95 eV. The photoemission intensity data sets over the energy-momentum space (E, k x , k y ) were collected with a Scienta R4000 energy analyzer with samples on a liquid He-cooled, three-axis goniometer at T = 20 K. The energy/momentum resolutions were 30 meV 0.01 Å −1 . The base pressure during measurements was <7 × 10 −11 mbar.
Graphene on Ru was prepared using the carbon segregation method [24,25]. Sample preparation was performed in an attached chamber with a base pressure of 1 × 10 −10 mbar and then characterized by low-energy electron diffraction (LEED). The (0001) surface of the Ru crystal was cleaned by alternately exposing the sample to oxygen (10 −8 mbar) and ultrahigh vacuum conditions at 1300 • C. The segregation was performed via a slow-cooling process of the Ru crystal from 1000 • C down to room temperature. Depending on the cooling rate, one or two layers of graphene on Ru(0001) could be grown.
Recent studies demonstrate the high quality of such graphene overlayers [24,26]. The initial graphene layer on the Ru(0001) surface exhibits a hexagonal superstructure with a periodicity of 30 Å [31], which was attributed to the lattice mismatch of about 10% between graphene (lattice constant a = 2.46 Å) and the Ru(0001) substrate (a = 2.706 Å) [27]. Ab initio calculations suggest that this mismatch is accommodated by a pronounced rippling, resulting in a position-dependent strength of interaction with the substrate [28,29], but experiments show partially contradictory results [24,26]. The initial graphene layer, while metallic, does not show a clear π -band crossing at E F [30], whereas the subsequent one and two layers show monoand bilayer graphene-like bandstructures [25], respectively. We therefore call the initial layer the buffer layer (in analogy with the situation on SiC(0001)) and subsequent layers the first, second, etc graphene layers.
Gold intercalation under graphene was accomplished by depositing a thick Au film (>3 ML) on top of the buffer layer, followed by light annealing, after which most of the gold evaporates, leaving a single layer intercalated underneath the buffer layer. As can be seen in figure 1, the buffer layer is transformed into a true graphene layer with sharp π-bands and a clear Fermi surface. That the remaining gold is underneath and not on top is obvious from the lack of attenuation of the resulting graphene ARPES signal. The spectral function of the buffer layer is characterized by the absence of well-ordered structure of the graphene π-bands in the vicinity of the Fermi level, in agreement with a previous study [30] that shows that the Dirac energy E D in the buffer layer on Ru is shifted by 2.6 eV 4 to higher binding energies (BEs) compared to those for pure graphite. This can be attributed to the strong interaction between this layer and the ruthenium substrate, leading to a strong hybridization between graphene π and Ru 4d valence band states [28].

Results and discussions
Such interaction leads to the formation of an unusual 'cloudy' structure around the K-point (shown by the dashed line in figure 1(a)) [30]. Although the interpretation of this cloudy feature as an energy band is not straightforward (since it is not predicted by DFT calculations [30]), we can take its general shape to indicate an electron pocket derived from the graphene π-band, but heavily modified by strong interactions of the graphene monolayer on ruthenium, and inhomogeneously broadened due to the spatially varying interaction strength.
The formation of the first graphene monolayer (on top of the buffer layer) on Ru(0001) leads to dramatic changes in the electronic structure of the system. We now observe a linearly dispersing π-band around the K-point that crosses the Fermi level, reflecting the massless behavior of electron carriers in the graphene layer. There is no apparent interaction between the bands in the two layers. The graphene layer, however, is n-doped with the position of the Dirac energy E D at 0.5 eV BE below the Fermi level E F . We conclude that both layers are doped by charge transfer from the substrate, but only the upper layer's bands strongly resemble pure graphene [25].
Previous studies of graphene on Ni(111) [31,32] show that upon intercalation with noble metals, the π -states in graphene recover nearly the same bandstructure as pure graphene, showing the linear dispersion of the π-bands in the vicinity of the Fermi level. This reflects the weakening of the interaction between the graphene layer and the substrate. Figure 1(c) shows the electronic structure as well as a photoemission intensity map at the Fermi level of the 1 ML graphene/Au/Ru(0001) system. Now, the buffer layer is transformed into a true graphene layer with sharp π-bands and a clear Fermi surface. That the remaining gold is underneath and not on top is obvious from the lack of attenuation of the resulting graphene ARPES signal. We estimate, based on core-level intensity measurements (not shown in this paper), that the Au layer thickness is about 1 ML, independent of the pre-deposited Au layer thickness. The same thickness of intercalated gold was obtained for the graphene/Au/Ni(111) system [33]. The spectral function around the -point still reveals weak photoemission intensity from the gold surface state, indicating residual gold islands on top of the graphene system [33].
The intercalation of Au underneath 1 ML of graphene on Ru(0001) leads to an energy shift of the π-band of the graphene layer to lower BEs compared to both single-layer and bilayer graphene on Ru(0001). This demonstrates the weakness of the interaction between the single graphene layer and the gold layer. The Fermi surface appears to be pointlike in figure 1(c); however, a close look at the dispersion of the π-states around the Fermi level (figure 2 (left side, lower panel)) reveals that the Dirac point is ∼150 meV above E F , consistent with a small p-doping of the graphene layer in the 1 ML graphene/Au/Ru(0001) system. A similar p-doping of graphene was recently observed in the case of deposition and annealing of a thin gold layer on the graphene monolayer on SiC(0001) [34].
In order to study the shape of the bands around E D , it is necessary to push the band crossing below the Fermi level by n-type doping. This was done by controlled deposition of potassium atoms on top of the 1 ML graphene/Au/Ru(0001) system [10], upon which the π-band and the Dirac point shift rigidly to higher BEs with increasing K dosage. Surprisingly, with increasing doping a clear energy gap for π-states becomes visible at E D (figure 2). Comparison of graphene layers on ruthenium bandstructures recorded at high energy and angular momentum resolution as a function of the interface composition is shown in figure 3. π * -bands, the K-point spectrum (and hence the Dirac crossing energies E D ) can be unambiguously determined. For the graphene/buffer layer system (figure 3(a)), we find that, within the limits of our experimental resolution, which account for 30 meV, the bandstructure at K exhibits no gap. Instead, it exhibits the appearance of a weak kink around E D , consistent with the influence of electron-plasmon coupling as reported for graphene on SiC [12,35] and predicted for free-standing graphene [15,16,18]. The energy distribution curve (EDC) at the K-point (see the right panel of figure 3(a)) can be represented by a single Voigt peak with a full-width at half-maximum (FWHM) of 100 meV. By contrast, n-doped graphene on Au on Ru shows the clear formation of an energy gap at E D ; an analysis of the EDC at the K-point shows that it requires two peaks (of FWHM 100 meV) to model the data, demonstrating that the bandstructure of this graphene layer exhibits a gap of about 200 ± 60 meV. Since we acquired the spectra in figure 3 by a fine sampling of the entire two-dimensional momentum range, we can be sure that the presented bandstructure cuts passed precisely through the K-points and therefore the observed gaps cannot be due to sample misalignment. A mechanism of gap opening at the K-point due to hybridization with gold states can be excluded, since there are no gold states near E D . Moreover, a gap opening due to the For both systems the photoemission intensity along the K-point is plotted and fitted with one Voigt peak for the buffer + first and with two Voigt peaks for the Au + first graphene layers on Ru(0001).
formation of a superstructure, as reported by Pivetta et al [36], can be excluded, since such a superstructure can easily be determined in our data sets via a sudden change in the bandstructure. Our measurements begin to show such a phase transition with higher potassium coverage. Finally, the band gap does not increase with higher potassium coverage, proving that the potassium is not the reason for the gap opening. Thus, we propose that the band gap in the 1 ML graphene/Au/Ru(0001) system results from a symmetry breaking of the two carbon sublattices in the graphene layer, which results in a weak breaking of the chiral symmetry, inducing a weak but finite intensity of the left band along the -K direction, between the two arrows in figure 3(b) [13,37,38]. The ratio of the left to right band intensities in figure 3(b) is about 35, which agrees with theoretical predictions for the size of a gap of 200 meV [13]. Within our statistics, there is no equivalent observable intensity for the graphene/buffer layer/Ru system (between the arrows in figure 3(a)), consistent with the lack of a gap at E D .

7
The appearance of the gap in gold-intercalated graphene is surprising. Calculations [11] indicate a weak bond between noble metals and graphene without a notable gap. While a detailed explanation of why gold intercalation opens a gap will depend on the exact microscopic structure of the interface, which is outside the scope of the present work, we can speculate that the incommensuration between graphene and Au lattice constants (2.46 and 2.81, respectively), neglected in the calculations [11], plays a role. Depending on the exact length scales, the K and K points of the graphene can be coupled, amounting to a breaking of the sublattice symmetry in real space that protects the Dirac point from opening a gap. But on the other hand, the strength of the photoemission satellite bands is greatly reduced for interfacial Au compared to the buffer layer, consistent with a related weak potential associated with the Au incommensuration. Therefore, we also see that the band gap results from a symmetry breaking of the two sublattices and is induced by the gold layer; a consistent explanation for the appearance of the gap in the Au case remains elusive. Local probes could help us to solve this issue.
Our results show that intercalation of gold under graphene can be a useful technique to restore graphene's unique properties when its bonding to a substrate strongly modifies its electronic properties. These changes can range from the modest, such as changing the natural doping of the graphene-substrate system, to the more drastic, as in the case where the unique properties of the graphene are lost due to strong substrate hybridization, as with the buffer layer on Ru(0001). Here no symmetry breaking can be observed, consistent with the fact that the buffer layer has the structure of graphene, but the strong bonding to the substrate kills the conical bands [24]. This is a particularly important consideration for the interface between graphene and contacts, either electronic or magnetic.
In conclusion, the electronic structure modification of a single graphene layer on Ru(0001) upon gold intercalation was studied by means of angle-resolved photoelectron spectroscopy. The spectral functions of the bilayer graphene film on Ru(0001) is characterized by the absence of any energy gap in the electronic structure. Surprisingly, the energy gap for the π-states is found after intercalation of Au monolayer underneath graphene monolayer on Ru. The appearance of such a gap in the electronic structure is assigned to the fact that the symmetry for two carbon sublattices is broken in the graphene/Au/Ru(0001) system due to the geometry of the system.