Bias-controlled plasmon switching in lithium-doped graphene on dielectric model Al2O3 substrate

Graphene doped by lithium atoms supports a strong Dirac plasmon, a weak acoustic plasmon and a strong interband plasmon Li(π + σ). Here we demonstrate that applying a positive or negative bias on the lithium-doped graphene causes the appearance (‘switching ON’) or disappearance (‘switching OFF’) of the Li(π + σ) plasmon and the ‘conversion’ of the Dirac plasmon into a strong acoustic plasmon. This has two important consequences: 1. bias-controlled UV optical activity of the Li-doped graphene and 2. bias-controlled position of the 2D plasmon centroid. These effects turn out to be very robust and independent of the details of the experimental setup, which means that they should be easily experimentally verified, and very attractive for potential applications.


INTRODUCTION
Experimental study of the crystal and electronic structure of single-layer graphene (SLG) on the Al 2 O 3 1-5 , SiO 2 6-8 , or SiC 9-12 substrates obtained by chemical-vapor deposition (CVD) and/or exfoliation techniques is a widely explored methodology and becomes a routine. Moreover, in the recent years, various technologies, such as metal-free or metal-assisted graphene growth, have been developed. Using a metal-free method one can obtain a graphene film on insulated substrates directly, but so far only nanometer-scale graphene crystallites have been obtained, unless higher temperature 5 or longer process times 13 experiments were conducted. On the other hand, using a metalassisted three-step method 14 the noble or transition metals surfaces (Cu, Ag, or Ir) can be used to obtain high-quality micrometer-scale graphene crystallites on insulating surfaces [15][16][17] , such as e.g. syntheses of high-quality graphene on Al 2 O 3 (0001) surface assisted by Cu(111) surface.
The plasmonic properties of doped graphene on Al 2 O 3 , SiO 2 , or SiC in infrared and THz frequency range (interesting for application) have been experimentally and theoretically widely explored 3,4,[10][11][12][18][19][20] . These experimental studies show that graphene, when doped by electron donors or acceptors, supports a collective electronic mode called the Dirac plasmon (DP), which can be exploited in many plasmonics applications [21][22][23][24][25][26][27][28][29][30] . Graphene doped by alkali atoms, such as e.g. Li, Na, K, Cs on different metallic surfaces, such as e.g. Ir(111), Cu(111), and Ni(111) are extensively studied in many experimental or joined theoretical and experimental studies [31][32][33][34][35][36][37] . In these studies the most attention is paid to achieving self-standing (decoupled from the surface as much as possible) graphene with the lowest Moire corrugation. The plasmonic properties of the graphene epitaxial growth on metallic surfaces, such as Pt(111), Cu(111), or Ir(111) have been extensively studied [38][39][40][41] , and it has been shown that the metallic surface abundantly donates electrons to the graphene π band so that it supports a strong DP, which modifies under the influence of strong metallic screening and becomes an acoustic plasmon, which authors also called 'sheet plasmon resonance'. The electronenergy-loss-spectra (EELS) measurements of the plasmon spectra on simple metallic surfaces 42 or in the alkali metal bilayers deposited on the Cu(111) or Ni(111) surfaces [43][44][45] showed a negative surface-plasmon dispersion but also evidence of a multipole surface plasmon. Very recently, the Dirac and acoustic plasmons in the lithium-doped and cesium-doped graphene on Ir (111) surfaces have also been studied theoretically 46 .
All these studies show that the alkali-doped graphene (AC x ), where the electron or hole injection is achieved chemically, by means of electron donors or acceptors, offers some unexplored and exciting plasmonic properties which are not present in the electrostatically doped (biased) SLG, where the electron or hole injection is achieved by applying an external voltage to pristine graphene. In our recent theoretical investigations 47,48 we demonstrated that the alkali-doped graphenes LiC 2 , LiC 6 , CaC 6 , and CsC 8 support very strong DP and sometimes (depending on the alkali atoms) a weak acoustic plasmon (AP). The mechanism of the formation of a strong DP is well known. Alkali atoms abundantly donate electrons to the graphene layer, its π band becomes heavily doped which causes a substantial increase of the effective number of the 'free' charge carriers (electrons) and thus the DP spectral weight. On the other hand the alkali atoms in AC x usually form a superlattice, i.e. they metalize and form a parabolic σ band crossing the Fermi level. This band supports another plasmon which interacts with the DP in the graphene and becomes an acoustic like branch or AP [49][50][51] . The LiC 2 also supports an interband (intra-system) Li(π + σ) plasmon which is built from transitions between parabolic occupied Li(σ) and unoccupied Li (π) bands in Γ point of the Brillouin zone (BZ). On the other hand, the LiC 6 supports an inter-band inter-system plasmon (IP) built from the interband transitions between C(π) and Li(σ) bands.
In order to provide an accurate description and capture all interesting plasmonic effects in the calculations, it is important to include the Coulomb screening coming from the adjacent substrate. Our recent theoretical studies 52 show that a strong Ir (111) screening completely destroys the AC x plasmonics, so that e.g. in the cases of Li and Cs-doped graphene the DP is strongly suppressed, etc. Something similar applies to other metallic substrates such as Al(111), Au(111) or Cu(111). Therefore, in order to conserve all plasmonic properties of the alkali-doped graphene it is more appropriate to use wide band-gap semiconducting substrates, such as SiO 2 , SiC, or Al 2 O 3 . Their frequencyindependent dielectric functions (for ω < Δ, where Δ is the bandgap) just slightly red shift the 2D plasmon energy and just slightly reduce the plasmon oscillator strength.
In this paper, we investigate the intensity of the 2D plasmons in lithium-doped graphenes LiC x ; x = 2, 6 deposited on the Al 2 O 3 surface, where special attention is paid to exploring how the additional hole or electron injection, achieved through electrostatic bias, influences the interplay between the intra-band DP and the intra-band AP (or an inter-band plasmon IP), and 'switches ON or OFF' the interband Li(π + σ) plasmon. We show that if the holes are injected in the LiC 2 or in the LiC 6 the weak Landau-damped DP will be converted into a strong AP or IP, respectively. The hole injection also causes the appearance ('switching ON') and disappearance ('switching OFF') of the Li(π + σ) plasmon in LiC 2 and LiC 6 , respectively. Moreover, for larger wave vectors Q the injection of electrons in LiC 6 causes the appearance ('switching ON') of the Li(π + σ) plasmon. Both systems support a strong long wavelength DP which does not exist in the electrostatically doped SLG (here and throughout the paper the acronym SLG is used exclusively for the chemically undoped single layer graphene). The diversity of these extraordinary plasmonic properties can be very useful for plasmonic applications and should be easily verified experimentally.
In section "Methods", we present the method used to calculate the effective 2D dielectric function ϵ(Q, ω) of the LiC x /Al 2 O 3 composite. In section "Results" we present the results for the EELS~− =[1/ϵ] in the LiC 2 /Al 2 O 3 and LiC 6 /Al 2 O 3 composites, and the influence of the electrostatic bias to these spectra. To demonstrate how interesting these results are, we compare them with the spectra in the electrostatically biased SLG, where these effects do not appear at all. Finally, we emphasize the effects which could be interesting for plasmonic applications.

LiC 2 /Al 2 O 3 composite
The systems we study consist of graphene doped by lithium atoms LiC x deposited on an Al 2 O 3 surface (the LiC x /Al 2 O 3 composite), as shown in Fig. 1. The graphene layer is in the z = 0 plane, and is located at the distance h = 3.2 Å 2 from the Al 2 O 3 surface. The alkali atoms adlayer is in the z = d plane. Figure 2a and c shows the projected band structures of the LiC 2 and LiC 6 , respectively. For comparison, Fig. 2b and d shows projected band structures of the LiC 2 /Al 2 O 3 and LiC 6 /Al 2 O 3 composites, respectively. The orange color denotes the bands with the predominant C,Li(π) character, while the magenta color denotes the bands with the predominant Li(σ) character.
A large van der Waals equilibrium separation h results in a small electronic overlap between the LiC x slab and the Al 2 O 3 surface which enables us to calculate the dynamically screened Coulomb interaction of LiC x /Al 2 O 3 composite by combining the LiC x noninteracting electrons response function χ 0 LiCx and Al 2 O 3 macroscopic dielectric function ϵ S , as will be explained below. This considerably reduces the unit cell size and significantly saves the computational time and memory requirements. This will be especially useful when studying the dynamical response in LiC x / Al 2 O 3 composite for different biases V ≠ 0 or E F ≠ 0.
We show the EELS intensities in lithium-doped graphene LiC 2 and LiC 6 for various electrostatic biases and for two different wave vectors Q. In order to demonstrate the robustness and diversity of the extraordinary plasmonic properties in chemically doped graphene LiC x , we compare them with the EELS intensities in the equivalently electrostatically biased SLG. All 2D structures are deposited on Al 2 O 3 surface, as shown in Fig. 1. It should be noted that we have chosen for the alkali atoms to be adsorbed on the graphene and the wide band-gap semiconducting Al 2 O 3 surface to be used as the substrate. This choice is important, because when the alkali atoms are intercalated between the graphene layer and the metallic substrate, as shown in ref. 46 where LiC 2 or CsC 8 are at the equilibrium separation h from the Ir(111) surface, the substrate destroys the DP and AP, although even a small displacement from the equilibrium position causes both plasmons to recover. This is what motivated us to use the semiconducting surface instead of a metallic one (in order to avoid strong metallic screening which destroys the DP) and to adsorb rather than intercalate the alkali atoms (in order to protect the Li(σ) band which supports the AP). This enables both the AP and DP to survive for the realistic equilibrium LiC x /Al 2 O 3 distances. Moreover the only effect of the insulating surface is that it slightly red shifts the 2D plasmon energy and slightly reduces the plasmon oscillator strength in comparison with the self-standing case. In other words, changing the height h only slightly influences the plasmon properties. This was verified computationally but is not presented here. Figure 3a and b shows the EELS intensities in LiC 2 / Al 2 O 3 composite for wave vectors Q = 0.054 a.u. and Q = 0.148 a. u., respectively, as functions of the Fermi energy E F (modified by the electrostatic bias). Our energy scale is set so that the Fermi level of the unbiased composite is E F = 0, so E F < 0 or E F > 0 means that the holes or electrons are injected in the sample, respectively. The upper (red) scale at the abscissa shows the Fermi energy with respect to the graphene Dirac point, e.g. the Fermi energy of the unbiased LiC 2 , with respect to the Dirac point, is E F = 1.78 eV (also shown by the vertical lines in the figure). The horizontal line (v π F Q) denotes the upper edge of C(π) intra-band and the sloped line (2E F À v π F Q) denotes the lower edge of the C(π) inter-band electron-hole continuum in the Dirac cone approximation. Figure 3a shows that the unbiased LiC 2 supports a very weak AP, very strong DP, and just emerging (for the wave vector Q = 0.054 a.u.) Li(π + σ) plasmon. The AP and DP are intra-band plasmons built from the intraband transitions within C(π) and Li(σ) bands crossing the Fermi level, as shown in Fig. 2a and b. Li(π + σ) is an interband plasmon built from the transitions between the parabolic Li(σ) and Li(π) bands around the Γ point, as denoted in Fig. 2a and b. If we inject extra electrons in the system (E F > 0) the number of the effective charge carriers increases so the DP frequency and intensity increases, while the AP and Li(π + σ) plasmon remain weak. It is important to note that the DP intensity is greatly enhanced and it becomes the dominant mode in the entire spectra. On the other hand, as can be seen in Fig. 3e, the DP in SLG for the equivalent bias (E F > 1.78 eV) does not even exist. For the larger wave vector Q = 0.148 a.u., as shown in Fig. 3b, the unbiased (E F = 0) LiC 2 supports a very strong Li(π + σ) plasmon, weaker (Landau damped) DP and weak AP. If we inject extra electrons in the system (E F > 0) the Li(π + σ) plasmon for (E F ≈ 0.25 eV) becomes even sharper and a more intensive collective mode. The DP frequency and intensity increases following the same pattern as in the SLG shown in Fig. 3f. We can also see that the DP in SLG is more intensive.
However, when holes are injected in the system (E F < 0) some extraordinary effects occur. In addition to the expected fast decrease of the energy and intensity of the DP, for E F < −0.5 eV we can notice the significant increase of the Li(π + σ) plasmon intensity, or 'switching ON' of the Li(π + σ) plasmon. On the other hand, as shown in Fig. 3e, at similar frequencies the SLG supports just a broad π plasmon, with frequency independent of the bias. For large hole doping (E F < −1 eV) the strong DP approaches the weak AP (with frequency almost independent of the bias), and at E F ≈ −1.3 eV these two modes overlap and hybridize, leading to the avoided crossing. We can see that with the increase of the hole injection the DP intensity weakens, while the AP intensity increases, so the AP assumes the role of the DP, and its frequency becomes dependent on the bias until it reaches ω = 0.
This effect is even more evident for the larger wave vector Q = 0.148 a.u., shown in Fig. 3b. As the hole injection increases the DP frequency and intensity decreases, almost the same way it does in the chemically intrinsic graphene, shown in Fig. 3f. For any hole injection the DP is Landau damped by the C(π) inter-band electron-hole excitations (since it is above the 2E F À v π F Q line) but for the hole injection E F < −1.2 eV it enters the C(π) intra-band continuum v π F Q. Again, for weak hole injection the AP frequency barely depends on the bias, but for stronger hole injection the AP intensity increases while the DP intensity decreases and its frequency approaches the AP frequency. Finally, for E F ≈ −0.75 eV we have the hybridization leading to the avoided crossing and the AP takes over. It becomes a well-defined collective mode and its frequency decreases with the increase of the hole injection, until it reaches ω = 0. For E F < −0.75 eV, contrary to the DP, the AP is below the v π F Q line and above the 2E F À v π F Q line, which means that it is completely immersed in the C(π) intra-band and interband electron-hole continuum. However, due to its Li(σ) character it remains a sharp and undamped plasmon mode.
The Li(π + σ) plasmon also shows interesting behavior, which could be very interesting for potential applications in the UV frequency range. Namely, already for the light hole injection E F ≤ −0.25 eV the Li(π + σ) intensity considerably increases so that its oscillatory strength becomes an order of magnitude larger than the Landau-damped DP (as also shown in Fig. 4b). The Li(π + σ) remains strong well-defined interband plasmon as the hole injection increases, until it reaches E F ≈ −1.2 eV when the plasmon intensity rapidly drops to zero. This interplay between the AP and the DP and the appearance of the strong Li(π + σ) plasmon, of course, does not occur in chemically undoped graphene, as can be seen in Fig. 3f. This is even more evident from Fig. 4, which show the evolution of EELS in the LiC 2 /Al 2 O 3 composite as a function of the increasing hole injection (positive bias) for the transfer wave vector, Q = 0.148 a.u. Figure 4a shows the unbiased sample (E F = 0) and the three plasmons we already described: a weak AP, a somewhat stronger DP, and a very strong Li(π + σ) plasmon, and Fig. 4b-h show how these plasmons change as we inject the holes in the system. Figure 4 also shows (magenta line) the real part of the effective 2D dielectric function (<ϵ). In Fig. 4a we can see that the <ϵ has 'kinks' at the DP and AP frequencies, but it does not have a zero. On the other hand the <ϵ has a zero exactly at the Li (π + σ) peak which means that it is a well-defined collective mode (plasmon). In the unbiased system the Li(π + σ) plasmon is still broad and dispersive, however, Fig. 4b shows that already for small hole injection (E F = −0.24 eV) it becomes a sharp plasmon, slightly red shifted. Figure 4c and d shows that with the further hole injection the Li(π + σ) plasmon becomes sharper and more red shifted. This phenomenon can be explained by observing the band structure in Fig. 2a, b. As the hole injection increases (i.e. the Fermi level decreases) the part of the Li(σ) parabolic band below the Fermi level becomes more similar to the part of the Li(π) parabolic band exactly above it. This means that for the larger biases all the occupied Li(σ) states can be almost perfectly transferred into the unoccupied Li(π) states. In other words, this causes coherent electron-hole transitions from the parabolic Li(σ) band into the parabolic Li(π) band and finally a well-defined collective mode, with energy higher than the energy of the singleparticle Li(σ) → Li(π) electron-hole transitions. Also, Fig. 4a-d clearly shows that the DP intensity and energy decrease with the increase of the hole injection, as expected. However, we also see something quite unexpected: as the DP intensity decreases the AP intensity increases and the mode is weakly red shifted. This phenomenon becomes especially intriguing for stronger bias.  Fig. 4e, the <ϵ starts has a zero at the AP. This classifies the AP as a well-defined collective mode, and in EELS it also appears as a sharp, welldefined peak. This becomes especially noticeable in Fig. 4f, g, showing the EELS for E F = −1.19 eV and E F = −1.43 eV, respectively. The AP takes over the entire spectral weight of the lowenergy EELS and it behaves almost as an ideal bosonic mode (or ideal harmonic oscillator) with <ϵ $ 2ω AP =ðω 2 À ω 2 AP Þ and where ω AP is the AP frequency. For even larger bias, E F = −1.67 eV, although the <ϵ still has a zero at the AP peak, and the AP is still a well-defined bosonic mode, the AP intensity starts to decrease. This is because the AP is mostly built from the transitions within the Li(σ) band, and for bias this large the Fermi energy is already very close to the bottom of that band, as can be seen at the Γ point in Fig. 2a, b. As a result of this, the number of the charge carriers involved in the formation of the AP becomes drastically reduced and the AP oscillator strength weakens. As already mentioned, for larger hole injections the AP frequency changes towards ω = 0. Figure 4e-h also show that for the larger biases the <ϵ still has a zero at Li(π + σ) plasmon peak, which means that it remains a well-defined collective mode. Moreover, the Li(π + σ) plasmon intensity rapidly decreases with the hole injection, even faster than the AP, although the reason is the same: the Li(σ) band gets less populated and consequently there are less available electrons which can be excited into the unoccupied Li(π) band. In order to demonstrate that the interesting plasmonic properties are not limited to specific Li atoms coverage, in Fig. 3c, d we show the EELS intensities in the LiC 6 /Al 2 O 3 composite for Q = 0.063 a.u. and Q = 0.149 a.u., respectively. We can see that for for Q = 0.063 a.u. the unbiased sample (E F = 0) also supports a strong DP and a much stronger (and red shifted in comparison with LiC 2 ) Li (π + σ) plasmon. Also at about ω ≈ 0.8 eV we can see the so-called interband plasmon (IP) which originates from the interband transitions between the C(π) and the Li(σ) bands, as indicated in Fig. 2c, d. This means that, contrary to the interband Li(π + σ) plasmon, the IP is an inter-system plasmon and represents the charge density oscillations between the graphene and the Li adlayer, perpendicular to the LiC 6 surface 48 . As we increase the hole or electron injection the DP behaves almost the same as in the LiC 2 . We can see that the Li(π + σ) plasmon in the LiC 6 exists mostly for electron injection (opposite from the LiC 2 ), where it develops in a very intensive plasmon, comparable with the DP. However, already for a small hole injection (E F < −0.4 eV) the Li(π + σ) plasmon suddenly disappears. Figure 2c, d show us that this happens because in this case the parabolic Li(σ) is much closer to the Fermi level of the unbiased system, and as the Fermi level is shifted to E F < −0.4 eV, the band becomes empty, so there are no more charge carriers to participate in the formation of Li(π + σ) plasmon. This enables the 'switching OFF' of the very strong Li(π + σ) plasmon by a small negative bias. This phenomenon, although in the opposite direction, occurs in the LiC 2 , where small positive bias 'switches ON' the Li(π + σ) plasmon, as demonstrated in Fig. 5. The IP is weaker but exists for all shown electron injections (E F > 0). For the hole injection (E F < 0) it slightly strengthens and for (E F < −0.4) its frequency decreases and it suddenly disappears. We need to point out something very interesting: the unbiased LiC 6 (similar to the unbiased LiC 2 ) supports very strong DP which, together with the Li(π + σ) for reasonable small electron injection becomes the dominant collective mode in the entire EELS. This is completely opposite to SLG which does not support any collective modes for the equivalent electrostatic biases, as can be seen in Fig. 3e.
For the larger wave vector Q = 0.149 a.u. shown in Fig. 3d and the electron injection (E F > 0) the LiC 6 supports a DP substantially stronger than the DP in the LiC 2 or in the SLG. This is unusual considering that the DP is here also above 2E F À v π F Q line, i.e. it is immersed in the inter-band C(π) electron-hole continuum. The Li (π + σ) plasmon does not exist for the hole injection (E F < 0), for the unbiased sample (E F = 0) it is broad and weak, and for the electron injection (E F > 0) it suddenly develops in a broad but strong plasmon mode. We can notice that even a very small electron injection (E F > 0.25 eV) causes the 'switching ON' of the Li (π + σ) plasmon. The IP is blue shifted and much stronger than the IP for the smaller wave vector Q. For a small hole injection (−0.3 < E F < 0 eV) the IP is very strong and for larger hole injection (E F < −0.4 eV) its frequency decreases toward ω = 0 until the mode suddenly disappears. For the electron injection (E F > 0) the IP's frequency barely depends on the bias but the mode remains substantially strong and well defined. We can notice that the IP in LiC 6 in many ways mimics the AP in the LiC 2 . It is the plasmon with  the lowest energy, for the hole injection it is strong and its frequency strongly depends on the bias, while for the electron injection it is weaker and its frequency weakly depends on the bias. As the DP weakens, the IP strengthens, and finally the DP-IP avoided crossing is noticeable. Actually, this correspondence is very unusual, considering that the IP is an inter-system and interband plasmon while the AP is an intra-system and intra-band plasmon.
For the hole injection (E F < 0), the LiC 6 also supports a very broad π plasmon, weaker but similar to the one in the SLG, shown in Fig. 3e and f. For the electron injection, especially when the Fermi energy is above the van Hove singularity at M point (which corresponds to E F > 1.8 eV with respect to the Dirac point) the π plasmon disappears. This is especially obvious in Fig. 3e. The LiC 2 does not support the π plasmon but just some remains of this mode which can be noticed in Fig. 3a.
Finally, we need to emphasize that the LiC 6 supports two very intensive interband plasmons; 1. the already described IP which is mainly in the IR frequency range 0.6 < ω < 1.5 eV and 2. the Li(π + σ) plasmon which is in the UV 3 < ω < 6 eV frequency range. Frequency and intensity of either mode can be easily manipulated by injecting the electrons or holes in the sample which can be very attractive from the aspect of their applications. For example, Fig. 3c shows that small hole injection in the LiC 6 causes the 'switching OFF' of the Li(π + σ) plasmon, and Fig. 3d shows that small electron injection causes the 'switching ON' of the Li(π + σ) plasmon. Moreover, Fig. 3d suggests that small hole injection can be used to 'switch OFF' the IP plasmon which exists in the unbiased system.

DISCUSSION
We need to emphasize that Figs. 4 and 5 show two very interesting physical phenomena which are experimentally feasible and could be very useful in plasmonic application.
1. Light hole injection (E F < −0.3 eV) of the LiC 2 /Al 2 O 3 system causes the appearance of a strong Li(π + σ) plasmon with a frequency in the UV range. As can be seen in Figs. 5 and 3a this effect is especially pronounced for smaller wave vectors Q = 0.054 a.u. when a small increase of the hole injection causes the appearance (or 'switching ON') of the Li(π + σ) plasmon. On the other hand, as shown in Fig. 3c, quite the opposite occurs in the LiC 6 where a small hole injection causes the disappearance (or 'switching OFF') of the strong Li(π + σ) plasmon. 2. Heavier hole injection (E F < −0.9 eV) of the LiC 2 /Al 2 O 3 system causes the AP to become extraordinarily strong, taking the role of the DP which gets completely suppressed. This is nicely demonstrated in Fig. 6 showing the interplay between the DP and AP plasmons in LiC 2 /Al 2 O 3 composite for three different biases. Applicational aspect of this effect is moving the plasmon oscillations from the graphene layer to the Li add-layer and vice-versa. Namely, the DP represents the in-plane charge-density oscillations predominantly localized within the graphene layer, while the AP represents the in-plane charge density oscillations which are predominantly localized within the Li add-layer 47 . This means that the plasmon can be moved from one to another crystal plane by changing the bias, as denoted in Fig. 6.
The weakening of the DP is not surprising. As shown in Fig. 3b and f, and already explained, for the hole injection E F < −0.9 eV (or E F < 0.88 eV in SLG) the DP is far above the inter-band line ω ¼ 2E F À v π F Q and it approaches the intraband line v π F Q which means that the DP is strongly damped by the C(π) intra-band and interband electron-hole excitations. However, the question why the AP intensity increases with the hole injection is very intriguing? The answer is the screening of the AP by the approaching DP. Figure 3a and b shows that, while the DP and the AP are far away, the AP's frequency barely changes as a function of bias. However, as the hole injection is increased, the DP (with the frequency highly dependent of the bias) reaches the AP, and the already described avoided crossing occurs. This means that AP and DP strongly interact exchanging their symmetry and other properties. The crucial consequence of this interaction is that for high hole doping the <ϵ has a zero the AP (see Fig. 4e), meaning that all the available 'free' charge carriers are employed in the formation of the collective mode, which results in the strong AP peak. The question is also why the AP is not damped by the C(π) intra-band and inter-band electron-hole excitations, even though for E F < −1.0 eV its frequency is ω AP < 1.5 eV, which means that it is immersed in the continuum of these excitations (see Fig. 3b). This is due to the symmetry reason, since the AP has Li(σ) intra-band character and it weakly interacts with the C(π) electron-hole excitations.
We demonstrated that the chemically doped graphenes LiC x / Al 2 O 3 ; x = 2, 6 support plasmons, such as the Li(π + σ) plasmon or AP, which do not exist in chemically undoped graphene (SLG). It is especially important that these plasmons can be easily manipulated by injecting extra electrons or holes in the sample by applying a bias voltage. For example, by changing the electron or hole injection of the LiC x /Al 2 O 3 sample the Li(π + σ) plasmon can be 'switched ON' or 'OFF' or the DP can be 'converted' into the AP (or the IP in the LiC 6 ), and vice versa. The plasmonic properties of LiC x /Al 2 O 3 composites for the electron (E F > 0) and hole (E F < 0) injections and for different wave vectors Q are highlighted in Table 1.
Finally, the crucial property of the composites studies in this paper is the robustness of these extraordinary plasmonic properties. The results presented in this paper, combined with some additional calculations, not presented here, show that the 'switching' and 'conversion' effects do not depend on the choice of the substrate, the concentration of the chemical doping, or the choice of the alkali atom used as the dopant. Also the effects do not depend on the relative position of the alkali addlayer, i.e. they will not significantly change if the alkali atoms were intercalated (between graphene and the substrate) instead of being deposited on the graphene layer. This means that these effects should be easily measurable without too much attention on the preparation of the sample.

Calculation of the effective 2D dielectric function
To calculate the Kohn-Sham (KS) wave functions ϕ nK and energy levels E n (k), i.e. the band structure, of LiC x , x = 2, 6 slabs and bulk Al 2 O 3 crystal we use the plane-wave self-consistent field DFT code (PWSCF) within the QUANTUM ESPRESSO (QE) package 53 . The core-electrons interaction is approximated by the norm-conserving pseudopotentials 54 . The XC potential in the LiC x is approximated by the Perdew-Zunger local density approximation (LDA) 55 , and in the Al 2 O 3 by the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) 56 . The ground state electronic densities for LiC 2 , LiC 6 , and Al 2 O 3 are calculated using the 12 × 12 × 1, 9 × 9 × 1, and 9 × 9 × 3 Monkhorst-Pack 57 K-point mesh sampling of the first BZ, respectively. For all systems the plane-wave cut-off energy is chosen to be 60 Ry (816 eV).
With respect to graphene, LiC 2 and LiC 6 form a 1 × 1 and ffiffi ffi 3 p ffiffi ffi 3 p 2D hexagonal Bravais lattice with the unit cell constant a = 4.65 a.u. and a = 8.056 a.u. 58  bands, respectively. In the χ 0 LiC2 and χ 0 LiC6 calculation the damping parameter is η = 20 meV and in χ 0 S calculation η = 100 meV. Even though the transfer wave vectors in the direction parallel to the slabs Q = (q x , q y , 0) considered in this investigation satisfy the condition Q = |Q| << 2π/a the crystal local field effects should be carefully treated. Namely, the strong dispersivity of the LiC x dielectric response in the perpendicular direction (z) requires the inclusion of the crystal local field effects in the z direction. This means that LiC x response functions are nonlocal in the perpendicular direction and can be Fourier transformed as χðz; z 0 Þ ¼ 1 are the reciprocal space vectors. The crystal local field energy cut off is 10 Ry (136 eV), which corresponds with 23G z wave vectors. The dielectric response of the bulk Al 2 O 3 crystal is calculated in an optical limit, i.e. the crystal local field energy cut-off is set to be zero.
The dynamically screened Coulomb interaction in the AC x slabs can be calculated by solving the Dyson equation Q e ÀQjzÀz 0 j is the bare Coulomb interaction 60 , and R c=2 Àc=2 dz. The interaction between the charge density fluctuation at z > −h and the charge density fluctuation at z 0 > Àh in the vicinity of a polarizable Al 2 O 3 surface is mediated by the surface screened Coulomb interaction w S instead of the bare Coulomb interaction v, where w S ¼ v þ D S e ÀQðzþz 0 þ2hÞ : jqj 2 χ S is the Al 2 O 3 macroscopic dielectric function, where q = (q x , q y , q z ) is the 3D transfer wave vector). When the LiC x is deposited on the polarizable Al 2 O 3 surface, and the replacement v → w S is made, the dynamically screened Coulomb interaction of the entire AC x /Al 2 O 3 composite is obtained by solving the 'screened' Dyson equation: The effective 2D dielectric function can then be defined as where v Q ¼ 2π Q , and finally the EELS is calculated as SðQ; ωÞ ¼ À 1 π =ϵ À1 ðQ; ωÞ.
The validity of the model Efficient extensive investigation of the doping-dependent plasmonics in LiC x /Al 2 O 3 composites heavily depend on two very rigorous approximations: 1. Rigid bands approximation (RBA), where we 'freeze' the band structure and the charging of the system is simulated by shifting the Fermi level. This allows us to calculate the band structure of LiC x only once which significantly simplifies the calculation. 2. Van der Waals limit, where we assume that the LiC x and Al 2 O 3 interact only via the long-range fluctuation-fluctuation Coulomb interaction and the band structure is weakly affected by the Al 2 O 3 substrate. This allows us to calculate the LiC x and the Al 2 O 3 dynamical response functions χ 0 ACx and D S separately, and then link them via Coulomb interaction, which saves the computational time tremendously. In order to use these approximations, we need to verify their validity.
The validity of the RBA The validity of the RBA can be checked by comparing the spectra calculated using the RBA with those obtained using the injected charge model (ICM) with the injected charge ΔQ TOT chosen to cause the RBA Fermi level shift E F . In the ICM we add extra charge to the unit cell, relax the unit cell and the atomic coordinates, calculate new KS wave functions and band structure and finally calculate the EELS.
We performed the ICM calculation for two characteristic RBA Fermi level shifts E F = −0.5 eV and E F = 0.5 eV. For the LiC 2 these shifts correspond to the extraction of 0.44 and the injection of 0.4 electrons per unit cell, respectively, while for the LiC 6 they correspond to the extraction of 0.77 and the injection of 1.06 electrons per unit cell, respectively. The characteristic parameters such as the injected charge ΔQ TOT , the relative changes of the lattice constant Δa/a and the change of the Li-C separation (with respect to the RBA) Δd are listed in Table 2. For LiC 2 we can see that the hole injection (ΔQ TOT = − 0.44) weakly affects the crystal lattice, causing only a 0.1% increase of the unit cell, while the Li-C separation remains unchanged. On the other hand, the electron injection (ΔQ TOT = 0.4) causes a 2.4% increase of the unit cell, while the Li-C separation decreases for even 0.48 Å. The opposite happens for LiC 6 , the hole injection (ΔQ TOT = −0.77) causes a −1.4% decrease of the unit cell, while the Li-C separation increases for 0.12 Å. The electron injection (ΔQ TOT = 1.06) causes a −0.1% decrease of the unit cell, and the Li-C separation almost does not change. Figure 7 shows comparisons of the EELS intensities calculated using the RBA (black solid) and the ICM (brown dashed), for two different wave-vector transfers and two different biases for each of the two systems, as described in the figure caption. Figure 7a shows the EELS intensity in LiC 2 for the hole injection E F = −0.5 eV (ΔQ TOT = −0.44), and we can see that the spectra agree perfectly, as could be expected considering that for the hole injection the ICM crystal structure changes only negligibly. However, as can be seen in Fig. 7b, for the electron injection E F = 0.5 eV (ΔQ TOT = 0.4) the spectra noticeably differ, i.e. the DP in the ICM spectrum is about 0.3 eV blue shifted. This is because the ICM Li-C separation decreases (with respect to the RBA one), the charge transfer from Li(σ) to C(π) band is larger, filling the Dirac cone and causing Wave vector Hole injection (E F < 0) Li(π + σ) 'ON' DP → AP Li(π + σ) 'OFF' DP → IP Electron injection (E F > 0) DP * DP * Li(π + σ) 'ON' DP* denotes very strong DP which does not exist in chemically undoped graphene (SLG).
the blue shift of the DP. Moreover, the DP obviously interacts more with different interband excitations and becomes broader. Also, the ICM spectrum shows a sharp peak at about 6.5 eV which does not exists in the RBA spectrum. Regardless of these differences the RBA and ICM spectra still qualitatively agree very well showing the most important features such as the weak AP, the strong DP and the Li(π + σ) plasmon. The LiC 6 spectra show the opposite trend, i.e. the agreement is perfect for the electron injection (due to unchanged Li-C separation and only minor changes of the unit cell), as shown in Fig. 7d, while for the hole injection E F = −0.5 eV (ΔQ TOT = −0.77), as shown in Fig. 7c the RBA and ICM spectra qualitatively agree very well, both spectra show the same features, a weak IP, a strong DP, and a Li(π + σ) plasmon, but the ICM DP is now about 50 meV red shifted which is a consequence of the 0.12 Å increase of Li-C separation, which reduces the doping of the Dirac cone and hence reduces the DP frequency. Also the ICM IP and Li(π + σ) plasmons are slightly more intensive. Figure 7e-h compare the RBA and ICM EELS intensities in LiC 2 and LiC 6 for the wave-vector transfer Q ≈ 0.15 a.u., while the parameters ΔQ TOT and E F are the same as in Fig. 7a-d. We can notice the same behavior as for the smaller wave-vector transfers. For LiC 2 when the holes are injected, the RBM and ICM spectra coincide, but when the electrons are injected, the ICM DP is blue shifted, although this time it is a much sharper (narrower) mode than the RBA one. In addition to that, the ICM AP is slightly blue shifted. For LiC 6 the hole doping causes the ICM IP and Li(π + σ) plasmon to be more intensive, while the weak DP is only slightly red shifted. For electron doping both spectra coincide showing important IP, DP, and Li(π + σ) plasmons. For larger hole (E F < −0.5 eV) injections in LiC 2 and larger electron (E F > 0.5 eV) injections in LiC 6 , the RBA and ICM spectra remain in good agreement. However, for larger electron (E F > 0.5 eV) injections in LiC 2 and larger hole (E F < −0.5 eV) injections in LiC 6 , the disagreement increases and the RBA can no longer be considered a reliable model. Finally, we can conclude that for E F ∈ [−0.5, 0.5] eV both ICM and RBA methods provide the most important plasmons such as AP, IP, DP, and Li(π + σ), and that their energies and intensities agree qualitatively well (and in some cases even perfectly well). The RBA only affects the intensities of the IP, AP, DP, or Li(π + σ) plasmons, and caused a small red or blue shift of the DP, but it does not contradict the interesting plasmonic phenomena which will be explained later. This definitely justifies the usage of the computationally much more efficient RBA method.
The validity of the van der Waals limit In the van der Waals limit we assume that the LiC x and Al 2 O 3 surfaces interact only via the long-range fluctuation-fluctuation Coulomb interaction and that the individual LiC x and Al 2 O 3 orbitals and band structures remain unaffected. In order to verify the validity of this limit we compare the band structures of the self-standing LiC x samples with the band structures of the LiC x /Al 2 O 3 composites. Special attention is paid to exploring how much the Al 2 O 3 (111) surface affects the parabolic Li(π) and Li(σ) bands, and the conical C(π) band, which are responsible for the formation of the AP, IP, DP, and Li(π + σ) plasmons.
The crystal structure of the LiC x /Al 2 O 3 composites with minimal strain consist of huge supercells which exceed 200 atoms. Applying bias, to the system (via ICM) would require additional relaxation of the crystal structure, which would be computationally extremely difficult and the plausibility of the obtained result would be questionable. Therefore, we rather use smaller cells with larger strains, taking into account that this should not disturb the plausibility of the results of the band structure. The Al 2 O 3 surface is modeled by three chemically compensated atomic layers O-Al-O obtained by cutting the bulk α-Al 2 O 3 polymorph along the (111) plane. The crystal structure of the LiC 2 /Al 2 O 3 composite is then modeled so that the Al 2 O 3 (111) surface is biaxially strained by 2.4% in order to match the 2 × 2 graphene unit cell. The orientation of the LiC 2 crystal is chosen so that the Li atoms match the (111) hollow sites. The supercell obtained in this way consists of 20 atoms. The crystal structure of the LiC 6 /Al 2 O 3 composite is modeled in an equivalent way, only the Al 2 O 3 is biaxially compressed by 11.3%, in order to match the graphene ffiffi ffi 3 p ffiffi ffi 3 p unit cell. The supercell obtained this way consists of only 15 atoms. The orientation of the LiC 6 crystal is chosen so that the C atoms match the position of the topmost oxygen atoms. In both cases the separation between the topmost oxygen layer and the graphene layer is fixed to h = 3.2 Å. The ground state electronic densities are calculated using the 13 × 13 × 1 K-point mesh sampling and the plane-wave cut-off energy is chosen to be 50 Ry. The crystal structures of the LiC x /Al 2 O 3 composites are sketched in Fig. 2 insets.
The arrows in Fig. 2a and b denote the inter-band transitions between the Li(σ) and Li(π) bands responsible for the occurrence of the Li(π + σ) plasmon in the LiC 2 , while the arrows in Fig. 2c, d denote the inter-band transitions between the Li(σ) and C(π) bands responsible for the occurrence of the inter-band inter-system IP plasmon in the LiC 6 .
We can see that depositing the LiC 2 on the Al 2 O 3 (111) surface does not destroy the graphene C(π) cone and parabolic or the Li(σ) bands. The only difference is that the parabolic Li(σ) band is moved slightly down, by about 100 meV. On the other hand, we can see that the charge transfer into the graphene C(π) cone is negligible and the Dirac point remains~−1.8 eV below the Fermi level. The effect of the substrate on the LiC 6 band structure is similar. The graphene C(π) and parabolic Li(σ) bands remain preserved. However, the Li(σ) band is shifted slightly up, by about 200 meV. Also the C(π) band is modified so that the gap at the Γ point slightly increases.
In conclusion, we can say that the relevant bands, the parabolic Li(π) and Li(σ) and the conical C(π) bands, are not changed significantly by the substrate, and that the modifications we mentioned are negligible and cannot affect the plasmonic phenomena. This means that the van der Waals limit can be considered as fully justified.

DATA AVAILABILITY
The data generated during this study is available from the corresponding author on reasonable request.