Probing Electronic Excitations in Mono- to Pentalayer Graphene byMicro Magneto-Raman SpectroscopyStephane Berciaud,*,† Marek Potemski,‡ and Clement Faugeras*,‡

†Institut de Physique et Chimie des Materiaux de Strasbourg and NIE, UMR 7504, Universite de Strasbourg and CNRS, 23 rue duLœss, BP43, 67034 Strasbourg Cedex 2, France‡Laboratoire National des Champs Magnetiques Intenses, CNRS/UJF/UPS/INSA, Grenoble F-38042, France

*S Supporting Information

ABSTRACT: We probe electronic excitations between Landau levels in freestanding N-layer graphene over a broad energyrange, with unprecedented spectral and spatial resolution, using micro magneto-Raman scattering spectroscopy. A characteristicevolution of electronic bands in up to five Bernal-stacked graphene layers is evidenced and shown to remarkably follow a simpletheoretical approach, based on an effective bilayer model. (N > 3)-layer graphenes appear as appealing candidates in the quest fornovel phenomena, particularly in the quantum Hall effect regime. Our work paves the way toward minimally invasiveinvestigations of magneto-excitons in other emerging low-dimensional systems, with a spatial resolution down to 1 μm.

KEYWORDS: Freestanding graphene, magneto-Raman scattering, electronic excitations, Landau levels, effective bilayer

Searching for materials with new functionalities anddeepening our knowledge on already identified structures

are primary directions in the research on novel two-dimensionalsystems, which include the family of Bernal-stacked N-layergraphene. Each member of this family displays very distinctelectronic properties. This is expected from theory1−4 andconfirmed in experiments on graphene and its bilayer, especiallywhen profiting from a conversion of two-dimensional electronicbands into quantum Hall effect (QHE) systems withcharacteristically spaced-in-energy Landau levels.5−10 Ofprime interest are high-quality specimens, often fragile and ofsmall lateral size, thus calling for adequate experimental probes.A well-established path toward obtaining intrinsically puregraphene consists in isolating freestanding layers.11−13 Suchhigh quality comes at the cost of the relatively small area(typically <100 μm2) of available samples and their greatenvironmental sensitivity. A series of freestanding N-layergraphene (N-LG) may be difficult to study with surface probes(e.g., angle resolved photoemission14,15 and scanning tunnelingspectroscopies16), as well as with electron transport measure-ments,5−7 which require uniform gate tunability, or opticalspectroscopy in the far-infrared range, with intrinsically poorspatial resolution.8−10,17,18 Our method of choice is micromagneto-Raman scattering spectroscopy (MMRSS), which isminimally invasive and combines high sensitivity with a

submicrometer spatial resolution, characteristic of visible-lighttechniques.Indeed, Raman scattering spectroscopy has been widely used

to study the electronic excitations in solids and particularly insemiconductors, including two-dimensional electron gases inthe quantum Hall effect regime.19 So far, however, these studieshave been limited to probing electronic excitations in thevicinity of the Fermi energy (intraband excitations, in case ofQHE systems). In contrast, the electronic Raman scatteringresponse of graphitic materials is much richer. It may involveboth intraband and interband (across the neutrality point)contributions, as theoretically predicted20,21 and observed inexperiments, e.g., on graphite,22,23 graphene on graphite,24 andcarbon nanotubes.25

Here, employing MMRSS, with transverse magnetic fields Bup to 29 T, we were able to directly trace the electronic Ramanscattering features associated with symmetric inter Landaulevels transitions in freestanding N-LG, from mono- topentalayer graphene. The dispersion of these excitations withthe magnetic field is a hallmark of the number of layers andpermits a precise determination of electronic dispersions. With

Received: April 28, 2014Revised: June 6, 2014Published: June 23, 2014

Letter

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increasing N, the band structure of N-LG becomes richer andricher but remains well accounted for by very a simpletheoretical model.In the latter model, referred to as the ef fective bilayer

model,1−3,17,18,26 we start with the electronic bands of graphite,which are very simply simulated using only two tight-bindingparameters, namely, the nearest neighbor hopping parameter γ0,which defines the Fermi velocity vF = 3/2aγ0/ℏ, where a =0.142 nm is the c−c bond length and the nearest neighborinterlayer coupling constant γ1. The band structure of N-LG isthen derived from two-dimensional cuts in the electronicdispersion of graphite, perpendicular to the transversemomentum (kz) direction, at particular values of θ = kz c/2 =(pπ)/(N + 1), where N is the number of layers, and p = ±1,±2,... ±⌊(N + 1)/2⌋, where ⌊⌋ denotes the integer part and c/2= 0.34 nm is the interlayer spacing in bulk graphite. As shownin Figure 1a−e, within this model, effective bilayers haveformally identical dispersions as that of bilayer graphene, with arescaled γ1 = 2γ1 cos θ,

3,2,17,26 which corresponds to half theenergy gap between their split-off bands. Monolayer graphene,(at θ = π/2, i.e., γ1 = 0) displays a well-known linear dispersion,with a slope given by vF. Bilayer graphene exhibits a set of fourhyperbolic bands, obtained at θ = π/3, i.e., γ1 = γ1. Trilayergraphene hosts a pair of graphene-like bands (at θ = π/2) andan effective bilayer with γ1 = √2γ1 at θ = π/4. In thisframework, tetralayer graphene displays two effective bilayers atθ = π/5 and θ = 2π/5, and pentalayer graphene possessesgraphene-like bands at θ = π/2 and two sets of effective bilayerbands at θ = π/6 and θ = π/3.

In the presence of a transverse magnetic field B, Landauquantization occurs, and the effective mono- and bilayers giverise to independent sets of Landau levels (LL). The energy Ln

θ

(L−nθ = −Ln

θ) of the nth electron (hole) LL, arising from thegapless bands in an effective bilayer is given by27,18

γ γγ=

+ | | + −

+ | | + +θ

| | ⎜ ⎟ ⎜ ⎟⎛⎝

⎞⎠

⎛⎝

⎞⎠L n E n E

E2

12 4

12 4n

12

12 1

4

12

12 1

4

where E1 = vF(2eℏB)1/2. At θ = π/2, one recognizes the well-

known LL dispersion of monolayer graphene: L|n|π/2 =√nE1. For

θ ≠ π/2, a nearly linear scaling of Lnθ with B is expected. The

corresponding dispersions are represented in Figure 1f−j. TheLL structure of N-LG becomes increasingly rich as N increases,and crossings between LL arising from distinct subbandsappear. As previously demonstrated,20−22 the inter LLtransitions which satisfy δ|n| = 0 (with energy L−n,n

θ = 2 ×L|n|θ ) are Raman allowed, while “optical-like” transitions, such

that δ|n|= ± 1, couple to zone center phonons and give rise tothe magneto-phonon resonance.28−30

An optical image of the sample used in our experiments isshown in Figure 2a. N-layer graphene specimens have beenprepared by micromechanical exfoliation of natural graphiteand deposited onto SiO2/Si substrates, prepatterned with anarray of 8 μm diameter circular pits, as in ref 13. Thefreestanding N-layer flakes of interest are readily identified byoptical contrast and Raman spectroscopy measurements at B =0 T13,31,32 (see also Supporting Information). In this work, onlyBernal-stacked N-LG were investigated.

Figure 1. Low-energy band structure and Landau levels of N-layer graphene. The electronic dispersions of mono-, bi-, tri-, tetra-, and pentalayergraphene, obtained from the effective bilayer model described in the text, are shown in a−e, respectively. The corresponding dispersions of theLandau levels arising from the gapless bands are shown in f−j for mono- to pentalayer graphene, respectively. Blue lines in f, h, and j correspond toLandau levels arising for the effective monolayer (θ = π/2), while red and green lines in g−j correspond to Landau levels arising from effectivebilayers obtained at a given quantized value of θ ≠ π/2. The first two Raman-active inter-Landau levels electronic transitions L−1,1

θ and L−2,2θ , which

satisfy δ|n| = 0 are shown with black arrows in f and g. The first two optical-like inter-Landau levels electronic transitions, L0,1θ (L−1,0

θ ) and L−2,1θ

(L−1,2θ ), which satisfy δ|n|= ±1, are shown with dashed gray arrows in f and g. Those excitations are responsible for the magneto-phonon resonances.

The calculations are performed with vF = 1.05 × 106 m/s and γ1 = 400 meV.

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The low-temperature micro magneto-Raman scatteringresponse of suspended N-LG has been measured with acustom-made setup. The excitation laser at λ = 514.5 nm (i.e., alaser photon energy of 2.41 eV) is injected into a 5 μm coreoptical fiber and then focused onto the sample with a highnumerical aperture aspherical lens. The unpolarized back-scattered light is collected by the same lens, then injected into a50 μm optical fiber coupled to a monochromator, equippedwith a liquid nitrogen cooled charge coupled device (CCD)matrix. The excitation laser power was set to ∼1 mW focusedonto a ∼ 1 μm diameter spot. The resulting intensity issufficiently low to avoid significant laser-induced heating andsubsequent spectral shifts of the Raman features. The samplewas held in a magnetic cryostat at a base temperature of 4 Kunder a residual He pressure and mounted on X−Y−Z piezostages, allowing us to move the sample relative to the laser spotwith submicrometer accuracy. The evolution of the Ramanspectrum with magnetic field was then measured on free-standing samples by slowly sweeping the magnetic field from B= 0 T to B = 29 T, while recording spectra on the fly. Thus,

each individual spectrum is the integrated response over δB ∼0.1 T. We verified, by recording selected spectra at fixed B, thatthis had no impact whatsoever on the line width of theelectronic Raman features discussed here. Each electronicRaman feature was fit as a function of B, using Lorentzianforms.Let us first consider the illustrative case of trilayer graphene.

Figure 2b shows selected Raman scattering spectra recorded atB = 0 T and at magnetic fields near 25 T. Two prominent field-induced changes are observable in these spectra.(i) Magnetic field-dependent sidebands appear on the low-

and high-energy sides of the G-mode feature. At B ∼ 26 T, theL0,1π/2 (L−1,0

π/2 ) and L−1,2π/4 (L−2,1

π/4 ) have energies close to that of theG-mode phonon (∼1585 cm−1 or 197 meV) and give rise tomagneto-phonon resonances (MPR).28−30 Details on MPR infreestanding N-LG will be reported elsewhere.(ii) Dispersive features appear near 1150−1450 cm−1 and

2000−2400 cm−1. Their integrated intensity is up to ∼10% ofthat of the G-mode feature, and their frequencies increase quasilinearly with B, as expected for effective bilayer bands. These

Figure 2. Observation of Raman-active electronic excitations in N-layer graphene. (a) Optical image of a mechanically exfoliated sample showingseveral N-LG flakes partly freestanding over 8 μm circular pits spaced by a 30 μm pitch. b) Raman scattering spectra of a freestanding graphenetrilayer at various magnetic fields. The first (L−1,1

π/4 ) and second (L−2,2π/4 ) Raman active electronic excitations, associated with the effective bilayer, are

clearly visible. Their evolution with increasing magnetic field is shown in the inset, which plots the same Raman spectra, after subtraction of theRaman spectrum recorded at B = 0 T. (c, d) Raman maps around the freestanding trilayer graphene region boxed in a, recorded at B = 22 T. Whilethe integrated intensity of the G-mode feature varies little over the scanned area (c), the ratio of integrated intensity of the L−1,1

π/4 electronic Ramanscattering (ERS) feature (around 1150 cm−1) to that of the G-mode feature shows a high contrast between the freestanding and supported regions(d). Parts e−i show selected Raman spectra at different magnetic fields, after subtraction of the Raman spectrum recorded at B = 0 T. The grayvertical bars mask residual contributions from the G- and 2D-mode features in N-LG, near 1585 cm−1, and 2700 cm−1, respectively, and from theunderlying Si substrate, near 1000 cm−1. Noteworthy, in trilayer graphene (g), the L−1,1

π/2 and L−2,2π/2 electronic excitations, associated with the effective

monolayer bands, as well as the L−3,3π/4 feature from the effective bilayer bands, which were not shown in b, are also clearly detectable. The L−1,1

π/2 andL−3,3π/4 features merge at fields near 29 T (see also Figure 3).

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features are tentatively assigned to the L−1,1π/4 and L−2,2

π/4

transitions, respectively.Figure 2c depicts a map of the G-mode integrated intensity

IG recorded at B = 22 T over the trilayer graphene area boxed inFigure 2a. A moderate change in IG can be seen near the edgeof the pit, while IG has similar values at the center of the pit andon the supported region. At this field, the L−1,1

π/4 feature appearsnear 1150 cm−1. Remarkably, the ratio of integrated intensity ofthe latter feature to that of the G-mode feature is hardlydetectable on supported TLG and reaches up to ∼10% on thefreestanding area. This demonstrates that (i) the ERS featuresare strongly damped on supported N-LG, presumably due tosubstrate-induced inhomogeneities and enhanced electronscattering rate and (ii) that our experimental approach allowsfor a spatially resolved and noncontact investigation of

electronic excitations in N-LG with a spatial resolution downto ∼1 μm.Figure 2e−i displays a set of representative Raman spectra,

measured on mono- to pentalayer graphene at different valuesof the magnetic field. In each N-LG specimen, electronicexcitations, with different dispersions as a function of themagnetic field, appear. These ERS features are well fit toLorentzian forms. This readily allows us to extract full widths athalf-maximum Γ, which grow moderately as a function of theenergy of the electronic excitation. Typical Γ are in the range50−200 cm−1, i.e., at least three times narrower than thoseextracted from magneto-absorption measurements on sup-ported monolayer graphene.9 This corresponds to a quasipar-ticle lifetime of ∼220 fs down to ∼50 fs, in line with typicalelectron scattering times deduced from magneto-transportmeasurements on high mobility freestanding graphene.11 For

Figure 3. Dispersion of the electronic excitations in N-layer graphene. Parts a−e show false-color maps of the micro magneto-Raman scatteringspectra of mono- to pentalayer graphene, as a function of the magnetic field, after subtraction of the spectrum recorded at B = 0 T. Horizontal lightblue bars mask residual contributions from the G- and 2D-mode features in N-LG, near 1585 cm−1, and 2700 cm−1, respectively, and from theunderlying Si substrate, near 1000 cm−1. The corresponding peak frequencies of the electronic Raman features extracted from Lorentzian fits areshown in f−j. The peak frequencies are determined with an experimental error that is smaller than the symbol size. The solid lines are calculateddispersions of the Landau levels assuming a linear dispersion for monolayer graphene and using the effective bilayer model. The solid lines follow thesame color code as in Figure 1. A same interlayer hopping parameter of γ1 = 400 meV was used for all calculations, while the Fermi velocity that bestfits our results is indicated in each panel.

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monolayer graphene, we can easily trace a first ERS feature,which energy increases from ∼1300 cm−1 at B = 3 T up to∼3500 cm−1 at B = 25 T. This feature is assigned to the L−1,1

π/2

transition. A fainter, second ERS feature, assigned to the L−2,2π/2

transition, emerges from the background near 2000 cm−1 at B =3 T, and its energy increases up to 3600 cm−1 at B = 11.2 T.For bilayer graphene, up to three ERS features, assigned to theL−1,1π/3 , L−2,2

π/3 , and L−3,3π/3 , are observed. For N > 2, the magneto-

Raman spectra then become increasingly rich.To clearly visualize electronic excitations, we now consider

the contour plot built from the magneto-Raman spectrarecorded as a function of B (see Figure 3) on a diffractionlimited spot. On these maps, the dispersion of the electronicRaman features identified in Figure 2 appear prominently. Thedifference between the dispersion of the ERS features in mono-and bilayer graphene is particularly striking. The high sensitivityof our setup allows us to trace up to 2, 3, 5, 7, and 9 excitationsin N = 1 to N = 5 layer graphene, respectively. As anticipatedtheoretically, monolayer-like dispersions are only observed forodd N, while bilayer-like dispersions appear for N > 1.Figure 3e−i shows the extracted frequency of all the

observable ERS features, along with fits, based on the modeldescribed above for the corresponding N. Interestingly, the LLdispersions observed in freestanding monolayer graphenedeviate significantly from the expected (nB)1/2 scaling andsuggest average Fermi velocities of ∼1.3 × 106 m/s,significantly larger than the values of ∼1.0−1.1 × 106 m/sfrom previous magneto-absorption studies on supportedgraphene.18

First, the relatively high values of vF observed in monolayergraphene likely stem from the reduction of dielectric screeningin freestanding graphene.33,34 Second, the peculiar scaling ofL−n,nπ/2 with n and B observed for N = 1 (see Figure 3a,f) is

presumably a consequence of many body Coulomb interactionsin freestanding graphene. For example, recent electrontransport measurements on freestanding graphene deviceshave revealed a logarithmic divergence of the Fermi velocityin the close vicinity of the Dirac point.33 This behavior has beenassigned to electron−electron interactions. In our work, fromthe Raman scattering spectrum measured at B = 0 T, weestimate a residual doping below ∼2 × 1011 cm−2,13,31 a value atwhich such interaction effects become significant.33 Acomprehensive analysis of the influence of many-body effectson the magneto excitons in freestanding graphene and,subsequently, on the evolution of the Fermi velocity in thepresence of a magnetic field,35 goes beyond the scope of thepresent study and will be discussed elsewhere.In comparison, for N = 2 to N = 5, the dispersions of all the

observed ERS features resemble the theoretical patternsintroduced in Figure 1 and are quantitatively reproduced bythe effective bilayer model. At a given value of θ, we observethat the L−n,n

θ transition exhibits a steeper dispersion as afunction of B for smaller N. Within the effective bilayerframework, and using a fixed value of γ1 = 400 meV, in keepingwith previous measurements on bulk graphite,18,26 thistranslates into a slight reduction of the Fermi velocity fromvF = (1.09 ± 0.01) × 106 m/s for N = 2 down to (1.05 ± 0.01)× 106 m/s for N = 5. We have also attempted to fit our resultsusing the values of L−n,n

θ derived from the Slonczewski−Weiss−McClure model for the dispersion of bulk graphite.36 Usingseveral additional fitting parameters, this model provides amarginally better fit to our data and also suggests a very similarreduction of vF with increasing N. Our observations also suggest

that for N > 1, the existence of low-energy, gapless electronicbands with finite curvature, and the subsequent finite density ofstates at the Dirac point at B = 0 T and increased degeneracy ofthe n = 0 LL at finite B, play an essential role in defining theFermi velocity. Altogether, the apparent decrease of vF withincreasing N is consistent with the value of vF = 1.02 × 106 m/sobserved in bulk graphite26 and with recent angle resolvedphotoemission spectroscopy measurements on graphenemonolayers deposited on various substrates.34

In conclusion, our results demonstrate the richness of theelectronic excitation spectra in N-layer graphene and reveals apeculiar dispersion of Landau levels in monolayer graphene,thus opening interesting avenues for the study of many-bodyeffects on its magneto-optical conductivity. The experimentalmethodology presented here permits the optical probing ofelectron−hole quasiparticles, from energies as low as ∼100meV in monolayer graphene, and down to ∼60 meV in (N >1)-layer graphene, using moderate magnetic fields of a few T. Inaddition, most of the electronic excitations presented in thiswork can readily be observed using magnetic fields below 12 T,accessible with commercially available superconducting mag-nets. Consequently, table-top micro magneto Raman scatteringexperiments, may be developed to unravel electronic excitationsin the close vicinity of the charge neutrality point of N-layergraphene and to further investigate the electronic dispersion ofthese systems. Finally, our work provides an impetus for studiesof (N > 3)-layer graphene in the Quantum Hall effect regime,4

in which new broken symmetry states37 can be expected due toextra crossings of Landau level and/or Landau level bunchingover a broad range of magnetic field. We also believe thatfurther improvement of the experimental arrangements willallow us to measure the excitations in a close vicinity to thelaser line, thus offering an optical probe of small energy gaps,such as, for example, those arising from lifting the spin or valleydegeneracy.38

■ ASSOCIATED CONTENT*S Supporting InformationSpatially resolved, low temperature micro-Raman character-ization of a freestanding graphene monolayer at zero magneticfield, comparison between the magneto-Raman scatteringspectra of freestanding and supported samples, false-colormaps of the differentiated micro-Raman scattering spectra ofmono- to pentalayer graphene as a function of the magneticfield. This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: stephane.berciaud@ipcms.unistra.fr.*E-mail: clement.faugeras@lncmi.cnrs.fr.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe are grateful to M. Orlita, P. Kossacki, and D.M Basko fornumerous discussions. We also thank Ivan Breslavetz fortechnical support and R. Bernard, S. Siegwald, and H. Majjadfor help with sample preparation in the StNano clean roomfacility. S.B. acknowledges support from the Agence nationalede la recherche (under grant QuanDoGra 12 JS10-001-01),from the CNRS and Universite de Strasbourg and from the

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LNCMI-CNRS, member of the European Magnetic FieldLaboratory (EMFL). M.P. and C.F. acknowledge support fromthe ERC-2012-AdG-320590 MOMB project and the ECgraphene flagship.

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