11356 Phys. Chem. Chem. Phys., 2013, 15, 11356--11361 This journal is c the Owner Societies 2013

Cite this: Phys. Chem.Chem.Phys.,2013,15, 11356

Evidence of confinement of the p plasmon inperiodically rippled graphene on Ru(0001)†

Antonio Politano,a Davide Campi,b Vincenzo Formosoac and Gennaro Chiarello*ac

High-resolution electron energy loss spectroscopy has been used to study the electronic response of

periodically rippled monolayer graphene grown on Ru(0001). A plasmonic mode, assigned to the

p plasmon, has been observed at around 6 eV. The dispersion curve of this collective mode indicates

plasmon confinement within the hills of the ripples. Moreover, we found that the corrugation of the

graphene sheet also significantly affects the damping processes of the p plasmon.

1 Introduction

Many of the unusual properties of graphene are related to itselectronic collective excitations.1–7 In graphitic systems, the ordinaryp or interband plasmon at 5–7 eV,3,8–11 arising by electric dipoletransitions between the p energy bands (p - p*),12 is a sensitiveprobe of the graphene band structure near the Fermi level.13 Theinvestigation of plasmon modes at graphene/metal interfaces canreveal how the electronic properties of these systems are influencedby the interaction with the substrate, which is a subject of significantinterest to evaluate the quality of the contacts between metallicelectrodes and graphene devices and, as a consequence, in thedevelopment of plasmonic devices working in the THz range.

Herein, we want to investigate the nature and the dispersionof the collective electronic excitations in graphene grown onRu(0001), an intriguing system self-nanostructured in a periodicarray of ripples.14–17 In fact, the lattice mismatch (9%) betweenC and Ru causes the formation of an incommensurate orreconstructed interface14,16 that can be described as a 12 �12 C overlayer overlaid on a 11 � 11 Ru(0001) supercell.14,16,18

Scanning tunneling microscopy (STM),14,16,18 low-energy electronmicroscopy,19 and He-atom diffraction14,15 experiments haveestablished that the graphene sheet is not perfectly flat but itexhibits ripples. Such a corrugated overlayer gives rise to anhexagonal arrangement of hills, which are approximately 2 nmwide and they are separated by each other by about 3 nm.14,16,18

STM experiments14,16,18 showed that the height modulationvaries between 0.6 and 1.5 Å, depending on tip conditions andtunneling parameters. Height and width of these ripples are

consistent with models which allow the carbon atoms to formdifferent types of bonds with the underlying substrate. Inparticular, carbon atoms located at the higher areas of thesuperstructure are adsorbed on three-fold sites (fcc, hcp) andthey scarcely interact with the substrate. Instead, carbon atomscloser to the Ru substrate occupy hcp and on-top positions andform a strong chemical bond with Ru. In the latter case, a stronghybridization between 2pz states of carbon atoms and the 4dz

2

orbitals of Ru20 occurs. Charge is accumulated on the C atoms atatop positions and depleted at the Ru atoms.19,21 It has beendemonstrated20 that the preferential direct C–Ru bond at atopsites results in a distribution of compressive and tensile strainsin the adlayer so as to cause the corrugation of graphene. Hence,the strong covalent bonding between graphene and Ru(0001) iscorrelated with the degree of graphene corrugation.20

The existence of curved regions in the graphene sheet withperiodically modulated electronic properties can strongly influencethe nature of its plasmon modes. However, to the best of ourknowledge, this point has not been addressed yet. On the otherhand, this issue has a crucial importance in the emerging field ofplasmonics in the THz range, for which graphene–metal contactsare omnipresent components.22–24

Present high-resolution electron energy loss spectroscopy(HREELS) experiments show that the p plasmon of graphene/Ru(0001) is characterized by an anomalous dispersion. Thefrequency of the p mode remains nearly constant up to a criticalwave-vector (E0.30 �1) and then it rapidly increases with theparallel momentum transfer. Such behavior is ascribed toplasmon confinement within graphene ripples.

2 Experimental sectionSample

Experiments were carried out in an ultra-high vacuum (UHV)chamber operating at a base pressure of 5� 10�9 Pa. The sample

a Dipartimento di Fisica, Universita degli Studi della Calabria, 87036 Rende,

Cs, Italy. E-mail: gennaro.chiarello@fis.unical.itb Dipartimento di Scienza dei Materiali, Universita Milano-Bicocca, 20125 Milano, Italyc Consorzio Nazionale Interuniversitario di Scienze Fisiche della Materia,

via della Vasca Navale, 84, 00146 Roma, Italy

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3cp51954f

Received 8th May 2013,Accepted 13th May 2013

DOI: 10.1039/c3cp51954f

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was a single crystal of Ru(0001). The substrate was cleaned byrepeated cycles of ion sputtering and annealing at 1300 K.Surface cleanliness and order were checked using Auger electronspectroscopy (AES) and low-energy electron diffraction (LEED)measurements, respectively.

Graphene formation

Graphene was attained by dosing ethylene onto the bareRu(0001) substrate held at 1150 K. The saturation of a singlelayer was reached upon an exposure of 3 � 10�8 mbar for tenminutes (24 L, 1 L = 1.33 � 10�6 mbar s).25 In situ LEEDexperiments show the growth of a single graphene layer, inagreement with previous He-atom scattering and STM experimentsby Politano et al. reported elsewhere.14,15 As a consequence of theexistence of ripples,14,15 the LEED pattern shows satellite spotscaused by the moire structure (Fig. S1, ESI†).

Further characterization of the MLG has been carried out bythe measurement of phonon modes26–29 (Fig. 1). The presenceof well-resolved ZA (out-of-plane acoustic), TA (transverseacoustic), LA (longitudinal acoustic), and LO (longitudinaloptical) phonons ensures the good order and crystalline qualityof the graphene sheet, in agreement with results reported inmicroscopic investigations.14,15,30,31

HREELS experiments

HREELS experiments were performed by using an electron energyloss spectrometer (Delta 0.5, SPECS). All HREELS measurementshave been carried out at room temperature.

The energy resolution of the spectrometer was degraded to6–8 meV so as to increase the signal-to-noise ratio of loss peaks.Dispersion of the loss features was measured by moving the

analyzer while keeping the sample and the monochromator at afixed position.

To measure the dispersion relation of the p plasmon, i.e.,Eloss(qJ) (where Eloss is the loss energy and qJ is the parallelmomentum transfer), values for the parameters Ep and yi,the incident angle, were chosen so as to obtain the highestsignal-to-noise ratio. The primary beam energies used for thedispersion, Ep = 70 eV, provided, in fact, the best compromiseamong surface sensitivity, the highest cross-section for modeexcitation and qJ resolution.32,33

As

�hqk! ¼ �h ki

!sin yi � ks

!sin ys

� �; (1)

the parallel momentum transfer, qJ depends on Ep, Eloss, yi andys according to:

qk ¼ffiffiffiffiffiffiffiffiffiffiffiffi2mEp

�h

rsin yi �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� Eloss

Ep

ssin ys

!(2)

where Eloss is the energy loss and ys is the electron scatteringangle.32,34

Accordingly, the integration window in a reciprocalspace35 is

Dqk �ffiffiffiffiffiffiffiffiffiffiffiffi2mEp

p�h

cos yi þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� Eloss

Ep

scos ys

!a (3)

where a is the angular acceptance of the apparatus (�0.51 in ourcase). To obtain the energies of loss peaks, an exponentialbackground was subtracted from each spectrum and resultingspectra were fitted by a Lorentzian line shape (Fig. 4b).

To extract the line-width of the p plasmon, the experimentallyobserved loss width DEloss has to be corrected according to theformula36

DEp ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDEloss

2 � DEexp2

q(4)

where DEexp, which depends on the angular acceptance and theenergy resolution of the spectrometer, is given by the transferwidth of the spectrometer.37

Calculations

Calculations were performed in the framework of the densityfunctional theory (DFT) as implemented in the QuantumEspresso code,38 using the Perdew–Burke–Ernzerhof (PBE)approximation39 and ultrasoft pseudopotentials.40

The band calculation was carried out using a 1 � 1 MLG/Ru(0001) cell fixing the lattice parameter at that of thegraphene and consequently adapting the Ru lattice parameteras in ref. 41.

A four-layer Ru slab with graphene adsorbed on the wideside and a vacuum region 20 Å wide was used. Plane waves wereexpanded up to a 30 Ry cutoff and the Brillouin zone wassampled over a 36 � 36 � 1 k-point mesh.

Fig. 1 HREEL spectrum of the MLG/Ru(0001) for an impinging energy of 20 eV.The incidence angle is 80.01 while the scattering angle is 35.01. Such scatteringconditions allow the observation of the phonon modes of the graphenelattice.27,28 The sample was oriented along the G%–K% direction.

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3 Results and discussion

Loss spectra of MLG/Ru(0001) recorded as a function of theimpinging energy Ep are reported in Fig. 2. They show a broadfeature at around 6 eV whose intensity increases with theprimary beam energy. In graphitic systems, features observedin this energy range are commonly associated with the collectiveexcitation of p valence electrons (p plasmon11,42–46). Anotherfeature is observed at around 15 eV and it is attributed to thep + s plasmon10,45 (inset of the same figure).

Previously, p plasmons have been observed at graphene/transition-metal interfaces characterized by both weak andstrong interaction with the metal substrate (MLG/Pt3 andMLG/Ni,42 respectively). However, for MLG/Ni(111), for whichp bands are disrupted,47,48 the observed collective mode hasbeen ascribed to an interface plasmon rather than to a properp plasmon.49

The interpretation of the surface electronic response ofMLG/Ru(0001) is particularly challenging due to the presenceof regions with different strengths of interaction with thesubstrate. The periodic modulation of the electronic propertiesinduced by the formation of the moire has been demonstrated byseveral experiments.18,50–52 In particular, STS measurements50

show that the graphene sheet at the top position of the hills isdecoupled from the Ru substrate and therefore graphene behavesas nearly-free-standing in the top regions of the ripples.50

To interpret our HREELS results in the framework of graphene bandstructure, we performed first-principles calculations of the electronband structure of MLG/Ru(0001) along the high-symmetry directionsof the surface Brillouin zone using the Quantum-Espresso code38

(Fig. 3). Calculations reveal that p and p* bands in the hills of theripples get connected with Dirac cones at K% (Fig. 3a), as it is expectedfor freestanding graphene, while the Dirac cone is destroyed in thevalleys (Fig. 3b). These results agree well with similar calculationsperformed for the same system using the VASP code.41

On the basis of these considerations, we assign the featurerecorded in Fig. 2 to a collective oscillation of free p-electroncharge located in the hills of ripples.

Fig. 2 HREEL spectra for MLG/Ru(0001) along the G%–K% direction, acquired inspecular geometry at an incidence angle of 55.01 with respect to the samplenormal as a function of the impinging energy. In the inset, the HREEL spectrumfor Ep = 100 eV is shown in the region from 8 to 30 eV.

Fig. 3 Band structure of graphene on Ru(0001) along the M% – K%–G%– M% pathobtained by means of DFT calculations with the carbon atoms at the positions (top,hcp) corresponding to the low regions and (hcp, fcc) corresponding to the highregions. The color scale represents the projected density of states for the pz states ofthe carbon atoms expressed in states/eV. The top panel represents the band structurein the top parts of the ripples (hills), while the bottom panel is related to the bottomparts of the ripples (valleys). Single-particle transitions around M% from p to p* bandsare mainly responsible for the occurrence of the p plasmon in graphene andgraphite.12 Such transitions are possible only on the top parts of the ripples, for whichthe joint density of states (JDOS) related to this p - p* single-particle excitation ishigh. By contrast, p bands in valleys have a vanishing weight at M% (see the color scale)and consequently the p plasmon is quenched in valleys. It should be remembered thatthe plasmon mode occurs at an energy which is higher than that of the single-particleexcitation originating it (see the book in ref. 69 for a review and ref. 12 for the specificcase of graphitic systems), i.e. the maximum of Im(�1/e) does not coincide with themaximum optical absorption (maximum of e2).

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The investigation of the dispersion relation op(qJ) of the pplasmon is crucial for understanding the details of the natureand of the propagation of this plasmon mode. HREEL spectrarecorded as a function of the scattering angle along the G%–K%

direction are reported in Fig. 4 (impinging energy Ep = 70 eV).Interestingly, we found that the p-plasmon frequency of MLG/Ru(0001) remains nearly constant up to a critical wave-vector qc

(E0.30 �1, Fig. 5). This finding contrasts with previousexperimental results attained for graphene grown on Pt(111)3

and SiC(0001)11 and for bulk graphite.53 In all these systems,the frequency of the p plasmon increases with the parallelmomentum transfer qJ. The dispersionless behaviour of thefrequency found in MLG/Ru(0001) for qJ o qc (qc E 0.30 �1) isa fingerprint of the occurrence of plasmon confinement,35,54,55

i.e. valence electrons oscillate independently in the singlegraphene quantum dot of diameter d = 2p/qc. In the presentcase, d results to be 21 � 3 Å. Such a value is in excellentagreement with STM experiments by Politano et al. reportedelsewhere14,15 and by Wintterlin and coworkers.16

Thus, the existence of ripples has a strong and evidenteffect on the localization and dispersion of the p plasmon.

Propagation of the plasmon mode occurs only for wavelengthssmaller than the average size of the ripples. For qJ > 0.30 �1

(shorter wavelength) the frequency of the p plasmon rapidlyincreases.

A key factor in the propagation of the plasmonic excitation isits lifetime. It is limited by the decay into electron–hole pairs(Landau damping).56 The p-plasmon is a mode which lies insidethe continuum of electron–hole excitations and therefore it isdamped even at qJ - 0.46

The measurements of the full-width at half-maximum(FWHM) of the plasmon peak provide information on dampingprocesses. In Fig. 6 we report the behavior of the FWHM versusqJ. The width of the p plasmon decreases from 3 eV at smallmomenta down to 2.6 eV at qJ E 0.23 �1. The FWHM is nearlyconstant for qJ > 0.23 �1. There is a strict relationship betweenthe dispersion of the FWHM and the electronic structure ofgraphene/Ru(0001) (Fig. 3).

As vertical interband transitions around M% are allowed, theplasmon lifetime is dominated by decay into the above-mentionedsingle-particle transition, as for graphite.36,57 Thus, the decaychannel of the p plasmon in graphene behaves differently withrespect to plasmons in metal systems, for which Landau dampingoccurs only after a critical wave-vector.32,35,37,58,59 The decaychannels for MLG/Ru(0001) decrease for increasing qJ as aconsequence of the predominance of nearly-vertical interbandtransitions in Landau damping processes of the p plasmon inthis system. In fact, for qJ a 0 the allowed transitions in the kspace are no longer vertical and such transitions are unfavourablein this system (see Fig. 3). On the basis of these considerations, weexpect that the lifetime should increase as a function of qJ. Theobserved decrease of the FWHM for increasing momenta (Fig. 6)agrees well with our picture. The existence of a critical wave-vectorin FWHM dispersion indicates that the plasmon can no longerdecay in electron–hole pairs for momenta higher than 0.23 Å�1.However, the residual damping of the plasmon at higher momentaremains quite high (2.6 eV). Damping processes are particularlycomplicated in MLG/Ru(0001) by the presence of periodically

Fig. 4 (a) HREEL spectra for MLG/Ru(0001) as a function of the parallelmomentum transfer qJ, calculated from eqn (2) (see the Experimental section).Loss spectra were acquired by using an impinging energy of 70 eV and anincidence angle of 651. The parallel momentum transfer has been varied bychanging the scattering angle. It is worth mentioning that, due to the very weakintensity of loss peaks (E10�4 with respect to the intensity of the elastic peak), anacquisition time of several hours has been required for each spectrum to reach asufficient signal-to-noise ratio. (b) Plasmon peak after background subtraction fora scattering angle of 611. The solid line represents a Lorentzian fit to the peak.

Fig. 5 Dispersion relation of the p plasmon for MLG/Ru(0001).

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modulated electronic properties.18,51,60 In fact, the existence ofripples limits plasmon propagation since ripples can also besignificant sources of electron scattering which limit charge-carrier mobility in graphene.61 This phenomenon is the maincause of damping for the p plasmon in MLG/Ru(0001). On thebasis of data reported in Fig. 6, we can establish that Landaudamping by creation of electron–hole pairs has a minor role withrespect to ripples-induced damping. It could be a consequenceof the corrugation of the graphene sheet on Ru(0001).17,18,20,62–66

By contrast, the FWHM of the p plasmon in the flat67,68 MLG/Pt(111) is 1.4 eV.3

3 Conclusions

We have investigated the nature of the p plasmon in periodicallyrippled graphene on Ru(0001). We found that the p plasmon inMLG/Ru(0001) is confined in the top regions of the ripples and it isquenched in valleys of the ripples as a consequence of the stronghybridization between Ru d bands and p states of graphene.Damping processes are strongly influenced by the presence ofripples while Landau damping by creation of electron–hole pairsplays only a minor role. Present findings are particularly signifi-cant for tailoring the properties of graphene applications based onthe propagation of plasmon modes. In particular, these results areparticularly significant for tailoring graphene–metal contacts to beused in THz plasmonic devices.

Notes and references

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Fig. 6 Behavior of the FWHM of the p plasmon of MLG/Ru(0001) as a function of qJ.

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