Effective Screening and the Plasmaron Bands in Graphene

Home , Plasmaron

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Andrew 3,4 tunnelling , ad rmtehl ad sn nl eovdPhotoEmissio Resolved Angle using bands hole gr subs the the different from of four bands environment on graphene dielectric for the screening on enviromental predicte depend been to has expected coupling is this of strength The excitation. osbeuei pamrnc devices. ”plasmaronic” in use possible a htpamrnadeetoi rpriso rpeecnbe can graphene of properties electronic and plasmaron dielectric effective that the determine to used are predictions 1 lcrnpamnculn ngahn a eetybe sh been recently has graphene in coupling Electron-plasmon on u Chang Jun Young , 1 .INTRODUCTION I. rtdsusdterl fitrcin be- interactions of role the discussed first 5 5 n nl eovdphotoemission resolved angle and 1 ET siuoNnsineCRadSul oml Superio Normale Scuola and Nanoscienze-CNR Istituto NEST, , G 2 fetv cenn n h lsao ad nGraphene in bands plasmaron the and screening Effective ,a 0 W ao Bostwick Aaron , 6 colo hsc,IsiuefrRsac nFnaetlSc Fundamental in Research for Institute Physics, of School RAter,ta hs r in are these that theory, -RPA 1 , 2 3 ac Polini Marco , 6,7,10 colo lcrclEgneig nvriyo Ulsan, of University Engineering, Electrical of School ri-omlSrse1 15 ragn Germany. Erlangen, 91058 1, Erwin-Rommel-Strasse rt-ae-ntttdrMax-Planck-Gesellschaft, der Fritz-Haber-Institut 8,9 .O arneBree ainlLaboratory, National Berkeley Lawrence O. E. 7 nvriySainC60 utnT 78712 TX Austin C1600, Station University 1 7 . et fPyis nv fTxsa Austin, at Texas of Univ. Physics, of Dept. oee oex- no however , rvdn moti- a providing aaawg46 49 eln Germany, Berlin, 14195 4-6, Faradayweg ag,Usn 8-4,SuhKorea South 680-749, Ulsan, Namgu, 1 2 4 7 iJo Jeon Ki-Joon , ekly aiona970 USA, 94720, California Berkeley, h depen- The . eateto oeua Physics, Molecular of Department 1 nvri¨tErlangen-Nürnberg,Universität erth ¨rTcnsh Physik, Technische für Lehrstuhl dacdLgtSuc (ALS), Source Light Advanced a ern13553,Iran. 19395-5531, Tehran 5 mi:[email protected] email: eaAsgari Reza , Dtd uy3 2018) 3, July (Dated: 2 r of ure later and he a- nt r- i- e 6 - t 3 lra Speck Florian , osato h neligsbtaelyr eas show also We layer. substrate underlying the of constant 6 i adtutr fgraphene of bandstructure tic fluorine , aesof layers rnfrigi nogahn.Wietesnl rpeela graphene single on the While graphene. into it transforming aeterl fsbtaesreigo h adstructure. band the on inve screening substrate to of suited role ideally the is gate graphene properties, unique other opsto fteSiC(0001) the of composition yfrhrtemldcmoiinaedculdfo h sub underlying the from strate/ decoupled are decomposition for thermal layers further subsequent by The graphene. of characteristic ture et niaearneo usrt fetv ilcrcco dielectric effective substrate of ( stants range a indicate ments de graphene const coupling n-type dependent, α of substrate single, function a spectral on only the ef- pends cases the sh all and characterize in bands We plasmaronic that the on substrates graphene. differing of the the fect in of differences screening considerable experi- fective exhibit previous to from results, expected, are mental These H-SiC. and F-SiC et fgahn nSCwt ordfeetitraelayer interface different four with (6 SiC on graphene of ments measure- (ARPES) Spectroscopy Photoemission Resolved gle t01 V(uSC,01 V(-i)ad07 V(F-SiC). eV 0.79 and (H-SiC) eV 0.18 (Au-SiC), eV 0.15 at scvlnl oddt h usrt.Ti rae a creates This substrate. the to bonded covalently is .5eV 0.45 odpn nteefciesreig hc nturn in which screening, effective the on depend to d rtsb vlaigtesprto fteplasmaron the of separation the evaluating by trates √ G 6 neednl aiuae,a motn setof aspect important an manipulated, independently √ ntefis eaoa abnlyrfre ytemlde- thermal by formed layer carbon hexagonal first the In la .MacDonald H. Allan , 6 3) peeset eew opr h teghof strength the compare we Here sheet. aphene eadeso h oiglvl nlsso h measure- the of Analysis level. doping the of regardless 3 √ w ogv iet pamrn quasiparticle ”plasmaron” a to rise give to own R pcrsoy oprsnwith Comparison Spectroscopy. n × 3 ǫ 30 20 S -SCi -yewt h ia crossing, Dirac the with n-type is SiC C- 6 18 6 √ ◦ ∼ rpeefre yitraaini -yewith p-type is intercalation by formed graphene √ ae htde o hwtelna adstruc- band linear the show not does that layer C n gold and 3) 4 3 87 aksOstler Markus , R nSC eopigi rmtesbtaeand substrate the from it decoupling SiC, on C to 30 e -62 ia Italy. Pisa, I-56126 re, ◦ ∼ 6 ecs(IPM), iences √ -i (henceforth C-SiC 19 7 3 . 8 aebe hw oitraaeunder intercalate to shown been have ae n xii h characteris- the exhibit and layer C niaigta,i diint many to addition in that, indicating ) 7 ase Horn Karsten , 4 14 11–13 hmsSeyller Thomas , rvosyhydrogen Previously . ufc,eeytidatom third every surface, G 0 6 W √ 2 l Rotenberg Eli , -RPA 3 -i) Au-SiC, C-SiC), 4 Luca , E D (6 at , √ 6,15–17 med 3 E ∼ yer sti- ant ow ef- n- × D s: - - - 2

To investigate the plasmaronic bandstructure, these intercalated systems were converted to n-type by chemical doping with K atoms.

II. BACKGROUND

The, n-type, Dirac cone picture of the electron dispersion near the Fermi energy, EF , in graphene is shown in Fig. 1 A for the non-interacting, single-particle description. In this case the bands are linear and form two cones which meet at a single point at the Dirac energy, ED . This picture does not take into account the couplingbetween the elementarycharges and the plasmons which leads to the creation of a second plasmaronic dispersion6,7,10,21,22. The new picture is schematically shown in Fig. 1 B where the hole dispersion, shown in red, is intersected by a second (plasmaronic) dispersion, shown in black. The Dirac crossing is split into three distinct crossings: the hole band crossing at E0 , the plasmaron band crossing at E2 and the ring like crossing of the hole and plasmaron bands at E1 .The Dirac energy, ED , is the crossing energy of the hole bands in the hypothetical non- interacting picture which can not be determined from the ARPES data directly. To overcome this in the following we will use the crossing of the electron- hole bands in the interacting case, E0 , as an approximation. FIG. 1. The linear band dispersion in; A, the non-interacting sin- The linear band structure of graphene leads to a linear scal- gle particle (bare band) description, and B, the case of interactions ing of the Random Phase Approximation (RPA) dielectric between elementary charges and plasmons. In C a linear cut of function, and hence the momentum and energy separation of the Dirac region in B (ky = 0) is shown. hole bands are shown 6,7,10,21,22 the hole and plasmaron bands, with kF and ED . This in red while plasmaron bands are shown in black. The Dirac en- separation can be determined directly from ARPES data by a ergy crossing, ED , in A is split into three crossings by the inter- line shape analysis of the spectral function in terms of a hole actions with the plasmons; E0 , the hole band crossing, E2 , the plasmaron band crossing, and the ring like crossing of the hole band (top) and plasmaron (bottom) band. When taking an en- E1 and plasmaron bands.The scaled momentum and energy widths of ergy vs. momentum cut (E(kx), at ky = 0) the bands form a the diamond region in C are given by δk = k+ k− / kF and ”diamond” as seen schematically in Fig. 1 C from which the | − | | | δE = E2 E0 / E0 EF respectively. In D a plot of the graphene scaled energy separation, δE = E2 E0 / E0 EF , and the Brillouin| zone,− showing| | − the| principle points and principle directions | − | | − | scaled momentum separation, δk = k+ k− / kF , can be referenced in the paper, is presented. determined. | − | | | In the absence of phonons, the plasmaronic band is predicted to merge with the hole band, and loses spectral weight (upper) and plasmaron (lower) bands6,7. The effective envi- close to the Fermi level, EF . This is because the electrons ronmental screening of the graphene layer, ǫ, is related to the only couple strongly to plasmons with the same velocity, a dielectric constant from the substrate, ǫS, and the dielectric condition that cannot be met close to EF . The plasmon and constant from the vacuum above, ǫvac 1, via the relation ≈ the hole band travel with different velocity, greatly reducing ǫ = (ǫS + ǫvac)/2 ǫS 2ǫ 1. In reality this theory ne- the composite particle’s lifetime. With phonons, the situation glects remote band⇒ contributions≈ − to screening in the graphene is more complicated, since the bare plasmon breaks up into layer and the polarizability of the K atoms used to electron 23–25 two modes . It is expected that this breakup will affect dope the graphene, and therefore what is found is an upper the spectral function near EF but to our knowledge these ef- limit to the dielectric constant. fects have not been calculated to date. In the one-particle Green function, Random Phase Approx- 7 imation ( G0W -RPA ) theory developed by Polini et al. and Hwang et al.10,21,22 the effective environmental screening of III. EXPERIMENTAL the graphene layer, ǫ, is related to a graphene effective cou- 2 pling constant, αG, via the relation ǫ = e /αG~vF 2.2/αG. Photoemission spectra were obtained from graphene on For clarity note that ǫ is different from the RPA∼ dynamical 6√3 C-SiC(0001) samples prepared by the high pressure Ar- 6 13 26 screening function, ǫ(q,ω), and that vF 1 10 m/s is gon method, of Emtsev et al. and Ostler et al. , and 6√3 ∼ × 26 the Fermi velocity. Increasing αG decreases the RPA dielec- C-SiC(0001) samples that were annealed in the presence of tric function and therefore increases the separation of the hole H, F or Au. Hydrogen6,15–17, ﬂuorine18 and gold27 have been 3

Increasing nh 13 -2 11 -2 12 -2 13 -2 ne = 1.2 x 10 cm nh = 7 x 10 cm nh = 6 x 10 cm nh = 4.5 x 10 cm A.iv 0.0 A.i A.ii A.iii

-0.2

-0.4

-0.6 Binding Energy (eV)

-0.8 B.ii B.iii B.iv 0.1 B.i () 0.0 y k -0.1

-0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2

-1 -1 -1 4 kx() kx ( ) kx ( ) kx ( ) 2 Graphene on6Ã3 x Graphene on Graphene on Graphene on o 0 6Ã3 R30 C-SiC Au-SiC H-SiC F-SiC

FIG. 2. Experimental spectral function of graphene on (6√3 6√3)R30◦ C-SiC, i, graphene on Au-SiC, ii, graphene on H-SiC, iii, and ◦ Graphene on F-SiC, iv, in the K K direction, A, and the Fermi× surface, B. The graphene on (6√3 6√3)R30 C-SiC sample is n-doped 13− −2 11 −2 × 12 −2 by the substrate (ne 1.2 x 10 cm ) while the graphene on Au-SiC (nh 7 x 10 cm ), graphene on H-SiC (nh 6 x 10 cm ) ≈ 13 −2 ≈ ≈ and Graphene on F-SiC (nh 4.5 x 10 cm ) are all p-doped by the substrate. ≈ shown to intercalate underthe 6√3 C layer, decouplingit from surements the samples were cooled to 20 K using a liquid the SiC substrate such that the π electrons are free to form the He-cooled cryostat and the pressure was∼< 2 x10−10 Torr. linear bands characteristic of graphene. The hydrogen inter- Electron doping was induced in all four samples by de- calation process follows the method of Riedl et al.15 with 6√3 positing small amounts of potassium onto the surface from an C-SiC(0001) samples annealed at 570 ◦C for 75 minutes SAES getter source. Charge is transferred from the randomly ∼ ∼ in H2. Treatment of the 6√3 C-SiC(0001) with fluorine fol- located potassium atoms to the carbon atoms in the graphene lows the previously published method of Walter et al.18, where lattice, leading to an increase in the electron doping of the ◦ the sample is heated to 200 C in the presence of a XeF2 graphene. Addition of progressively more potassium atoms crystal and a sacrificial∼ Mo plate. The sample is then soni- allows for any doping level between the starting doping level cated for several hours in ethanol to remove a molybdenum and a limit of 6 1013 e/cm2. Above this limit the density oxide layer formed during the process leaving a fluorine inter- of potassium atoms∼ × cluster into a disordered version of the K calated graphene layer. To intercalate the Au approximately 2 x 2 structure28 which provides little doping to the graphene 10 monolayers of Au atoms was deposited on the 6√3 C- and is sufficient to significantly scatter the outgoing electrons SiC(0001) samples which were then annealed to 600 ◦C leading to a broadening of the graphene π bands. for 3 minutes, similar to the approach of Gierz et.∼ al27. ∼ ARPES was performed on all four samples at the Elec- tronic Structure Factory endstation (SES-R4000 analyzer) at IV. RESULTS AND DISCUSSION beamline 7 of the Advanced Light Source, Lawrence Berke- ley National Laboratory. A photon energy of 95 eV was used A. Spectral function of clean samples for photoexcitation with an overall energy resolution of 25 meV and momentum resolution of 0.01 A.˚ The graphene∼ The experimental spectral functionsfor the four samples (i - on 6√3 C-SiC(0001), H-SiC and F-SiC∼ intercalated samples iv) considered are shown in Fig. 2 A, for the K K direction. were transported through air to the experimental chamber and Renormalization of the bands by phonons in each− case is indi- annealed to 500 ◦C, 400 ◦C and 500 ◦C respectively cated by the increase in spectral intensity, and a corresponding ∼ ∼ ∼ 29 to remove surface contaminants. The graphene on Au-SiC ”kink” in the bands between EF and 200 meV . For the samples were prepared in a connected vacuum chamber prior n doped spectra (graphene on 6√3 C-SiC∼ sample, Fig. 2 A.i) to measurement and annealed to 300 ◦C. During the mea- it was previously assumed that the bands below and above the ∼ 4

Increasing αG αG = 0.05 αG = 0.1 αG = 0.4 αG = 0.5 A.i A.ii A.iii A.iv 0.0

-0.5

0 -1.0 /E B E -1.5

-2.0

-2.5 0.0 B.i B.ii B.iii B.iv

-0.5

0 -1.0 /E B E -1.5

-2.0

-2.5 -1 0 1 -1 0 1 -1 0 1 -1 0 1 ky/kf ky/kf ky/kf ky/kf 0.0 C.i C.ii C.iii C.iv -0.5

0 -1.0 /E B E -1.5

-2.0 4 Intensity (arb. units) Graphene on Graphene on (6Ã3 x Graphene on Graphene on o o H /SiC 0 Au /SiC 6Ã3 R30 ) R 30 C/ SiC F /SiC

FIG. 3. Experimental spectral function of graphene on Au-SiC, i, graphene on (6√3 6√3)R30◦ C-SiC, ii, graphene on F-SiC, iii, and × graphene on H-SiC, iv, in the K K direction, A, and the K Γ direction, B. As opposed to 1 the order is now in terms of increaseing αG − 13 −2 − . All samples are n-doped to ne 6 x 10 cm by the addition of K atoms to the surface. All of the plots are presented with the energy ≈ scaled to the Dirac energy (Escaled = EB/E0) and the momentum scaled to the Fermi vector (kscaled = k/ kF ). The results of the energy | | line profile peak fitting to the electron hole bands and the plasmaron bands are shown in red and black respectively, while the k/ kF = 0 line profile and fitted peaks are shown in C. The separation of the hole and plasmaron bands increases from left to right and in all cases| two| bands (hole and plasmaron) are observed with the the hole(plasmaron) band showing greater intensity above (below) the Dirac crossings.

Dirac crossings are offset by an energy shift, δE20,30. This away from the K point the three-fold symmetry of the Bril- offset causes a ”kink” at the Dirac crossing ( -0.5 eV). A louin zone around the K point results in the trigonally warped signiﬁcant variation in the position of the Dirac∼ energy below Fermi surfaces observed in Fig. 2 B.i and B.iv. (Fig. 2 A.i) and above (Fig. 2 A.ii, A.iii and A.iv) the Fermi The anisotropy in the Fermi surface intensity has also been energy is evident for p and n doping of the graphene respec- studied31,32 and is related to the chiral nature of the electron tively, with hole doping increasing from left to right. states in graphene on account of the two sublattices. The ex- The doping variation is also clear from the size of the ex- tinguishing of intensity in the negative (positive for n-doped perimental Fermi surfaces presented in Fig. 2 B.i - B.iv. The samples) ky direction is strongly affected by symmetry break- Dirac cone picture described above (Fig. 1 ) implies that the ing, as is seen in bi-layer graphenesamples31,33. Therefore the Fermi surface in each case should be circular, this is only the lack of intensity in the negative (positive for n-doped samples) case for the Au-SiC (Fig. 2 B.ii) and H-SiC (Fig. 2 B.iii) sam- ky direction in the current samples rules out strong symmetry ples. However, the Dirac picture of the bandstructure is only breaking due to the substrate31,32 and the associated forma- valid close to the K point, i.e. for the small Fermi surfaces tion of a gap from causing the observed offset of the upper in Fig. 2 B.ii and B.iii. As the momentum values increase and lower bands as was proposed previously34. This approxi- 5

1.0 1.0 0.5 A.i B.i f 0.0 0.5 /k y k -0.5 width 0.0 -1.0 1.0 0.0 A.ii B.ii 0.5 0.5 0

/E 1.0 B 0.0 E 1.5 -0.4 0.0 0.4 -0.4 0.0 0.4 2.0 ky/kf ky/kf 0 2 4 60 2 4 6 A, Graphene on B, Graphene on (6Ã3 x 13 -2 13 -2 o o ne(10 cm ) ne(10 cm ) Au-SiC 6Ã3 R30 ) R 30 - SiC Graphene on Graphene on (6Ã3 x 1.0 o o Au-SiC 6Ã3 R30 ) R 30 C-SiC

1.0 (fraction of max. value) 0.5 C.i 0.5 D.i width Amplitude

f 0.0 0.0

/k 1.0 y

k -0.5 0.5 -1.0 0.0 C.ii D.ii 0.0 (fraction of max. value) Amplitude

0 0.5 -0.4 0.0 0.4 -0.4 0.0 0.4

/E 1.0 B ky/kf ky/kf E 1.5 C, Graphene on D, Graphene on F-SiC H-SiC 2.0 bare band amplitude plasmaron band amplitude 0 2 4 60 2 4 6 13 -2 13 -2 bare band Gaussian width plasmaron band Gaussian width 1.0 ne(10 cm ) ne(10 cm ) 0.5 Graphene on Graphene on FIG. 5. Peak amplitudes and Gaussian widths from the peaks F-SiC H-SiC shown in Fig. 3 for Graphene on Au-SiC, A, Graphene on (6√3 ◦ 0.0 6√3)R30 C-SiC, B, Graphene on F-SiC, C, and Graphene on H-× SiC, D, in the K Γ direction. In all cases we observe a similar increase (reduction)− in the amplitude (Gaussian line width) of the FIG. 4. Constant energy ( E1 ), i, and constant momentum (k = hole band peaks, shown in red. The reverse is true for the plasmaron 0), ii, intensity profiles as a function of K doping for Graphene on ◦ band peaks, shown in black. The fitted positions from Fig. 3 clearly Au-SiC, A, Graphene on (6√3 6√3)R30 C-SiC, B, Graphene × show that for ky / kF < 0 (ky / kF > 0) the positions are below on F-SiC, C, and Graphene on H-SiC, D, in the K Γ direction. (above) the Dirac crossing. All of the plots are presented with the energy scaled− to the Dirac energy (Escaled = EB/E0) and the momentum scaled to the Fermi vector (kscaled = k/ kF ).The momentum ( δk ) and Energy ( δE ) separations in i and| ii are| constant except close to the zero doping tum scaled to ED and kF respectively. Line shape analysis level, where the vanishing density of states act to converge the hole is performed by non-linear least squares fitting of the spec- and plasmaron bands. tral function at fixed wave vector, k, for which an example is given in Fig.3 C (k=0) for each of the samples. The results of peak fitting to the hole (upper) and plasmaron (lower) bands mation has been shown to be valid at the high photon energies are represented by the red and black dotted lines respectively. 35–37 employed here . The constant energy (binding energy ( EB )= ED ) and constant momentum ( k = 0) intensity maps from spectra similar to Fig.3 B are plotted as a functionof potassium dopingin Fig. B. Influence of electron doping on the spectral function 4 i and ii. The normalized width of the spectra, corresponding to the energy and momentum width of the ”diamond” region, Let us recall that the separation between the hole and plas- in Fig. 4 are remarkably constant except at low doping where maron bands is constant as a function of chemical doping the scaling relationship is expected to break down and phonon when normalised to ED and kF . Here we analyze this sep- interactions are expected. As this scaling relation is unique to aration for four different substrates as a function of doping. Coulombic electron-electron interaction effects this provides In Fig. 3 we present the experimental spectral functions from strong support for the model. 13 −2 each of the samples, doped to ne 6x10 cm by the ad- Representative Energy Distribution Curves (k/ kF = 0) dition of potassium to the surface∼ in the K K (Fig. 3 A) obtained from the spectral functions in Fig 3 B are| presented| and K Γ directions( Fig. 3 B), with energy− and momen- in Fig 3 C. Lorentzian- Gaussian peaks are fitted to the pro- − 6

d defect model for the structure of the 6√3 C layer based on de- 0.5 k (Width of Diamond region) fects observed in STM data, and another defect based model 0.6 was presented by Kim et al39. In the Qi model38 a signiﬁ- 0.4 cant deviation from the structure of defect free graphene is proposed and therefore a large potential barrier would need 0.3 to be overcome to transform the 6√3 C layer into defect free 0.4 graphene. This is in contrast to the relative ease with which atomic layers are intercalated under the 6√3 C layer(eg. Au19 0.2 , F18 and H15 presented here) resulting in essentially defect 0.2 free graphene. 0.1 Qi et al38 and Kim et al39 propose a structure for the 6√3 C layer, based on STM measurements, and use this to calculate 0.0 0.0 a band structure for both the 6√3 C layer and the graphene on the 6√3 C layer. Contributions to the electronic structure from the 6√3 C layer close to the Dirac energyare used to ex-

E (Height of Diamond region) 0.2 0.4 0.6 d a plain the apparent gap in the ARPES spectra of graphene on G (effective coupling constant) 6√3 C-SiC. The experimental spectral function of the buffer layer has been investigated previously12 and none of the de- FIG. 6. The energy separations, δE , (in black) and momentum tailed ARPES spectral features predicted by the models of separations, δk , (in red) of the ”diamond” region as a function of Qi et al38 or Kim et al39 were observed. Importantly, neither graphene effective dielectric constant, αG , as determined from one model correctly predicts the insulating behaviour of the 6√3 particle Green’s function calculations within the Random Phase Ap- C layer, with no states above -0.4 eV binding energy observed 7 proximation ( G0W -RPA ) . The values for αG that correspond to experimentally12. Defect models cannot, therefore, explain the experimental widths shown in Table I are indicated by dashed the experimental observations of either the 6√3 C layer or lines. graphene on 6√3 C- SiC, and the deviation from linear behaviour at ED is due to the formation of plasmaronic bands in all four of the samples presented here, including graphene on files indicating that two bands are observed in all cases. The 6√3 C-SiC. Lorentzian linewidth for each peak is fixed at 0.1, while all other parameters are fitted. The separation of∼ the two peaks is obvious in the fluorine and hydrogen intercalated samples, C. Effective screening analysis Fig. 3 C iii and iv, however it is clear that a second component is needed to arrive at a reasonable description in the case of the Au intercalated and 6√3 C samples. The positions of the In Fig. 6 the variation of the width and height of the dia- peaks determined from these fits are overlayed on Fig.3 A and mond region ( δE and δk respectively) with graphene effec- B in red (hole band) and black (plasmaron band) and provide tive coupling constant, αG , as determined from G0W -RPA a good description in all four cases. At high binding energy theory is shown. These values were determined by generating only the plasmaron band is observed, the hole band emerges a theoretical spectral functions for a range of αG values and from the plasmaron band close to the lower Dirac crossing, fitting peaks to determine the height and width of the diamond and the two bands are separated. After passing through all region. The experimental widths, heights and the correspond- three Dirac crossings the plasmaron band curves back up to ing coupling constant (derived from these by comparison with meet the hole band, with the separation of the bands at the theory) are indicated by dashed lines and recorded in Table I. Dirac crossing, E1, being different for each of the samples. As described in section II the effective coupling constant can The amplitude (circles) and Gaussian linewidth (crosses) of be used to determine the dielectric constant, ǫ, and an upper the fitted peaks are shown in Fig. 5. We observe a decrease limit to the substrate effective dielectric constant, ǫS, which in the amplitude, and corresponding increase in the linewidth, are also listed in Table I. The metallic substrate, Au, provides of the plasmaron band with increasing momentum. The re- the highest effective screening (ǫS 87), an order of magni- ≈ verse is true for the hole band. This behaviour is predicted by tude larger than F (ǫS 10)or H (ǫS 7.8). Interestingly the ≈ ≈ the -RPA plasmaron theory of Polini et al. and Hwang supposedly electronically decoupled 6√3 C layer (ǫS 43) G0W ≈ et al.7,10,21,22 and provides further support to the existence of provides a relatively high effective screening. This can be at- plasmaron bands in graphene on all four substrates. tributed to the presence of dangling Si bonds, which are quite 6 There is strong debate about the source of the deviation of polarizable . the upper and lower bands in graphene on 6√3 C-SiC, with both the plasmaron bands20 and the existence of a symmetry breaking-induced gap34,38,39 proposed. Our work shows that D. Comparison to G0W -RPA theory the variation of the shape of the bands in Fig. 3 can be ac- counted for purely by electron-electron interactions (In any In order to provide a detailed comparison between theory case, symmetry breaking would be expected to be very weak and experiment we present in Fig. 7 the calculated spectral 38 for graphene on Au, H, or F). Qi et al. have presented a functions on the basis of the G0W -RPA theory of Polini et 7

0.5 A.i A.ii A.iii A.iv 0.0

-0.5 0

/E -1.0 B E -1.5

-2.0

-2.5 -1.0 0.0 1.0 -1.0 0.0 1.0 -1.0 0.0 1.0 -1.0 0.0 1.0 0.5 kx/kf kx/kf kx/kf kx/kf B.i B.ii B.iii B.iv 0.0

-0.5 0

/E -1.0 B E -1.5

-2.0

-2.5 3 -1.0 0.0 1.0 -1.0 0.0 1.0 -1.0 0.0 1.0 -1.0 0.0 1.0 ky/kf ky/kf ky/kf ky/kf α = 0.5, ε Å 7.8 0 αg = 0.05, εs Å 87 αg = 0.1, εs Å 43 αg = 0.4, εs Å 10 g s

7 FIG. 7. One particle Green’s function calculations within the Random Phase Approximation ( G0W -RPA ) of the spectral function of 2 graphene in the K K ( A ) and K Γ ( B ) directions for the effective coupling constants (αG = e /ǫ~vF 2.2/ǫ ) found experimentally. Overlayed are the experimental− ﬁtted− positions from Fig.3 for Graphene on Au-SiC, i, Graphene on (6√3 6√∼3)R30◦ C-SiC, ii, Graphene on × F-SiC, iii, and Graphene on H-SiC, iv. Above the lower Dirac crossing, E2 , good agreement between the experiment and theory is observed, however below E2 the hole (red) and plasmaron (black) bands quickly hybridize, deviating from the experimental prediction. The intensity at high binding energy is also over-estimated by the theory (see Fig. 3).

theoretical work needs to be undertaken to accurately describe TABLE I. Effective screening constants for Graphene determined the spectral function below E . from experimental spectral functions: Energy ( δE ) and momentum 2 ( δk ) separation of the hole (upper) and plasmaron (lower) bands, The data presented indicate that the separation of the hole 2 graphene effective coupling constant ( αG = e /ǫ~vF 2.2/ǫ ), and plasmaronic bands can be modified by the use of var- the graphene effective dielectric constant (ǫ) and the substrate∼ effec- ious substrates, which alter the effective dielectric coupling tive dielectric constant (ǫS 2ǫ 1) in the graphene. Doping of graphene is possible without ex- ≈ − Substrate δE δk αG ǫ ǫS erting an influence on the band separation by the addition of Au-SiC 0.12 0.04 0.09 0.02 0.05 0.01 44 9 87 18 potassium to the surface, thereby allowing the plasmaronic ± ± ± ± ± 6√3 C-SiC 0.21 0.02 0.16 0.01 0.1 0.04 22 8 43 16 and electronic band structures to be separately manipulated. F-SiC 0.40±0.05 0.29±0.03 0.4±0.05 5.5± 0.7 10±1.3 H-SiC 0.49±0.02 0.34±0.01 0.5±0.03 4.4±0.3 7.8± 0.5 ± ± ± ± ± V. CONCLUSION al.7 in the K K ( A ) and K Γ ( B ) directions using the experimentally− determined− alpha values. Overlayed The shape of the spectral function of graphene on are the experimental fitted hole (red) and plasmaron (black) SiC(0001) and the presence of side bands to the linear bands bands obtained for Graphene on Au-SiC, i, Graphene on 6√3 near the K point of the Brillouin zone has recently been in- C-SiC, ii, Graphene on F-SiC,iii, and Graphene on H-SiC, iv. terpreted in terms of the formation of coupled hole-plasmon In all cases good agreement is found between theory and ex- quasiparticles (plasmarons). Here we study graphene, on four ◦ periment above the high energy Dirac crossing, E2 . Below different interface structures (the (6√3 6√3)R30 recon- × E2 the experimental hole and plasmaron bands quickly merge struction, and the SiC - graphene interface intercalated with in contrast to the prediction of the G0W -RPA theory. The gold, hydrogen or fluorine), using angle-resolved photoemis- experimental intensity (see Fig. 3) in this high energy region sion. Our data show that similar side bands are found in all is also poorly described by the theory indicating that further cases as revealed by energy and momentum distribution curve 8 line shape analysis. These show the scaling of the separation ACKNOWLEDGMENTS with the energy of the Dirac point and the Fermi wave vector. The separation of the plasmaronic side bands and the bands unaffected by hole-plasmon coupling is found to strongly vary with interface structure. We use G0W -RPA calculations to determine an upper limit to the effective dielectric constant of The Advanced Light Source is supported by the Direc- the underlying substrate interfacial layer; this is found to vary tor, Office of Science, Office of Basic Energy Sciences, of from ǫS 7.8 for hydrogen to ǫS 87 for Au intercalation. the U.S. Department of Energy under Contract No. DE- Graphene∼ is thus an ideal candidate∼ for investigating the ef- AC02-05CH11231.Work in Erlangen was supported by the fective screening in the context of hole-plasmon interactions. ESF and the DFG through the EUROCORES program EURO- We also show that plasmaronic and electronic properties of GRAPHENE. A.W. acknowledges support by the Max Planck graphene can be separately manipulated. Society.

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