Exploring graphene-substrate interactions: plasmonic excitation in Sn-intercalated epitaxial graphene

Graphene plasmons, including those in intercalated graphene, are an important research focus, with the promise of enabling light manipulation and providing a unique platform for gaining fundamental insights into many-body electronic interactions. In the present work, we discuss the results of low-energy plasmonic excitations in epitaxial quasi-free monolayer graphene formed by intercalation of Sn beneath the buffer layer (BL) on 4 H-SiC(0001). The quantitative analysis of the sheet plasmon dispersion revealed that the Sn-induced ( 1×1 ) interface is metallic and results in formation of charge-neutral graphene. A redshift of the 2D plasmon was found, but only after doping with potassium. The Sn-diluted interface, revealing a ( 3×3 ) reconstruction and resulting in intrinsically n-type doped graphene, behaves comparably to the BL for epitaxial monolayer graphene (MLG). Furthermore, it seems that a dipolar coupling of the longitudinal charge density fluctuations in graphene to the interface layer triggers the formation and the loss energy of a plasmonic multipole component, which therefore makes it suitable for studying proximity effects of excitations in electronically weakly coupled 2D heterosystems.


Introduction
Graphene possesses unconventional 2D electron gas properties, e.g. a constant group velocity and a high charge carrier mobility, giving rise to groundbreaking transport phenomena [1][2][3].The collective excitations of this relativistic electron gas were shown to be a promising alternative to noble-metal plasmons because of the strong confinement and long plasmon propagation distances [4].
Graphene plasmons are captivating quasiparticles with vast potential for diverse applications.Notably, sheet plasmons are adjustable and operate within the terahertz to mid-infrared frequencies [5].Furthermore, the robust interaction of graphene plasmons with incident light allows for the concentration and manipulation of light at subwavelength scales.Consequently, graphene stands as a promising material in realizing quantum plasmonics for the next generation of nanoscale opto-electro-technology, ultrasensitive sensors, and quantum computing [6][7][8].However, in order to harness this potential for any application, a deeper understanding of defects and substrate effects is crucial.Using metallic 1D and 2D systems generated via epitaxy on semiconductor substrates, lifetime and confinement effects of collective excitations could be correlated in detail with the atomic structure [9][10][11][12].
For a comprehensive structural control coupled with the ability to fine-tune electronic effects, epitaxial graphene (EG) stands out as the material of choice.Through the sublimation of Si atoms at high temperatures, graphene can be epitaxially grown on the SiC(0001) surface in a controlled and scalable manner [13,14].Notably, this growth process leads to the formation of an intermediate state called the buffer layer (BL), mirroring the structural arrangement of free-standing EG while chemically bonded to the substrate [15].
Introducing various elements into the BL/SiC(0001) interface enables the formation of large-area quasi-freestanding monolayer graphene (QFMLG) sheets with adjustable properties [16,17].Simultaneously, chemically shielded quantum layers, formed by the interface layer adjacent to graphene, are anticipated to exhibit unconventional properties [18][19][20].Recently, there is an interest in high-Z elements owing to their fascinating intrinsic properties.Group-IV elements, e.g.Pb or Sn, have garnered attention due to their robust spin-orbit coupling and correlated electronic behavior, evidenced by phenomena like the Mott insulating state, chiral superconductivity, topological edge states, and more, observed thus far on semiconducting surfaces [21,22].The formation of 2D interface layers in proximity to quasi-free-standing graphene is a superb template to reveal new quantum materials but also to study the interactions of collective excitations in each of the 2D system.
In this paper, we studied the collective modes in QFMLG on the SiC(0001) surface formed by intercalation of Sn atoms.Using different temperature protocols during and after intercalation, both Sn(1 × 1) and Sn( √ 3 × √ 3) phases were formed with respect to the SiC lattice as found by electron diffraction.By means of angle-resolved electron energy loss spectroscopy (EELS), the plasmon dispersions were measured in detail and compared to MLG samples.The analysis showed that for Sn(1 × 1) and Sn( √ 3 × √ 3) phases charge neutral and moderately n-type doped QFMLG were formed, respectively.The dispersion of the sheet plasmon is similar to that measured for MLG, i.e. seems to be rather insensitive to the doping and environment.While sheet plasmons of the metallic Sn(1 × 1) phase itself were not found, instead, the loss energy of multipole components of graphene seems to be sensitive to the interface and allows studying proximity effects by plasmon spectroscopy.

Experimental details
All experiments were performed in an ultra-high vacuum system operating at a base pressure of 5 × 10 −9 Pa.A high-resolution spot profile analysis low energy electron diffraction (SPA-LEED) setup was used to control and study the Sn intercalation process and interface structures [23].The plasmonic excitations were measured using high-resolution EELS combined with a LEED unit (EELS-LEED), which enables simultaneously high energy and momentum resolution, typically around 25 meV and 0.001 Å −1 .
BL samples used for Sn intercalation and MLG for reference were grown epitaxially by Si sublimation on n-type 4 H-SiC(0001) substrates as described in detail in reference [24].Subsequently, the samples were transferred to the SPA-LEED chamber through air and degassed at 870 K for several hours by direct current heating.Following this process, sharp (6 3)R30 • reconstruction spots indicative of longrange ordered BL structures were observed, as shown in figure 1(a).
Sn deposition was carried out in-situ using an electron-beam evaporator with a deposition rate of 0.15 monolayer/min by maintaining the sample at room temperature.This was followed by annealing the sample at 1120 K for 10 min, resulting in an intercalated Sn(1 × 1)interface.To form diluted Sn interface structures, revealing a ( √ 3 × √ 3)R30 • symmetry,the sample was annealed at 1320 K for 2 min.For the EG/Sn(1 × 1) phase, partially grown BL surfaces were employed to prevent potential plasmonic signals from unexpected overgrown MLG.The entire intercalation process was monitored by SPA-LEED as exemplary presented in figure 1.Further details about the Sn intercalation are reported in [25].Potassium (K) was deposited at a sample temperature of 60 K cooled by liquid He.

Sn intercalation: SPA-LEED studies
In figure 1, we present a set of high-resolution SPA-LEED patterns for the clean BL, as well as after Sn intercalation and subsequent potassium adsorption.Starting with the BL surface, the LEED pattern clearly shows the (1 × 1) spots of the SiC(0001) surface and the BL, marked with 'S' and 'G' , respectively.Besides, the LEED pattern reveals characteristic spots originating from the (6 √ 3 × 6 √ 3) reconstruction.Imperfections easily break the symmetry of this large unit cell, and the smaller (6 × 6) quasi-cell is also seen in the diffraction experiment.The electron energy of 150 eV is close to an out-of-phase scattering condition.The full width at half maximum (FWHM) at these energies is mainly limited by the transfer width of the instrument (∼200 nm), underlining the high quality of the graphene substrates.More details about the preparation and Sn phases can be found in a recent study [25].
We deliberately utilized a slightly undergrown BL sample to eliminate any plasmonic signals stemming from parasitic MLG patches often formed at step sites.Consequently, the LEED image exhibits a faint and broad intensity at the ( √ 3 × √ 3)-positions relative to the substrate.This becomes quite obvious when comparing undergrown BL (u.BL, black) and full coverage BL (BL, magenta) line scans shown in figure 1(e).
As evident in figure 1(b), Sn intercalation leads to a significant suppression of diffraction spots originating from the BL, indicating the formation of a new interface.Additionally, the specular spot and graphene (1 × 1) spots reappear and are now accompanied by a distinct bell-shaped background characteristic of a free-standing graphene layer, as already stated in previous works [26,27].A direct comparison of high-resolution spot profiles between the pristine and intercalated surfaces (figure 1(e)) reveals the absence of this background on non-graphenized surfaces, thus serving as a clear indicator of successful intercalation and the formation of QFMLG.In order to tune the excitation energy of the sheet plasmon, we performed doping experiments using potassium (K) deposition.In figure 1(c), we present an image recorded following a 2 min K deposition at 60 K, followed by partial removal at 570 K. Remarkably, we did not observe any discernible K-induced periodic patterns both before and after annealing, probably due to the small amount of adsorbed K. Nevertheless, it is worth noting that K adsorption leads only to a slight suppression of all diffraction spots.We want to point out that the Sn(1 × 1) samples used for the K deposition were not annealed higher than 1120 K in order to prevent any Sn desorption from the interface [25].Upon K deposition, the FWHM is only slightly increased to 1%-2% surface Brillouin zone, i.e. the concentration of K adatoms is around 0.1% of a monolayer (2 × 10 12 cm −2 ).phase at 1320 K for 2 min.It is interesting to note that a √ 3 reconstruction of Sn on the SiC(0001) surface has been previously characterized as a 2D Mott system [22].

Electronic excitations
Next, we will present electron energy loss spectra acquired from the above-mentioned surfaces.In figure 2, the loss spectra recorded at Γ-point from the clean BL/SiC(0001), as well as after Sn intercalation and subsequent K doping, are shown.The spectrum of the BL phase reveals two distinct increases in intensity at around 0.8 eV and 3 eV, which reasonably agrees with the bulk band gaps reported for BL (≈1 eV) and SiC (3.2 eV), respectively.These features lack any dispersion and appear most intense at k || = 0, showing their interband transition character.Moreover, loss peaks around 150 meV are present, which can be attributed to dipolar active Fucks-Kliewer (FK) phonon modes of the SiC surface, being more pronounced for the clean surface [28,29].Higher harmonics of the FK mode were also seen, in particular for the clean surface.After Sn intercalation at 1120 K, in order to form a Sn(1 × 1) interface structure, the loss spectrum undergoes a significant change.Notably, the interband loss related to the BL is replaced by an exponential background, coinciding with a decrease in FK loss intensity.The emergence of this Drude tail serves as a distinct indicator of mobile carriers within the system.Consequently, this confirms the transformation of the semiconducting BL into the metallic QFMLG through Sn intercalation.Moreover, upon adsorption of K, the slope of the Drude background becomes more intense, supporting the idea that potassium further acts as a n-type dopant.Sheet plasmons: Furthermore, the collective excitations of the charge carriers in these low dimensional systems and their characteristic sheet plasmon dispersion were studied.In figure 3(a), we show the loss spectra of the fully intercalated phase at a finite wave vector (k || = 0.48 Å −1 ).Irrespective of the primary electron energy, no plasmonic loss at a finite energy and momentum was found.As shown in figure 1(b), the appearance of the bell shape component points towards a suspended graphene layer upon Sn intercalation.Therefore, we can draw some important conclusions from these findings: First, the graphene is charge neutral, which is in accordance with previous ARPES measurements [30].The absence of plasmonic excitation in charge-neutral graphene is attributed to its unique linear electronic band structure [31].At charge neutrality, the Fermi level coincides with the Dirac point, where the density of states becomes zero [3].Secondly, either the intercalated Sn-phase does not provide metallic states that allow for the excitations of sheet plasmons, or the graphene perfectly screens the metallic interface layer so that at least a long-range dipolar interaction is disabled.Albeit the background increases with increasing the primary electron energy but without any new distinct losses, we exclude impact scattering as a dominant channel for the excitation of plasmons as well.
However, upon doping, the Fermi level shifts, and the density of occupied states becomes non-zero [3], thus enabling an intraband π-plasmonic excitation in graphene, e.g. as reported before [32][33][34].In the present case, after mild doping of the chargeneutral EG/Sn(1 × 1) surface by adsorption of K, clearly plasmon losses appear and disperse as shown in figure 3(b) for the Γ → K direction.The same plasmon loss energies were found with momentum transfer along the Γ → M direction, demonstrating the isotropy of the sheet plasmon.
In figure 3(c), we present a series of loss spectra for the Sn-intercalated sample, which exhibited the √ 3 diffraction spots (cf figure 1(d)).Notably, these spectra reveal also dispersing plasmonic losses.However, this metallic behavior seems to be intrinsic to graphene for this intercalated phase, obviating the need for additional K doping.This particular phase was derived from the fully saturated Sn-intercalated phases through a subsequent hightemperature annealing process.The presence of the √ 3 -reflexes in figure 1(d) signifies a partially saturated interface, leading to n-doping of the graphene.
The plasmon losses are energetically rather broad, basically due to short lifetimes caused by scattering at residual imperfections [11].In addition, a second, higher frequency mode is also apparent, as we will show below in more detail.This is a so-called multipole plasmonic excitation and has been observed so far for EG layers and screened pure metallic surface states [35,36].
In order to extract quantitatively the positions and the FWHMs of the plasmon losses, the spectra were fitted by the scheme shown in figure 4(a).After subtracting a constant background, the Drude tail was considered by employing an exponential decay.Then, the line shape was fitted with two Gaussian functions in order to precisely extract the plasmon loss energies at various wave vectors.Figure 4(b) compares the sheet plasmon dispersions of the K-doped EG/Sn(1 × 1) surface, the clean EG/Sn( √ 3) phase and MLG on SiC(0001).All dispersions extrapolate to zero energy at long wavelengths (k || = 0).This is typical for low-dimensional plasmons, since the restoring forces between the charged particles decrease with increasing plasmon wavelength [38].The EG/Sn(1 × 1)+K surface displays the lowest dispersion slope, indicating a distinct behavior.On the other hand, the plasmon dispersion of the EG/Sn( √ 3) surface closely resembles that of MLG on SiC(0001).Apart from the low wave length regime, the dispersion curves are comparatively linear.This is a rather robust feature of graphene, and this universal behavior was observed on different substrates and interfaces [11,35].For MLG, a small kink at around 0.06 Å −1 is obvious, which arises from a resonant coupling between the sheet plasmon and single-particle excitations, resulting from interband transitions in graphene and is related to doping level [32].Following Stern's remarks [37], the dispersion of the sheet plasmon energy can be quantitatively described within the random phase approximation by: Here, E F is the Fermi energy, v F the Fermi velocity, ϵ r and ϵ 0 are the relative and vacuum permittivities, respectively, e is the elementary charge of the electron, and h the reduced Planck constant.Accordingly, the sheet plasmon energy is influenced by two key factors: electrostatic interactions with the surrounding dielectric medium and the kinetic energy of the charge carriers.Thereby, the electrostatic interactions dominate at small wave vectors (long wavelengths), and their impact diminishes as wave vectors increase.The kinetic energy term, on the other hand, is independent of the electrostatic term and becomes more dominant for larger wave vectors.Moreover, in the case of graphene, the velocity of the charge carriers is independent of E F .
For a 2D relativistic electron gas, the Fermi energy is given by E F = hv F √ π n 2D , where n 2D is the charge carrier density.Consequently, in graphene, the plasmon frequency scales as ω S ∝ n 1/4 2D .As mentioned above, the EG/Sn(1 × 1) phase revealed collective excitations only after doping with K.The fact that the plasmon dispersion is, compared to MLG with an intrinsic charge carrier concentration of around 1 × 10 13 cm −2 , not shifted to higher plasmon energies supports our estimate of a low K concentration.Indeed, a shift of the plasmon dispersion was reported for potassium concentrations above 10 13 cm −2 [39].
The evaluation of the linear behavior of the sheet plasmon dispersions for MLG gives a Fermi velocity of v F = 1.02 × 10 6 m s −1 and carrier concentration n 2D = 1.3 × 10 13 cm −2 (E F = 430 meV) in reasonable agreement with ARPES measurements [40].This shows that the concentration of the charge carriers, as well as the environment, play a rather minor role.This behavior has also been observed in the past for graphene on other supports [35].For the EG/Sn( √ 3) phase, almost identical values for the relative permittivity (ϵ r ≈ 6.5) and Fermi velocity were deduced compared to MLG.The carrier concentration is slightly lower n 2D = 7.8 × 10 12 cm −2 referring to a Fermi energy of E F ≈ 330 meV.
Compared to the other two phases, the EG/Sn(1 × 1)+K phase shows a red shift and deviates from the linear behavior for large k || -values.Within the simple theory, only the linear trend can be evaluated in detail.The analysis revealed here a carrier concentration of n 2D = 7 × 10 11 cm −2 (E F ≈ 90 meV) induced by K doping.Assuming a typical charge transfer of 0.6-0.8electrons per K atom [39], we obtain from the EELS analysis a K concentration of around 1 × 10 12 cm −2 , which is in reasonable agreement with the estimate from our SPA-LEED experiments.Interestingly, the analysis revealed a significantly higher relative permittivity of ϵ r = 10.5 and a considerably lower Fermi velocity of v F = 0.95 × 10 6 m s −1 pointing to a renormalization of graphene's band structure.Apparently, the dielectric environment has a strong effect on the dispersion.The higher dielectric permittivity indicates most likely the metallic character of the Sn(1 × 1) phase, compared to the BL and the Sn( √ 3) reconstruction.This is in agreement with the conclusion discussed in the context of figure 2, and the strong redshift of the graphene dispersion, as well as the renormalization of the band structure may hint towards plasmonic coupling, e.g.Coulomb drag effect, between graphene and the metallic 2D interface layer [41].
Multipole modes: Up to now, we have focused on discussing the dispersion of sheet plasmons, i.e. the longitudinal oscillation of a 2D electron gas.Similar to surface plasmons, the sharp localization of charge carriers leads to monopole excitations.In addition, when charge smearing occurs along the z-direction, it enables the emergence of multipole modes.For such modes, the longitudinal charge density either shifts in-or out-of-phase relative to the direction perpendicular to the surface.In the case of surface plasmons, this has been worked out in great detail by Liebsch [42].Unfortunately, the theoretical description of 2D electron gases lags behind in advancement.In the context of plasmonic coupling between 2D electron gases and its impact on Coulomb drag effects during electronic transport, both in-phase and anti-phase modes have been outlined [41].This seems to be significant even in pristine graphene monolayer supported by various substrates [35].By intercalation, we strongly change the environment of the graphene, i.e. the electronic properties of the intercalated phase should be reflected in the analysis of multimode losses.As briefly mentioned in the context of figure 4(a), a multipole plasmon loss at higher loss energies was included in the analysis of our data.
Figure 5 compares the monopole sheet (ω S ) and multipole (ω M ) plasmon dispersions for the EG on Sn(1 × 1) and Sn( √ 3) phases.For both cases, two dispersions show almost the same qualitative behavior.In the short-wavelength limit, which is resolvable in our experiments, the ω M extrapolates to zero energy at k || , revealing its truly 2D nature as the ω S mode.As shown in figure 4, the dispersions for the monopole excitations for the different systems are quite similar.However, loss energies for the multipole modes vary, as seen by the different ratios of the components, at least in the range of low k || -values.Namely, ω M /ω S is 1.6 for the EG/Sn(1 × 1) and 1.1 for the EG/Sn( √ 3) surfaces.Here, we want to mention that this quantity was previously measured to be 2.0 and 1.6 for the EG on Ir(111) and BL/SiC(0001) surfaces, respectively [35], i.e. the splitting is apparently larger on a rather conductive support.
Since there are, unfortunately, no quantitative considerations on this interesting phenomenon yet, we have to restrict ourselves here to a qualitative discussion.The fact that the coupling of the multipole mode of graphene on metallic substrates exhibits the greatest splitting, e.g.measured for EG/Ir(111) [35,43], suggests an influence of image charges at this point.On a perfect metal, longitudinal charge density fluctuations in graphene induce an out-ofphase mirror charge density fluctuation in the support.Consequently, the original monopole mode with a dipolar field distribution is inevitably superimposed by a multipole mode component with a more complex field distribution originating from a kind of hybrid collective oscillation.In a way, these inphase and out-of-phase modes represent the analog of the acoustic and optical modes of lattice vibrations.The less conductive, but also the thinner the metallic substrate, the out-of-phase mode can only partially develop, coming along with a redshift of the loss energy.In comparison of EG on a pure metallic Ir(111) surface to EG on an Sn( √ 3) interface, a redshift of ∼45 % for the multipole plasmon energy is found.This finding is in agreement with the relative permittivities determined from the analysis of the sheet plasmon dispersions discussed in the context of figure 4(b).In principle, the inherent coupling of plasmonic excitations in graphene should also be reflected in their intensities.In fact, the relative intensities of the multipole modes are highest on metallic substrates.As a result, the two modes could be clearly resolved for EG/Ir(111) in former studies [35,43].

Summary and conclusion
In this study, we investigated plasmonic excitations in graphene with varying concentrations of intercalated Sn, composing different interface periodicities.In the presence of an intercalated Sn(1 × 1) phase, neutral graphene is formed, and its plasmonic excitations can only be activated by mild electron doping resulting from the adsorption of K.For a diluted intercalation phase, identified by the formation of √ 3-reflexes in SPA-LEED graphene becomes intrinsically n-doped, as confirmed by a quantitative analysis of the plasmon dispersion.Thereby, the monopole mode appears to be primarily dependent on the Fermi velocity rather than the surrounding environment and doping.A slight redshift, particularly in the regime of large kvalues, was observed for the Sn(1 × 1) configuration, potentially induced by Coulomb drag or structural effects.
Similar to all studies on plasmonic excitations in graphene, the analysis reveals the existence of a socalled multipole mode, which should emerge through charge smearing or, more generally, by the coupling of 2D plasmons [42].The systematic analysis indicated that the multipole mode in EG apparently develops through out-of-phase oscillations of image charges in the substrate.This represents a proximity effect, essentially allowing the investigation of interfaces of such weakly coupled 2D systems.Interestingly, we were not able to identify any sheet plasmon excitation of the Sn monolayer itself.Either its excitation is suppressed due to structural imperfections, or the aforementioned dipolar interaction of longitudinal density fluctuations in graphene with the substrate is predominant.Further theoretical descriptions of plasmonic coupling in stacked 2D layer systems are beneficial and would pave the way for a better understanding of quantum plasmonic effects in low-dimensional electron gas systems.

Figure 1 .
Figure 1.SPA-LEED images of a clean buffer layer structure (a), Sn intercalated (1 × 1) phase (b), and a Sn(1 × 1) phase after subsequent deposition of K at 60 K and partial removal at 570 K (c).The corresponding SiC 'S' and EG 'G' first-order diffraction spots are marked.The SPA-LEED image of the sample containing Sn( √ 3 × √ 3)-reflexes, marked by the magenta circles, is shown in (d).(e) High-resolution spot profiles recorded along the graphene lattice vector through the 00 spot.All SPA-LEED data were recorded with 150 eV primary electron energy at room temperature.

Figure 1 (
d) displays the diffraction image of a sample containing the Sn( √ 3 × √ 3)R30 • √ 3 in the following) structure in relation to SiC lattice.This structure was obtained by annealing the Sn(1 × 1)

Figure 2 .
Figure 2. Electron energy loss spectra (semi-log plot) obtained for the bare BL/SiC(0001) surface (black), EG/Sn(1 × 1) after intercalation (green) and subsequent K deposition (red).The black dashed lines approximate the exponential Drude decay, and the blue dashed lines mark the Fuchs-Kliewer (FK) phonon modes and its higher harmonics (see inset).The position of the band gaps for BL and 4 H-SiC are marked with black and orange lines and coincide nicely with the onset of the interband transitions seen here for BL/SiC(0001).

Figure 3 .
Figure 3. (a) Electron energy loss spectra for the as-prepared EG/Sn(1 × 1) at fixed k || = 0.48 Å −1 .(b) Loss spectra of EG/Sn(1 × 1) after deposition of K for various k || -values at E = 20 eV.(c) Loss spectra at different k || -values for the EG/Sn( √ 3) surface at E = 20 eV.The dotted lines in (b) and (c) are guides to the eyes and highlight the dispersion of the sheet plasmon.