Room temperature observation of the correlation between atomic and electronic structure of graphene on Cu(110)

Abstract

In this work we have used atomically-resolved scanning tunneling microscopy and spectroscopy to study the interplay between the atomic and electronic structure of graphene formed on copper via chemical vapor deposition. Scanning tunneling microscopy directly revealed the epitaxial match between a single layer of graphene and the underlying copper substrate in different crystallographic orientations. Using scanning tunneling spectroscopy we have directly measured the electronic density of states of graphene layers near the Fermi level, observing the appearance of a series of peaks in specific cases. These features were analyzed in terms of substrate-induced perturbations in the structural and electronic properties of graphene by means of atomistic models supported by density functional theory calculations.

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Introduction

The extensive research focused on graphene in the last years has revealed several intriguing properties that confer enormous potential for application and a continuous source of new physical phenomena.^1–3 There is special interest in the study of its electronic properties for future applications in nanoelectronics as a result of the unique aspects that characterize its band structure. In particular, the behavior of graphene at room temperature and in contact with different materials is of great importance, should one incorporate it into an electronic device.

Although the first synthesis of graphene started from graphite exfoliation,⁴ epitaxial graphene has been obtained by SiC substrate sublimation⁵ and chemical vapor deposition (CVD) performed on different catalytic metal⁶ surfaces such as Ni⁷ and Cu.⁸ CVD growth of graphene on copper substrates is one of the most studied systems, since this method can provide isolated monolayers or a complete film of high quality, depending on the time of growth and carbon precursor supersaturation, making this a quite robust growth technique.⁸ The island shape depends on the environment where the growth is performed, making substrate orientation, temperature and hydrocarbon pressure very important factors.

For a better understanding of the phenomena involved in CVD growth, several studies have already been carried out using different experimental methods.^9–12 Wofford et al.⁹ observed the formation of polycrystalline islands at temperatures below 790 °C due to heterogeneous nucleation at surface imperfections, while above this temperature well-ordered graphene is formed. Murdock et al.¹⁰ identified single-layer graphene domains aligned with zigzag edges parallel to the 〈101〉 direction on Cu(111) and Cu(101) under low-pressure growth conditions, while under atmospheric pressure conditions hexagonal domains are formed. Meca et al.¹¹ showed that anisotropic diffusion leads to diverse island shapes with small features such as dendrites, squares, stars, hexagons, butterflies and lobes. Finally, Wang et al.¹² recently observed a strong dependence of surface dynamics such as sublimation and surface premelting on grain orientation, while island nucleation drastically decreases for graphene coverages above 30%. It was also shown that graphene domains are formed on copper plateaus surrounded by step bunches, which impose an anisotropic strain on the graphene sheets. It has also been reported in the literature that graphene induces surface reconstruction of copper.¹³ It is now recognized that structural modifications of the copper surface represent a platform for the understanding of the interplay between the electronic and structural properties of epitaxial graphene.

A number of groups have studied the electronic behavior of graphene interacting with specific substrates. Using scanning tunneling microscopy and spectroscopy (STM/STS) Li et al.¹⁴ measured the electronic local density of states (LDOS) through the dI/dV tunneling spectrum of decoupled graphene on a graphite substrate and observed a linear-shaped spectrum, as to be expected for this material for energies close to the Fermi level. However, this electronic density of states may change depending on the interaction between graphene and the underlying substrate, which in turn depends intrinsically on the growth process. Studies of graphene on Ru,¹⁵ SiC¹⁶ and Cu^17,18 have shown this kind of effect. Sutter et al.¹⁵ observed a non-linear dI/dV spectrum for a graphene monolayer on Ru and attributed it to the strong interaction between these two materials. Brar et al.¹⁶ observed a gap in the dI/dV spectrum of graphene on SiC, ascribing it to a possible excitation of a phonon mode. A similar effect was reported by Zhang et al.¹⁹ for graphene on SiO₂ using a field effect device. Finally, strong oscillations in the LDOS were observed in graphene nanobubbles on Pt.²⁰

Jeon et al.¹⁸ studied graphene on Cu(111) grown by a low temperature CVD process and observed a Moiré pattern and its respective dI/dV spectrum with a nearly linear dependence with energy. However, deviations from this behavior were observed for voltages as low as 150 mV, showing that a linear response for higher voltages may be difficult to attain. In contrast, Gao et al.¹⁷ observed a dI/dV spectrum of graphene that was very similar to the corresponding spectrum for a bare copper substrate, which they attributed to a strong interaction of the graphene layer with the substrate. Despite all these different modifications on the electronic properties of graphene, the role of the substrate seems to be unclear in some cases.

In the present work we have studied different domains of graphene islands grown at high temperature in a low pressure CVD (LPCVD) process, prior to the formation of a complete film on a polycrystalline copper substrate. STM and STS techniques were used to correlate the atomic structure to the electronic band modification. The STM images revealed different Moiré patterns as a result of the epitaxial match between graphene and copper.

The STS spectra evidenced the change of the LDOS and the appearance of peaks at different energies. From a comparison of different regions of the substrate we found that the change of the LDOS from linear behavior depends on a number of factors:

• The electronic density of states of the STM tip.

• The local electronic density of states of the substrate.

• A homogeneous strain induced by the substrate.

• A periodic strain present due to the stacking of carbon atoms on the underlying substrate lattice.

While the first two factors are well-known, the effect of the substrate stress on graphene’s electronic properties depends on the homogeneity of this interaction. A homogeneous strain induced by the substrate leads to the appearance of non-periodic peaks similar to Landau states and can be modeled as a strain-induced pseudo-magnetic field.²⁰ In our work the epitaxial match between graphene and the Cu(110) surface was carefully analyzed, with the observation of nearly rectangular domains where strong Moiré patterns and a series of periodic peaks in the tunneling spectrum take place. The STS spectra were analyzed theoretically, which allowed us to model the effect of the strain modulation responsible for the Moiré patterns on the electronic structure. Using first-principles calculations we show that the presence of periodic peaks in the electronic density of states is a consequence of the periodic strain present in graphene and imposed by the substrate, revealed by the Moiré pattern periodicity and symmetry.

Methods

The sample was grown by resistively heating a Cu foil at 940 °C in a cold wall high vacuum chamber with a base pressure of 10⁻⁶ Torr. The carbon precursor was paraffinic oil vapor at a partial pressure of 10⁻⁴ Torr. The surface of the commercial high-purity copper foil substrates consisted of Cu grains with random crystallographic orientations.^21–23 However, the high temperatures and low pressures that are typical of our growth conditions often produce a massive rearrangement of the Cu surface. In the course of this process, Cu grains can develop a disordered surface layer due to the surface pre-melting. The occurrence of this phenomenon depends on the packing density of the Cu grain and is less expected to occur on closed-packed surfaces as (111), but may take place on open surfaces such as (110) at temperatures below the melting point.²² As a result, high index Cu grains with open geometries continually rearrange into lower energy configurations such as (111), (100) and (110), all observed in our substrates.

The copper surface catalyses the dissociation of hydrocarbons and the carbon atoms reorganize predominantly in monolayer graphene islands. The growth conditions were such that a strong dependence between the graphene domain morphology and the crystallographic orientation of the underlying copper grain was observed, which was attributed to the sublimation and self-diffusion of the copper atoms. Electron backscattered diffraction analysis²⁴ revealed the epitaxial relationship between the Cu surface orientation and the shape of the graphene domains. Four-lobed domains with square and rectangular symmetries are associated to Cu(001) and (110) surfaces, respectively. Six-lobed (referred to here as hexagonal) and star-shaped domains are found on (111) and on high index (113) surfaces. Micro-Raman spectra of as-grown domains acquired on different Cu crystallographic surfaces have shown 2D/G peak intensity ratios of ∼3 and a 2D peak width of 32 cm⁻¹, as to be expected for sp² hybridized graphene.²⁴ For more details, see Cunha et al.²⁴

To characterize the sample, we used optical and atomic force microscopy (AFM), which provided us with information about the shape of the graphene islands, as well as their roughness, allowing a posterior correlation with the STM images and STS spectra. To analyze our sample using optical microscopy, part of it was oxidized in air for 10 seconds at 150 °C to generate optical contrast between graphene and copper. AFM images were obtained using a XE-70 SPM Park Instruments microscope using a doped silicon cantilever from nanosensors with a nominal spring constant of ∼42 N m⁻¹ and a nominal resonance frequency of 75 kHz.

STM and STS experiments were performed using a Nanosurf microscope. Freshly cleaved Pt–Ir tips were used in an air environment at room temperature. Spectroscopy data were obtained by measuring current vs. voltage profiles at selected regions with and without Moiré patterns and the dI/dV curves were obtained as the derivative of the current data. STS measurements were first optimized on graphite and MoS₂ to observe typical tunneling spectra of semimetal and semiconductor surfaces, respectively. Tunneling spectra of graphene domains were taken near the center of each domain to avoid the influence of edges and defects. The reproducibility of tunneling spectra was tested by comparing individual measurements at the same region as well as different regions with the same Moiré pattern. Only reproducible measurements were considered.

Our first-principle calculations were based on density functional theory^25,26 as implemented in the SIESTA code.^27,28 For the exchange–correlation potential, we used the generalized gradient approximation (GGA).²⁹ We employed norm-conserving Troullier–Martins³⁰ pseudopotentials in the Kleinman–Bylander³¹ factorized form, and a double-ζ basis set composed of finite-range numerical atomic pseudofunctions enhanced with polarization orbitals. A real-space grid was used with a mesh cutoff of 350 Ry.

We used two supercell types in our calculations. The first one was built with hexagonal symmetry and a lattice parameter of a = 23.76 Å. For this case, the band structures and densities of states were calculated with a k point sampling in the Brillouin zone given by a 150 × 150 × 1 Monkhorst–Pack grid.³² The band structure plots are shown within the supercell Brillouin zones, which do not coincide with those derived from a graphene primitive cell. We also used a rectangular supercell, in which case the density of states calculations were performed with a 200 × 200 × 1 Monkhorst–Pack grid.

Results and discussion

Optical and atomic force microscopy

The optical microscopy image in Fig. 1a shows different grains of the polycrystalline copper substrate, containing several graphene islands with an average size of 15 μm to 20 μm (in lighter orange color) and traces of polish of the copper foil. From these images, it is possible to visualize the different shapes of the islands of graphene, as highlighted in Fig. 1b–e. As shown in Fig. 1b, the graphene domains in the Cu(110) surface have rectangular symmetry and are perfectly oriented. Careful analysis revealed that our sample is predominantly composed of this crystallographic orientation.

Fig. 1 (a) Optical microscopy image showing various grains of polycrystalline copper and the graphene domains in lighter orange. Graphene domains with different symmetries are delimited by dashed lines. A closer zoom of each domain type is shown in: (b) two-fold (R-rectangular), (c) four-fold (S-square) and (d) six-fold (H-hexagonal) symmetries. (e) Islands of graphene with undefined (U) shapes crossing grain boundaries.

We also observed domains with square (four-fold) and hexagonal (six-fold) symmetries, respectively, as shown in Fig. 1c and d, but these are rare, especially the square ones. We also observed that graphene domains may cross grain boundaries (Fig. 1e) forming islands of undefined shape.

An AFM analysis of our sample allowed us to characterize in greater detail the graphene domains. We were able to identify two main types of regions. The first one is indicated in Fig. 2a, where a graphene domain with rectangular symmetry, typical of graphene on Cu(110), is presented. A magnification of this domain (Fig. 2b) reveals a region with terraces approximately 100 nm in length. The profile indicated by the blue line (longitudinal) in Fig. 2b, along one of these terraces, shows a height variation of 1 nm (Fig. 2c, right plot), characterizing atomically flat regions separated by terrace steps of approximately 5 nm (Fig. 2c, left plot).

Fig. 2 AFM images of graphene domains. (a) Phase image of a graphene island with rectangular symmetry. (b) Phase magnification of the highlighted region in (a). (c) Transversal (T) and longitudinal (L) profiles along image (b). (d) Phase image of a graphene island with nearly hexagonal symmetry. (e) Topography magnification of the highlighted region in (d). (f) Transversal (T) and longitudinal (L) profiles along image (e). Scale bars are (a) 4 μm, (b) 0.5 μm, (d) 4 μm and (e) 0.5 μm. The spherically shaped particles that appear in the AFM images are SiO₂ contaminants derived from quartz pieces or from silica vacuum grease.

The second region shown in Fig. 2d shows a nearly hexagonal island, probably stemming from the Cu(111) surface. Magnification of this region reveals a corrugated surface, as depicted in Fig. 2e, formed by a series of stripes separated by terrace steps of 30 nm (see transversal profile of Fig. 2f, left panel), showing that this region is not nearly as flat as the Cu(110) one. The profile indicated by the red (longitudinal, along the step) line in Fig. 2e shows the presence of terraces separated by steps of 5 nm as presented in Fig. 2f, right plot.

Scanning tunneling microscopy and spectroscopy

Using STM we have identified several different regions within the graphene domains, some of which can be seen in Fig. 3a–f. In Fig. 3a and b we show very flat regions with no terraces. This region possesses a smooth topography (Fig. 3a), indicating that the graphene layer only touches the substrate on a few regions and there is probably very little strain imposed by copper. The medium resolution image shown in Fig. 3b reveals a nearly perfect graphene sheet. The inset in this figure presents the Fourier transform (FFT) of this image as nearly perfect graphene. This region therefore is essentially composed of graphene with no homogeneous or periodic strain imposed by the substrate.

Fig. 3 Large area STM topography images showing different surfaces with graphene domains. Low and medium resolution images of (a, b) a very flat graphene area, (c, d) of an area with an approximately hexagonal Moiré patterns and (e, f) of a region with a nearly rectangular Moiré pattern. The insets in figures (b), (d) and (f) present FFTs of the corresponding images. Scale bars are (a) 15 nm, (b) 4 nm, (c) 100 nm, (d) 4 nm, (e) 50 nm and (f) 5 nm.

On the other hand, two other regions shown in Fig. 3c–f present plane terraces very similar to those observed by AFM images. There is a striking difference between these two areas of the sample. The low resolution image of Fig. 3c exhibits very steep terrace steps similar to those observed by AFM for the hexagonal graphene domains of Fig. 2d and e. A medium resolution image of this same region (Fig. 3d) reveals a weak Moiré pattern. The FFT inset shows that although a well-defined symmetry is not observed, superstructure peaks are found near the central spot, indicating a periodic arrangement of the lattice. Otherwise, the region shown in Fig. 3e exhibits longer terraces with very small steps as observed for the graphene regions of Fig. 2a and b. The medium resolution image (Fig. 3f) reveals a nearly rectangular Moiré pattern (see black solid lines). The Fourier transform (inset Fig. 3f) corroborates this result. One observes inner FFT peaks with a two-fold symmetry as well (see dashed red lines). Due to the symmetry of the Moiré pattern we can ascribe this region to the Cu(110) surface.

We have also performed a spectroscopic analysis of these same regions to establish a connection between the local electronic properties and the atomic structure. In Fig. 4a and b we present a high-resolution image of the flat graphene region and its dI/dV spectrum, which is proportional to the LDOS. Together with this spectrum we can see an estimation of the Dirac cone for T = 0 K (solid blue line) displaced by δE_F = 32 meV, which represents a shift in the Fermi energy and indicates a small negative charge transfer from the substrate to graphene. In addition, the dashed line in the spectrum represents a non-zero density of states in comparison with the Dirac line. The solid line, representing the Dirac cone together with the substrate DOS, was drawn simply by an offset of the dashed line, which in turn was obtained from two tangent lines to the STS spectrum for very low voltages. The increase in the density of states, indicated by the constant DOS_s, represents the influence of the density of states of the copper substrate. A natural broadening is also embedded on the curve of approximately 4K_BT ∼100 meV, which is more important near the Dirac point in a limited range of −50 meV to 50 meV.³³ This is a consequence of the temperature at which the experiment was conducted (300 K). However, this effect does not seem to be very significant even at room temperature. As one can see, our experimental data exhibit approximately linear behavior for a very limited range (from −150 mV up to 300 mV).

Fig. 4 High resolution STM topography images and their STS spectra for (a, b) nearly flat graphene, (c, d) hexagonal and (e, f) nearly rectangular Moiré patterns. Scale bars are (a) 1.5 nm, (c) 1.5 nm and (e) 1 nm.

The electronic density of states of the STM tip and the LDOS of the copper substrate also leads to an increase of dI/dV, which is particularly seen at a sample bias of −380 mV as was observed by Gao et al.¹⁷ (see arrow in Fig. 4b). We also observed, in comparison with the dashed line in the spectrum, a superlinear variation of the dI/dV curve for voltage moduli above 300 mV. Although this graphene sample seems to be unstrained by the substrate, the effect of the copper density of states is clearly observed.

Significant changes are noticed in the spectra for areas where one can observe Moiré patterns. In Fig. 4c it is possible to observe the presence of an approximately hexagonal and weak Moiré pattern and in Fig. 4d we notice a complete change of the dI/dV spectrum with the appearance of peaks in the density of states identified by the black arrows. The peaks are not pronounced but they constitute a significant change in the electronic properties of graphene. This shows that a slight disturbance caused by the substrate is sufficient to destroy the linearity of the density of states. Measurements on the bright and dark regions of this STM image yielded essentially identical STS spectra. On the other hand, we identified in the region shown in Fig. 4e a much better defined Moiré pattern with a nearly rectangular periodicity (with 0.8 nm × 2.3 nm). As previously, we observe in Fig. 4f a completely different STS spectrum without linear features, but again with a number of peaks, indicated by arrows, at different energies.

Levy et al.²⁰ have studied the effect of strain in graphene nanobubbles grown on Pt(111) and observed a series of peaks in the LDOS. They modeled this effect by introducing an homogeneous strain in the graphene lattice and observed the appearance of strain-induced pseudo-magnetic Landau states. The relationship between the peak energy E_n and its level n follows:

where is the cyclotron resonance frequency, v_F is the Fermi velocity and B_s is the pseudo-magnetic field.²⁰ Pseudo-magnetic fields in excess of 300 Tesla were inferred.

In Fig. 5a and b we present E_n as a function of for the Moiré patterns of Fig. 4c and e, respectively. For the case of the hexagonal Moiré pattern of Fig. 4c this relationship is clearly observed, showing that the substrate imposes a homogeneous stress.

Fig. 5 (a) Relationship between peak energy E_n and its level n for (a) weak Moiré pattern and (b) nearly rectangular Moiré pattern. A least squares fit of curve (a) yielded .

For the case of the nearly rectangular Moiré pattern of Fig. 4e this relationship is not respected. Although it remains closer to a linear variation, an energy gap smaller than ΔE_g = 200 meV seems to be present. This indicates again an effect of the substrate on the electronic properties of graphene.

Graphene/Cu(110) epitaxial relationship by surface X-ray diffraction

The STM results lead us to conclude that the Cu(110) surface strongly affects the electronic properties of graphene. Therefore, we decided to investigate whether there is any epitaxial relationship between the graphene layer and the underlying surface that could indicate a larger interaction between graphene and that particular copper surface. In order to determine such a relationship, we have performed grazing incidence X-ray diffraction measurements on the surface of our sample.

The sample was taken to the X-ray diffraction beamline XDS of the Brazilian Synchrotron Light Source. This wiggler beamline delivers 10¹⁴ photons/second on the sample with an energy of 8.00 keV (wavelength 1.54 Å) and an energy resolution of ΔE/E = 10⁻⁴. The diffraction geometry is shown in Fig. 6a. The X-ray beam illuminates the graphene/copper surface at a grazing incidence angle α_i = 0.3°. After scattering at an angle 2θ, the X-ray photons are collected by a Pilatus 300K X-ray detector covering an exit angle of 0.3°. Since the scattering plane is parallel to the surface of the sample, only the two-dimensional graphene and copper planes perpendicular to the surface contribute to the scattering. In order to measure individual Cu(110) domains, the X-ray beam size was chosen to be of approximately 50 × 50 μm² (defined by slits), i.e., smaller than the typical grain size. The sample was aligned by fixing the detector at the position of the Cu(2−20) peak, i.e., q = 4π/λ sin(2θ/2) = 48 nm⁻¹, and maximizing the diffracted intensity as a function of the sample azimuthal angle ϕ as well as its horizontal position.

Fig. 6 (a) Grazing-incidence X-ray diffraction geometry used to infer the epitaxial orientation between graphene and Cu(110). (b) Radial scan along the Gr(10) → Cu(2−20) direction.

Once the Cu(2−20) peak intensity was maximized, X-ray scans following the radial line (ϕ = 2θ/2) through the graphene (10) peak towards the Cu(2−20) peak were performed. In Fig. 6b we present this radial scan. The graphene (10) peak is observed at q = 29 nm⁻¹, showing it is perfectly aligned with respect to the Cu(2−20) direction. We also observed two additional X-ray peaks at a distance of Δq = 7.85 nm⁻¹ = 2π/(0.8 nm) from the Cu(2−20) X-ray peak. These correspond exactly to correlation peaks due to the effect of the periodic strain (with a period of 0.8 nm, as observed in Fig. 3f and 4e) induced by the graphene layer on the copper substrate, showing that the periodic strain is also observable on the copper lattice.

One must mention that a similar effect of periodic strain in graphene is also present and might be observed in the same radial scan near the graphene (10) peak. However, due to the extremely small signal to noise ratio, the graphene correlation peaks could not be detected.

These results show that not only the graphene layer formed on the Cu(110) surface is epitaxial but also that the substrate can generate small and periodic displacements of the graphene carbon atoms from their equilibrium position, thus generating the Moiré pattern. According to Newton’s 3^rd law, this is simply a response of the graphene film to the periodic stress imposed by the copper substrate.

Modelling of periodic graphene superstructures with static displacements

The combination of well-defined Moiré patterns and the appearance of several peaks in the STS spectra suggests an interplay between structural and electronic properties which we shall now address within the density functional theory formalism. In our model, an important ingredient is the thermal reconstruction of the copper surface underneath the graphene, a process that has been described in different contexts^11,24,34 and which plays a prominent role during the CVD growth of our samples.²⁴ We make the reasonable assumption that the net effect of these atomic rearrangements is to provide a periodic strain field acting on the carbon atoms. As a consequence, the C–C bonds within a supercell defined by the Moiré pattern will be distorted, following the thermal rugosity induced by the copper substrate. The detailed description of such strain field is a formidable task that is beyond the scope of the present work. Instead, we mimic its effect by randomly displacing the carbon atoms within a supercell around their equilibrium positions and in all three directions. The magnitude of the displacements is limited by a parameter that varies between zero (perfect graphene) and 0.10 Å. In all cases, we performed band structure calculations and determined the density of states, paying special attention to the convergence in the number of k points so as not to produce spurious density of state peaks.^35,36

To begin the discussion, we apply this model to the case in which a Moiré pattern produces a hexagonal supercell with parameter a = 23.76 Å. The structural models, band structures and corresponding density of states are shown in Fig. 7a–c, respectively, for three values of the displacement magnitude parameter Δ = 0.00 Å, 0.05 Å and 0.09 Å. Important features are clearly verified in the results. First, for Δ = 0.05 Å, it is possible to see in the density of states diagram the emergence of the phenomenology observed in our experiments. Second, at least one peak in the density of states may be easily ascribed to the combined effect of zone folding (due to the superlattice cell) and the atomic distortions. Indeed, at an energy around ±0.5 eV the bands fold at the M point, which, by itself, does not introduce any characteristics in the density of states, as seen in the plots for Δ = 0.00 Å. However, for values of Δ different from zero, a small gap opens up at this point at around this energy value, and the bands approach the M point with reduced slopes, which contributes to an increase in the density of states. Also, there is a definite tendency towards gap opening at the K point with larger distortions, as can be seen in the band structure for Δ = 0.09 Å (Fig. 7b).

Fig. 7 (a) Distorted (Δ = 0.50 Å and Δ = 0.09 Å) structural models for graphene supercells with bond lengths indicated by the color scale. The structural models of graphene supercells were generated using Visual Molecular Dynamics (VMD 1.9.2)³⁷ with the TopoTools plugin.³⁸ (b) Band structures and (c) density of states for perfect graphene (Δ = 0.00 Å) in red lines and the structural models shown in (a) in black lines.

These conclusions are not restricted to hexagonal supercells. To represent more realistically the nearly rectangular Moiré patterns observed in the experiments, we built graphene supercells as illustrated in Fig. 8a and b (side and top views), in which the same distortion scheme previously described was applied. The presence of the copper substrate in the figure is only schematic – by adding it to the figure we aim to emphasize the connection of the graphene-only calculation with the experimental system in which the distorted copper lattice is responsible for the perturbed C–C bonds in the periodic fashion dictated by the Moiré pattern. We considered four structures corresponding, respectively, to four values of the parameter Δ = 0.00 Å, 0.01 Å, 0.05 Å and 0.10 Å. The supercells with Δ ≠ 0.00 Å are slightly strained (4.35% and −0.60% in the armchair and zigzag directions, respectively) to make them commensurate with the copper substrate (not explicitly taken into account in the calculation).

Fig. 8 (a, b) Two views of the structural model for a graphene supercell with Δ = 0.10 Å. The underlying copper substrate is schematically shown for visualization purposes. The distortions of the C–C bonds are indicated by the same color scale as in Fig. 7. (c–f) Density of states (black lines) of the graphene rectangular supercells with four values of parameters: Δ = 0.00 Å (perfect graphene, unstrained supercell), Δ = 0.01 Å, 0.05 Å and 0.10 Å, respectively. The distortion scheme (Δ ≠ 0.00 Å) is applied to a slightly strained supercell (see text), whose density of states is shown as a reference in red lines in all plots. (g) Band structures corresponding to the strained rectangular supercell with Δ = 0.00 Å and Δ = 0.05 Å (left and right panels, respectively).

The corresponding density of states are shown in Fig. 8c–f, while two examples of band structures (Δ = 0.00 Å and Δ = 0.05 Å) are shown in Fig. 8g in the left and right panels, respectively. Again, we see the emergence of the experimental phenomenology, which becomes quite evident for the most distorted structure (Fig. 8f). We mention that the absence of the Moiré pattern in some experimental images indicates a smaller coupling between graphene and copper, which prevents our distortion model to be applied to these samples. In these cases, we expect a minute influence of copper atoms on graphene, justifying the absence of additional peaks in STS spectra.

This theoretical analysis leads us to conclude that the interplay between homogeneous and periodic strain is a crucial ingredient to understand the electronic properties of graphene. Microscopy measurements are not appropriate experimental techniques for the quantification of inter-atomic distances and/or displacements. The use of other structure determination techniques such as X-ray or electron diffraction is therefore essential for the prediction of the electronic properties of graphene interacting with different substrates.

Conclusions

We employed a combination of techniques to investigate the electronic properties of epitaxial graphene on a copper substrate. STM was used to locate different graphene domains, to detect the appearance of Moiré patterns and to qualitatively probe the degree of coupling with the substrate. Through STS spectra, we were able to characterize the electronic properties in distinct regions of our sample, showing that in Moiré domains the larger coupling led to the appearance of peaks in the LDOS, whereas in the decoupled regions the LDOS assumed the linear-shaped curve characteristic of isolated graphene.

The theoretical analysis of STS spectra showed that the presence of periodic peaks in the electronic density of states is a consequence of the periodic strain present in graphene and imposed by the substrate. We have directly shown that graphene is very sensitive to the underlying substrate and that a Moiré pattern can completely change its electronic properties. This knowledge, together with the understanding of the behavior of the system graphene/substrate under ambient conditions, is essential for future applications, especially in the design of nanodevices.

Acknowledgements

The authors acknowledge experimental support by the Brazilian Synchrotron Light Source (LNLS). Financial support was provided by Instituto Nacional de Ciência e Tecnologia (INCT NanoCarbono). We also acknowledge additional funding by CNPq, CAPES and FAPEMIG and computational support from LCC-Cenapad-UFMG and Cesup-UFRGS.

Notes and references

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