INTRODUCTION

Currently graphene continues to attract significant research interest due to its great potential for practical application in electronics and spintronics [1–4] due to the linear dispersion of electronic π states near the \({{\bar {\text{K}}}}\)‑point of the Brillouin zone (BZ), the so-called Dirac cone [5, 6]. This feature is responsible for a number of unique phenomena, for example, non-dissipative electronic transport [5]. Furthermore, modification of the graphene Dirac cone structure is of fundamental importance paving the way towards advanced applications of this material in novel electronic devices, such as graphene spin filters and field-effect transistors [7–10]. Specifically, tuning the gap at the Dirac point is required for graphene transistor, while spin-orbit and/or exchange splitting of the π states is needed for utilizing graphene as an active element in spintronic devices. Thus, the functionalization of graphene via contact with different substrates and adsorbed and/or intercalated atoms is widely used to tune its electronic properties on demand [3, 11–16].

Interaction of graphene π states with d states of a metal substrate leads to a strong modification of the band structure. In a series of experimental works with Ni(111) and Co(0001) [3, 17, 18], the authors demonstrate that graphene–metal interfaces enable observation of the induced exchange spin polarization of the graphene π states. Intercalation of Au atoms under graphene leads to an anomalously large induced spin-orbit splitting of the graphene π states due to hybridization with Au d states [19]. One of the most intriguing substrates is Pt(111), where graphene states hybridize with platinum d states near the Fermi level [11, 20, 21]. Platinum \(5d\) states are strongly spin-polarized, resulting in topologically non-trivial spin texture of the Dirac cone of graphene [20]. On the downside is that the Dirac point in Gr/Pt(111) is located above the Fermi level, thus the peculiar topological phase has not yet been revealed experimentally.

On the other hand, adsorption of alkali metals (AM) can overcome this problem by producing charge transfer from AM atom to graphene layer, which leads to n-doping of the graphene π states [22–26]. Adsorption and intercalation of Na on graphene-supported on Ni, Ir and Au/Ni substrates were shown to substantially increase the Dirac cone binding energy [22, 24, 27]. Furthermore, introduced charge doping can increase the chemical reactivity, open a gap at the Dirac point [22, 27, 28] and even induce many-body effects, such as electron-phonon coupling, that result in superconducting graphene [29–31].

Finally, one of the most exciting “sandwich” structures are graphene-supported thin metal layers [32–36]. Two dimensional metal/graphene structures exhibit an increased strength and fatigue limit as compared to graphene-unsupported metal films [34, 37], thus improving the functionality of thin-film metal structures for their use in flexible electronic devices [33, 38].

In this work, we study experimentally and theoretically the electronic and spin structure of graphene on Pt(111) substrate after Na adsorption. We probe the electronic structure of the initial and Na-adsorbed systems by means of angle-resolved photoelectron spectroscopy (ARPES) [39]. We complement our experimental results by theoretical insights from the density functional theory (DFT) calculations which facilitate our interpretation of the atomic and electronic structure of the synthesized systems and the effect of Na adsorption.

METHODS

Synthesis and photoemission experiments were carried out in situ under ultrahigh vacuum conditions at the BUS and RGBL-2 beamline of the BESSY II synchrotron radiation facility (HZB Berlin).

A clean Pt(111) single crystal was prepared by repeated cycles of Ar sputtering and annealing at 1300 K. The sample order and cleanliness of the surface were verified by low energy electron diffraction (LEED) and X-ray photoemission spectroscopy (XPS). The graphene monolayer was synthesized on the Pt(111) surface using chemical vapor deposition (CVD) method by propylene (\({{{\text{C}}}_{{\text{3}}}}{{{\text{H}}}_{{\text{6}}}}\)) cracking during 60 min at a pressure of 1 × 10–7 mbar and at the sample temperature of 1200 K.

To form the Na/Gr/Pt(111) system, Na atoms were deposited at room temperature (RT) onto the Gr/Pt(111) sample in ultrahigh vacuum conditions at  a pressure of 3.4 × 10–9 mbar and a rate of ~0.4 ML/min where 1 ML is taken as the graphene monolayer. Note, the thickness of graphene is taken to be 3.4 Å as the distance between the layers of graphite [40]. Sodium atoms were evaporated from the commercial getter onto graphene. The deposition rate of sodium was controlled using quartz microbalance. The quality of the synthesized structure was checked by means of LEED and XPS.

DFT calculations of the electronic structure were performed at the Computing Center of SPbU Research park using the pseudopotential method with localized pseudoatomic orbital basis as implemented in the OpenMX software package [41, 42]. The basis set used in our work contained five basis functions \((s2p2d1)\) for C atoms, six \((s3p2d1)\) for Na atoms and eight basis functions \((s3p2d2f1)\) for Pt atoms, which was sufficient for an accurate description of the electronic structure. To describe the exchange-correlation energy, the local spin density approximation (LSDA) [43] was applied. A reciprocal space grid 6 × 6 × 1 was used to sample the BZ of the unit cell in the self-consistent field (SCF) procedure. Unfolding of the band structures from the calculated supercell to the graphene primitive BZ cell was performed according to [44]. The models of calculated Gr/Pt(111) and Na/Gr/Pt(111) slab systems were produced by VESTA software [45]. The interfaces were modeled by periodic slabs consisting of seven Pt atomic layers covered by a rotated graphene monolayer, such that the resulting system on both sides could be described as \({\text{Gr}}(\sqrt 3 \times \sqrt 3 )R30^\circ {\text{/Pt}}(111)\) reconstruction and a vacuum region, which extends over 12 Å. The atomic positions in each unit cell were optimized within the scalar relativistic approximation until the forces on each atom were less than 1 mRy/bohr (3 × 10–2 eV/Å).

RESULTS AND DISCUSSION

To study the dispersion relations of graphene at various stages of the system formation, we measured ARPES spectra of the graphene π states in the \(\bar {\Gamma }{{\bar {\text{K}}}}\) direction at an incident photon energy of 120 eV (see Figs. 1a–1d).

Fig. 1.
figure 1

(Color online) The ARPES spectra of graphene π states in the \(\bar {\Gamma }{{\bar {\text{K}}}}\) direction of graphene BZ: the Gr/Pt(111) system before (a) and after (b) sodium atoms deposition (2.6 ML) at RT. The white and black dashed lines indicate the π-states arising from 0° and 30° rotational domains of graphene. Panels (c) and (d) show the corresponding dispersion maps after taking the second derivatives of intensity with respect to energy; the overlayed red lines are the calculated and unfolded carbon bands in the \(\bar {\Gamma }{{\bar {\text{K}}}}\) direction. (e) The model of the atomic structure of the calculated \({\text{Gr}}(\sqrt 3 \times \sqrt 3 )R30^\circ {\text{/Pt}}(111)\) system with ABC stacking order. Panel (f) demonstrates the calculation of sodium (green), carbon (red) and Pt (black) states near the \({{\bar {\text{K}}}}\)-point. Panel (g) shows the ball-and-stick models of several investigated adsorption configurations for low (long top, long hollow, long bridge) and high (short bridge) concentrations of Na. Hereinafter, the unit cell drawings are produced by VESTA software [45].

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Before discussing the ARPES images it should be noted that the domain structure of the system strongly depends on the synthesis parameters. According to previous publications [11, 20, 46] it is well-known that CVD-synthesized graphene on a Pt(111) substrate at a temperature of 1200 K often gives two domain structures (with 0° and 30° rotational domains relative to the underlying Pt(111) substrate). These two configurations are discernible by LEED and the corresponding images are shown in our previous works [11, 20]. Additional rotated domains with the angles close to the mentioned values sometimes may form; they can be clearly seen in the LEED patterns also presented in [11, 20]. The reflexes from 30° rotational graphene domains exhibit the \((\sqrt 3 \times \sqrt 3 )R30^\circ \) superstructure relative to Pt(111). Figures 1a and 1b shows 0° and 30° rotational domains by dashed lines.

The angle-resolved photoemission spectra of the pristine Gr/Pt(111) system in Fig. 1a,c exhibit a Dirac cone, which is formed by the π states corresponding to the domain rotated by 30°. The Dirac point is shifted by 0.35 eV above the Fermi level at \({{k}_{x}} = 1.7\) Å–1 corresponds to p-type doping of graphene due to the charge transfer from graphene to Pt atoms. As we noted above, there are other branches of the π states that correspond to 0°-rotated graphene domains which manifest themselves as additional weak branches (dashed lines) with maximum binding energies of approximately 2.4 eV at \({{k}_{x}} = 1.3\) Å–1. We focus on the 30°‑rotated domains in this work since they prevail on the surface of the sample. The Pt \(5d\) states can also be seen in Figs. 1a, 1c in the binding energy region of 0‒2 eV; they also cross the \(\pi \) states of graphene slightly below the Fermi level. In the second derivative image (panel (c)), one can see the avoided-crossing effects at the intersections of Pt bands and the graphene states, which were studied previously [11, 20] and which lead to spin polarization of the graphene Dirac cone [20].

In order to study the influence of Na atoms on the electronic structure of graphene/Pt(111), we provided sodium deposition on top of graphene in situ at RT and measured the ARPES spectra under these conditions. The Na concentration was increased until no changes were observed in the ARPES spectra (2.6 ML). As expected, the deposition of Na leads to a shift of the Dirac point towards higher binding energies up to 1.2 eV at \({{k}_{x}} = 1.7\) Å–1, which points to the charge transfer from Na to carbon atoms and consequently to n-doping of graphene (Figs. 1b, 1d). Moreover, it is seen that the lower and upper parts of the Dirac cone do not touch each other, thus forming a gap-like feature at the Dirac point. The previous work on Na adsorption onto graphene [22] also confirms such a large Dirac point shift which makes both π and π* states observable simultaneously, hence, the Dirac point gap can be identified. For example, in the [24], the charge transfer from intercalated Na to graphene induces a shift of the Dirac point to 1.3 eV below the Fermi level. In earlier works [22, 47] it was shown that the Dirac point gap may be induced by Na atoms because of the sublattice symmetry breaking, non-uniform charge distribution or many-body effects.

In the investigated Na/Gr/Pt(111) system it can be seen that graphene–Pt \(5d\) hybridization effects differ from those of the pristine Gr/Pt(111) system. The intersections of the graphene π and Pt \(5d\) states are located in the energy region of 0.5–1.5 eV that includes the energy position of the Dirac point. Avoided-crossing effects result in local breakages of the graphene π state dispersion, so the Dirac point gap may be of hybridization origin. It should be noted that we exclude the possibility of intercalation of Na atoms under graphene due to the absence in this case of visible hybridization of the graphene π states with the platinum d-states, which we clearly observe in the ARPES data. A detailed discussion of this issue is presented in Supplementary material.

In order to study the changes of the electronic structure theoretically we carried out DFT calculations, and as a first step we found out which Na adsorption sites are stable. Figure 1e illustrates the arrangement of Pt atoms with ABC stacking order and the graphene layer on top of Pt in the model unit cell \({\text{Gr}}(\sqrt 3 \times \sqrt 3 )R30^\circ {\text{/Pt}}(111)\) cell. All analyzed positions for different concentrations of Na are summarized in Table 1 with their adsorption energies and resulting Dirac point positions. Figure 1g contains the corresponding images of Na atomic positions relative to graphene and platinum, where the latter is resolved into distinct layers.

Table 1. Analyzed Na atomic positions for sparse and dense concentrations are labeled as long and short respectively, with their adsorption energy per adsorbed atom and the Dirac point binding energies as well as Na concentrations with respect to graphene monolayer in the corresponding unit cells
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Among the low concentrations configurations, the long top position is the most stable with respect to the adsorption energy; the long bridge position turned out to be slightly less stable. The values of adsorption energies in these positions (–0.65 and –0.56 eV, respectively) are in good agreement with calculations of optimized structures of Na-adsorbed graphene reported in [48]. However, the Dirac point binding energies for these two positions (0.67 and 0.70 eV, respectively) do not agree with the experimental value of 1.2 eV obtained here. The long hollow position has the adsorption energy of –0.06 eV and is highly unstable with respect to the other two long positions.

If the concentration of Na is larger, the short bridge sodium position is the most favorable to form a dense Na monolayer in case of additional Na deposition on top of the filled low-concentration lattice. The corresponding Dirac point position agrees almost perfectly with its estimated value of 1.2 eV extracted from the experimental data. The slight energy disadvantage of the short top adsorption and huge energy disadvantage of the short hollow positions render the short bridge lattice the only one that may form under prolonged Na deposition.

Despite the fact that the long top configuration is the most energetically favorable one, the doping value in the experiment indicates the formation of the dense short bridge structure. Thus, the Na layer possesses the graphene lattice constant due to its supporting role. This growth process of the Na monolayer is also confirmed by the ARPES data in the Supplementary material (Fig. S2). The estimation based on the XPS data shows that a sodium overlayer of 1.6 Å thickness was adsorbed on the Gr/Pt surface, which corresponds exactly to a dense sodium monolayer (details are provided in the Supplementary material). In accordance with our model of the Na/Gr/Pt system, we obtained the calculated unfolded graphene band structure, shown in Fig. 1d by red markers. Graphene bands of the pristine system are shown in Fig. 1c. Additionally, Fig. 1f shows the calculated bands of graphene and Pt for the system after Na deposition, where the avoided-crossing effects can be seen in more detail.

The ARPES band maps of the Na/Gr/Pt(111) system after Na adsorption in the direction orthogonal to \(\bar {\Gamma }{{\bar {\text{K}}}}\) are shown in Fig. 2a, where Pt \(5d\) states and the graphene Dirac cone can be observed. In Fig. 2a the lower part of the Dirac cone is seen, but at higher binding energies, the strong hybridization with Pt states results in a complicated picture. One can resolve π* state dispersing from the Fermi level to ~0.9 eV; note the absence of the visible intersection of the upper and the lower parts of the cone, so there may be a Dirac gap in the range 0.9–1.6 eV. The hypothetical non-disturbed Dirac cone is marked by the red dashed lines. Two new branches with less intensity appear inside the region enclosed by the π* branches just below the Fermi level, see Figs. 2a, 2b (new branches are marked with green dashed lines). Two weak peaks related to graphene Dirac cone (2) and new Na-related (1) branches can be seen in the energy distribution curves (EDC) spectrum in Fig. 2c taken along the momentum cut indicated in Fig. 2b by the dashed line. To explain this experimental feature of the Na/Gr/Pt(111) electronic structure, we show the calculation results in Fig. 2d overlayed onto the dispersion map of this system after taking second derivative of intensity with respect to energy. Here red markers correspond to unfolded graphene states and green markers correspond to folded sodium states which resemble the Kanji symbol. These folded states contain two almost linear branches and a third parabolic branch, all three intersecting at a single point centered at \({{\bar {\text{K}}}}\).

Fig. 2.
figure 2

(Color online) (a) Experimental ARPES dispersion maps of Gr/Pt(111) electronic states after Na deposition (2.6 ML). The red dashed lines are a schematic representation of the graphene Dirac cone and the green dashed lines are that of sodium states. Panel (b) presents the expanded region of the dispersion map from (a). Panel (c) shows the energy distribution curves (EDC) for the \({{k}_{y}}\) momentum value along the cut indicated in (b). In panel (c) two peaks with numbers (1) and (2) indicate states related to graphene Dirac cone and new Na-related branches, respectively. Panel (d) shows the dispersion map from (a) after taking second derivative of intensity with respect to energy with superimposed unfolded carbon (red) and Kanji symbol-like (2 × 2) folded sodium (green) calculated bands for short bridge configuration. All dispersion maps are taken along the direction orthogonal to \(\bar {\Gamma }{{\bar {\text{K}}}}\).

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The unfolding procedure mentioned in [44] is used to investigate the effects of small perturbations imposed on some superstructure. In our calculations, the two-dimensional sodium layer lattice is exactly commensurate to the graphene lattice and it is possible to define the 1 × 1 Na unit cell whose primitive vectors are the same as those of graphene shown in Fig. 3c. The mutual arrangement of the graphene and Pt(111) BZs is shown in Fig. 3d. However, if the unfolding procedure for Na is executed using that 1 × 1 cell, the resulting band structure depicted in Fig. 3a differs severely from its folded counterpart in Fig. 3b. This difference is only qualitative; the folded band structure is consistent with the experimental ARPES data showing the presence of additional features around the Fermi level, whereas the unfolded band structure is not.

Fig. 3.
figure 3

(Color online) DFT calculated unfolded to 1 × 1 (a) and (2 × 2) folded (b) bands of Na for the direction orthogonal to \(\bar {\Gamma }{{\bar {\text{K}}}}\). (c) Top view of the mutual atomic arrangement in 2 × 2 supercell of graphene. (d) The mutual arrangement of the graphene (red), Pt(111) (blue) and the Na(2 × 2)/Gr/Pt (black) BZs.

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Therefore, such difference indicates that the perturbation of the Na layer induced by the Gr/Pt(111) substrate is significant. Careful inspection of the crystal cell used in the calculations reveals that all sodium positions in the short bridge arrangement in Fig. 1g are perfectly equivalent with respect to graphene atoms, but only two of four sodium atoms are in equivalent positions with respect to the first Pt layer, whereas the other two are not (the platinum atoms appear shifted sideways from these sodium atoms). This points to some sort of strong interaction between Na and Pt that is mediated by the graphene layer in-between.

Another indication of such interaction is the charge transfer taking place between Na and Pt atoms, which is described in Table 2. One can see that in the Gr/Pt(111) system, carbon atoms and Pt bulk (2nd‒6th layers) atoms lose some electrons to the first Pt layer, which can be attributed to an expected interaction between graphene and platinum. The Na/Gr/Pt(111) system, however, is different: the first Pt layer pulls even more charge density, and that excess density comes exclusively from Na atoms since graphene and Pt bulk only accept electrons (the charge differences relative to non-deposited system are \( + 0.17e\) and \( + 0.02e\), respectively). This indicates the strong interaction between the first Pt layer and the Na monolayer. We believe that the large differences of adsorption energies between different positions described in Table 1 can be explained by this Na–Pt interaction as well.

Table 2. The charge distribution between Na, C and Pt atoms (1st layer and 2nd–6th layers) in Gr/Pt(111) and Na/Gr/Pt(111) systems
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Figure 4 contains the spin textures for graphene and sodium eigenstates extracted from the performed DFT calculations along the direction orthogonal to \(\bar {\Gamma }{{\bar {\text{K}}}}\). The spin texture for the states with graphene \({{p}_{z}}\) contribution is shown in panel (a), where numerous spin-dependent avoided-crossing effects originating from the interaction between Gr \({{p}_{z}}\) states and Pt \(5d\) spin-polarized bands can be seen in agreement with previous work [20]. Panel (b) displays the spin texture for the states with Na contribution, where the aforementioned spin-polarized structure resembling the Kanji symbol can be clearly observed in some areas. The parabolic branch bears strong weight but a small spin splitting which is reversed when the \({{\bar {\text{K}}}}\) point is crossed. An additional thin band slightly above the bold parabolic band has a small weight but almost full spin polarization; this band is attributed to the Pt states with small admixture of Na states. The cone-like branches of Na states are strongly spin-polarized in the binding energy region of 1.5–3 eV. This observation lends further evidence to our interpretation that the graphene layer mediates the spin-dependent interaction between Na and Pt accompanied by the corresponding charge transfer (see Table 2).

Fig. 4.
figure 4

(Color online) The calculated k-resolved spin structure of the states with graphene contribution (a) and sodium contribution (b) in the direction perpendicular to \(\bar {\Gamma }{{\bar {\text{K}}}}\). The spin quantization axis is orthogonal to the electron quasimomentum k.

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CONCLUSIONS

We present a combined study of the effects of Na adsorption on the electronic properties of Gr/Pt(111) by ARPES and ab initio DFT calculations. The results obtained allows us to state that adsorbing sodium atoms forms the dense short bridge configuration on top of the Gr/Pt(111) system due to the supporting interaction with the substrate. Adsorption of the dense sodium layer leads to a charge transfer from Na both to graphene atoms and atoms of the first Pt layer which causes a shift of the graphene Dirac point to the binding energy of 1.2 eV, rendering n-doped graphene. Hence, this allowed us to experimentally observe the gap-like feature in the Dirac point.

The system with adsorbed Na can be characterized by the strong coupling between Na and spin-polarized Pt \(5d\) states. The ARPES map demonstrates the emergence of the Kanji symbol-like states with two additional graphene-like branches just below the Fermi level. This feature is explained within the DFT framework by the formation of the Na layer 2 × 2 superstructure that leads to emergence of the partially spin-polarized Na folded bands in the electronic structure of Na/Gr/Pt(111). This superstructure effect takes place thanks to the graphene supporting role, which via the charge transfer with the platinum substrate, facilitates the short bridge structure for the sodium layer.

Based on the data presented in this work, it is possible to propose further investigation of this system in three main directions: generation of spin currents in spintronics and investigation of a possible superconducting state of Na monolayer. Undoubtedly, this work can contribute to further research and development of spintronics and valleytronics devices based on new quantum effects and principles of building energy-efficient and high-speed computational logic.