Bilayer graphene inclusions in rotational-stacked multilayer epitaxial graphene

0.48 MB·English

by  M. Orlita

Magneto-optics of bilayer graphene inclusions in rotational-stacked
multilayer epitaxial graphene
M. Orlita,1,2,∗ C. Faugeras,1 J. Borysiuk,3 J. M. Baranowski,4 W. Strupin´ski,5 M. Sprinkle,6
C. Berger,6,7 W. A. de Heer,6 D. M. Basko,8 G. Martinez,1 and M. Potemski1
1Laboratoire National des Champs Magn´etiques Intenses,
CNRS-UJF-UPS-INSA, 25, avenue des Martyrs, 38042 Grenoble, France
2Institute of Physics, Faculty of Mathematics and Physics,
Charles University, Ke Karlovu 5, 121 16 Praha 2, Czech Republic
1
3Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Al. Lotnikow 32/46, Poland
1
0 4Institute of Experimental Physics, University of Warsaw, Hoz˙a 69, PL 00-681 Warsaw, Poland
2 5Institute of Electronic Materials Technology, PL 01-919 Warsaw, Poland
6School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
n 7Institut N´eel/CNRS-UJF BP 166, F-38042 Grenoble Cedex 9, France
a 8Laboratoire de Physique et Mod´elisation des Milieux Condens´es, UJF and CNRS, F-38042 Grenoble, France
J
(Dated: January 25, 2011)
3
2 Additionalcomponentinmulti-layerepitaxialgraphenegrownontheC-terminatedsurfaceofSiC,
whichexhibitsthecharacteristicelectronicpropertiesofaAB-stackedgraphenebilayer,isidentified

] inmagneto-opticalresponseofthismaterial. Weshowthattheseinclusionsrepresentawell-defined
l
l platform for accurate magneto-spectroscopy of unperturbedgraphene bilayers.
a
h
PACSnumbers: 71.55.Gs,76.40.+b,71.70.Di,78.20.Ls
-
s
e
m I. INTRODUCTION resonancesignalofasmallflakeusingthegate-controlled
. differential technique. The optical response at a fixed
t
a Theabsenceoftheenergeticgapintheexcitationspec- magnetic field was then studied as a function of the car-
m trum of graphene1 is considered as a possible drawback rier density. Such differential spectroscopy was efficient
- preventingthestraightforwardapplicationofthisemerg- incaseofexfoliatedgraphenemonolayers,14,18butitpro-
d vides more complex results when applied to the bilayer
ing material in electronics. This is despite numerous
n
efforts, such as those implying surface patterning2 and graphene. In this latter system, the change of the gate
o
c substrate- or adsorbents-induced interactions.3–5 The voltageaffectsnotonlythe carrierdensitybutalsomod-
[ possibility to open and tune the band gap in the bilayer ifiessignificantlythebandstructureanddatainterpreta-
tion is by far more elaborated.20
graphenehasrecentlybeendemonstratedbyapplyingan
2
electricfieldperpendiculartothegraphiticplanes6–8 and In this paper, we demonstrate that certain class of
v
7 this is a key element to constructa transistor,the build- previously reported AB-stacking faults21–24 in other-
6 ingblockofelectroniccircuits. Thebandgapengineering wise rotationally-ordered multilayer epitaxial graphene
7 is “typical” of the bilayer and is not reported in tri- and (MEG),13,25–27 show the characteristic features of well-
1 more-layer graphene specimens where semi-metallic be- defined graphene bilayers. These inclusions, identi-
0. havior dominates.9 From the viewpoint of applications, fied here in magneto-transmission experiments, repre-
1 thebilayergraphenethusbecomesalmostequallyappeal- sent therefore a suitable system for accurate magneto-
0 ing material as graphene itself. spectroscopy studies of unperturbed bilayer graphene.
1
Optical spectroscopy has played an important role in
:
v investigations of the bilayer graphene,6,10,11 as, for in-
i stance, it allows to directly visualize the electric-fieldin- II. SAMPLE PREPARATION AND
X
duced energy gap in this system.7,8 On the other hand, EXPERIMENTAL DETAILS
r
onlyrelativelyscarceinformationhasbeenuptonowcol-
a
lected from magneto-optical measurements.12 This fact The growth of MEG samples studied here was per-
might be surprising when noticing the potential of Lan- formed with a commercially available horizontal chem-
dau level (LL) spectroscopy which has been widely ap- ical vapor deposition hot-wall reactor (Epigress V508),
plied to other graphene-like systems. Magneto-optical inductively heated by a RF generator. Epitaxial MEG
methods have, for example, convincingly illustrated the films were grown on semi-insulating 4H-SiC(000¯1) on-
◦
unconventional LL spectrum in graphene, have offered a axis C-terminated substrates at 1600 C in Ar atmo-
reliableestimateoftheFermivelocityorinvokedthespe- sphere. The growth rate was controlled by the Ar pres-
cific effects of many-body interactions between massless sure ( 100 mbar) which was found to directly influence
∼
Dirac fermions.13–19 the evaporation rate of Si atoms.
So far, the only magneto-optical experiments on the Tomeasurethe infraredtransmittanceofoursamples,
bilayer graphene have been reported by Henriksen et we used the radiation of a globar, which was analyzed
al.,12whosucceededtoprobearelativelyweakcyclotron- byaFouriertransformspectrometeranddeliveredtothe
2

1.8
n=1 n=2 n=3 n=1
C B = 31 T 2.2
1.7 B B = 12 T B FIG.1: (coloronline)Transmissionspec-
n=1
n=2 n=3 28 T 2.0 tra of MEG with 100 layers recorded
1.6 n=4C 10 T B at the selected mag∼netic fields below 12
Relative transmission 1111....2345 SiC reststrahlenband nnn===352nn=C4=3 nC=4DC ED 6 FTDEG8 T SiC reststrahlenband BBB n=n1=1n=n22=01 T24n =nT2=236n =T2C 1111....2468 Relative transmission asstcsiniptianotrtledinaelocyrhsnta-liimLsbevsnoLeoadlblvrayeeaktt,nrnee1ioadddn6tneBgosbTdirftoatSiotiponnhinhCIsepcc.=naaoWiesrrnetr1mhsesaseo(tapnranoebo)oaonul5savdannetyptmhdeoeterhra(settteb,lurce)tahrrc,rbnetarsrsentetiido-----
1.1 C D E F G H I 4 T B B = 16 T 1.0 graphene bilayer, following the coding
1.0 2 T n=1 BilaLy-en(r- nt-r1a)−n>siLtion+n1s(n:) 0.8 Lcshe−sifnsti(ev−den−svp1e)erct→itcraaLllniyn+1bp(yna)r.0ts.1F4(oar)ancadlnadr0it.(2yb,3),suarrcee--
0.9 0.6
100 150 200 250 300 350100 150 200 250 300 350 spectively.
(a) Energy (meV) (b) Energy (meV)
sample via light-pipe optics. The transmitted light was We denote those lines by Roman letters, following the
detected by a composite bolometer kept at T =2 K and initial work and notation of Sadowski et al.13,28 These
placed directly below the sample. Measurements were dominant spectral features are equivalent to the charac-
carriedoutinsuperconducting(B =0 13T)andresis- teristic lines observedinthe magneto-opticalresponseof
tive (B = 13 32 T) solenoids with s−pectral resolution exfoliated graphene monolayers.14,15,18 The subsequent
−
of 0.5 and 1 meV in the range of magnetic field below absorption lines labelled here as B I correspond to
→
and above B =13 T, respectively. All presented spectra transitions L−m(−m−1) Lm+1(m) with m = 0 7 be-
→ →
were normalized by the sample transmission at B =0. tween LLs in graphene: E = sign(m)E m, where
m 1
The samples were characterizedin micro-Ramanscat- E = v 2~eB . The apparent Fermi vpelo|cit|y is ex-
teringexperimentswhich,similarlytopreviousstudies,21 tr1actedFtopbe|vF |= (1.02 0.02) 106 m.s−1. Intrigu-
revealed, depending on location, single-component 2D ± ×
ingly, the L−1(0) L0(1) transition exhibits a significant
band features, characteristic of graphene simple elec- →
broadening above 16 T, which could be tentatively re-
tronic bands and of decoupled graphitic planes in multi-
lated to electron-phonon interaction. This effect will be
layerepitaxialgraphenegrownontheC-faceofaSiCsub-
discussed elsewhere.
strate,ormulti-component2Dbandfeaturescharacteris-
The main focus of the present work are other spec-
tic of Bernal stacked graphite. In this paper, we present
tral features, i.e., the transmission dips denoted by
transmission data obtained on one particular specimen
n=1, n=2, ...n=5 in Fig. 1. These absorption lines
withahighnumberofgraphiticlayers( 100)andgrown
∼ are significantly weaker than the dominant “graphene
onaSiCsubstratewithareducedthicknessof 100µm.
∼ lines”, but are still well resolved in our spectra. As it
Due to this latter condition, the spectral region of total
can be seen in Fig. 2, in contrast to the dominant tran-
opacity of the sample only covers the SiC reststrahlen-
sitions, these weaker lines follow a nearly linear in B
band ( 85-120 meV), i.e., it is significantly narrower
as com∼pared to the case of the preceding studies.28,29 dependence. Asthisbehaviorischaracteristicofmassive
particles and because graphene bilayer is the simplest
In spite of these efforts to expand the available spec-
graphene based system with such particles, we antici-
tral range,a relativelyweak transmissionwas still found
pate that electronic excitations within graphene bilayer
aroundtheenergyof200meV,duetodouble-phononab-
inclusions are responsible for the n=1, n=2, ...n=5
sorptions in the underlying SiC substrate and transmis-
transitions. The energyladder ε of LLs in a graphene
n,µ
sion spectra are affected by strong interference patterns bilayer can be easily calculated30,31 within the standard
due to the relatively thin substrate. These two effects
four band model which only considers the two most rel-
prevented measurements in the energy range below the
evant coupling constants γ and γ (se e.g. Ref. 32 for
0 1
reststrahlenband of SiC.
their definitions):
III. RESULTS AND DISCUSSION 1
ε =sign(n) γ2+(2n +1)E2+
n,µ √2h 1 | | 1
Typical transmission spectra of the investigated sam- 1/2
ple are shown in Fig. 1. The dominant absorption lines µ γ4+2(2n +1)E2γ2+E4 . (1)
q 1 | | 1 1 1(cid:21)
whichareobservedinthesespectrashowthecharacteris-
tic √B-dependence (see Fig. 2) and correspondto inter- Here, a positive (negative) integer n indexes the elec-
LL transitions in electrically isolated graphene sheets. tron (hole) LLs. µ = 1 accounts for the topmost
−
3
valence- and the lowest conduction-band, whereas µ=1 can say that the relative intensity of these “bilayer”
corresponds to two other, split-off bands. As illustrated lines increases with the total number of layers in MEG
in the inset of Fig. 2, optically active inter Landau level and these transitions are practically invisible in spec-
transitions in a graphene bilayer fulfill the n n 1 imens with less than 10 layers reported in very first
| | →| |±
selection rule. The energies of such transitions are plot- magneto-spectroscopy studies.13,28 This finding serves
ted in Fig. 2 with black solid lines. Those lines account as an indication that we indeed observe graphene bi-
for the transitions within the µ = 1 bands. To re- layer inclusions and not regions of a local AB-stacking
−
produce the experimental data, we have adjusted the γ which might be also speculated to appear in rotation-
1
parameter whereas the Fermi velocity v which defines ally stacked multilayers. Such Moir´e-patterned AB-
F
E (i.e. the intra-layer coupling γ = 3150 meV) has stacked areas have been recently visualized in MEG by
1 0
been fixed at the value derived from the monolayer-like STM/STS measurements.36–38 We further assume that
transitions. A fair agreement is obtained between the twisted graphene layers which results in the Moir´e pat-
calculated (solid lines in Fig. 2) and measured energies ternedbilayershouldnot provideus with sowell-defined
of n=1, n=2, ...n=5 transitions. Optical absorptions AB stacked bilayers as we observe in our data. Let us
involving LLs of higher indexes (e.g. n=6, n=7 and also note that if we compare the relative intensity of ob-
n=8, see Fig. 2) could also be observed in the spectra, served transitions, we can roughly estimate that in none
nevertheless, these lines are very weak and only visible oftheinvestigatedsamplestheratiobetweenbilayersand
in a limited range of magnetic fields. Traces of inter-LL monolayers exceeded 10%.
transitions due to split-off bands (µ = 1 in Eq. 1), can We should also emphasize that the appearance of
bealsoidentifiedinourdataandexperimentsfocusedon Bernal-stackedfaultsinMEG,whichhaveaformofwell-
this particular set of transitions are in progress. defined bilayers, is not a signature of bulk graphite. In
A pronounced departure of the observed bilayer tran- this well known material, the K-point electrons indeed
sitions from the linearity in B clearly shows the limits mimic massive carriersin the graphene bilayer,but with
of the parabolic approximation which is often used for an effective inter-layer coupling 2γ1 instead of γ1 in a
graphenebilayersinthe closevicinityofthek=0point, realgraphenebilayer.31,39–41Thistwofoldcouplinginthe
and within which the LLs are strictly linear with the effective bilayer model for K point electrons implies a
magnetic field.32,33 As can be seen in Fig. 2, the posi- characteristic effective mass twice enhanced in compari-
tions of all these lines can be very well reproduced with son to that of massive Dirac fermions in true graphene
a parameter γ =(385 5) meV, and these experiments bilayer and consequently, also a twice lower energy sep-
1
thus refine the value o±f this parameter reported previ- arationbetween adjacentinterband inter-LL transitions,
ously from optical studies at zero magnetic field.6,10,11 cf. Fig. 2 of this paper with the fan chart in Ref. 40.
Theintriguingsplittingofthen=1andofthen=2lines The remaining unclarified point of our study is the
at high magnetic fields is beyond our simple model and splitting of the bilayer lines, which is clearly visible for
will be discussed later on. transitions n=1 and n=2 around B = 17 and 26 T,
respectively. In the following, we discuss two different
The simplified model of LLs in the pristine bilayer
scenarios for this splitting. One possible explanation in-
graphene provides us with reasonably accurate descrip-
vokes the electron-hole asymmetry, reported recently in
tion of its magneto-optical response, even though it ne-
graphenebilayersgraphene.6,10,11 Basedonthis assump-
glects the electron-hole asymmetry (mainly induced by
tight-bindingγ ,∆′ parameters),6,8,10,11 aswellasapos- tion, the magnitude of the splitting for the n-th transi-
4 tion, relative to the transition energy is expressed by:42
sible gap opening at the charge neutrality point. Never-
theless, it should be noted that the optical response of 2(∆′/γ +2γ /γ )
1 4 0
the graphene bilayer has only been unambiguously iden- .
n(n+1)+ (n+1)(n+2)
tified above the reststrahlenband of the SiC substrate
p p
and therefore, we cannot exclude a possible appearance For the values ∆′ = 0.02 eV, γ = 0.4 eV, γ /γ =
1 4 0
of an energy gap, up to a few tens of meV, at the k=0 0.05,6–8,10,11 our measured value for n = 1 (about 0.08)
point. For the same reason, we can only estimate a very is very well reproduced. However, the splitting due to
higher limit for the carrier density in the studied bilayer electron-hole asymmetry should be seen for all magnetic
of2 1012cm−2. However,therealcarrierdensityisvery fields, while, as can be seen in Fig. 1b, we only observe
×
likely similar to that of the surrounding (electrically iso- it in a relatively narrow range of B.
lated)graphenesheets,i.e. below1010 cm−2,asreported Perhaps a more natural explanation for this line split-
inRefs.16and22. Wealsopointoutthatrelativelynar- tingwouldbeanavoidedcrossingbetweenthetransition
row linewidths of the order of 10 meV (relaxation time L−n(−n−1) Ln+1(n) and some other transition with a
in sub-picosecondrange) serve as an indication of rather much small→er oscillator strength, so that it is not seen
high electronic quality of these bilayer inclusions, com- far from the crossing point. One can see directly from
parableor evenbetter than other bilayersystems.12,34,35 Fig. 2 that the bright transitions n = 1,2 are crossed
Equivalentbilayer-likespectralfeaturesarerecurrently by the dark (i.e., dipole-inactive in case of a zero trigo-
identified practically in all studied specimens, neverthe- nal warping) transitions L0(−4) L4(0), L0(−7) L7(0),
→ →
less, with a strongly varying intensity. In general, we respectively, approximately at the observed values of B
4
We have speculated this mode coupling could be
IHGF E D C due to electron-phonon or electron-electron interac-
=8 tions. Electron-phonon interaction, which could be en-
350 n n=5 L7(0) hanced due to the proximity of the transition energy
300 n=7 n=6 =4 n=3 n=2 L0(-7) n=1 ((s21y59m06mmmeteerVyV))(,tthomisuthsptahtobnoefontehxiecsluzRdoeandme-acdenunteaecrttioovpet)th.icealSdppifflhietortneinonngt
n L4(0) due to Coulomb interaction can be evaluated to be
250 L0(-4) 0.04(e2/4πε ~v )(γ γ /γ ),42 i.e. only about 3 meV in
0 F 1 3 0
eV) B the absence of dielectric screening, e2/4πε0~vF = 2.2.
m200 Hence, the mechanism of the possible strong coupling
Energy (150 45 n = 1 n = 2 n = 3 n = 4 btieotnwseiesnathpeuzLz−le1(w−h2)ic→h rLem2(a1)inasntdoLb0e(−c4la)r→ifieLd4.(0) transi-
3
2
SiC Lm 1
100 Reststrahlenband
m = 0 IV. CONCLUSIONS
n=0 -1
50 -2
-3 We probed graphene bilayers embedded in multilayer
L-n(-n-1) Ln+1(n) --45 epitaxial graphene on the C-terminated surface of SiC.
0 TheseinclusionscanbeviewedasAB-stackedfaultsinan
0 5 10 15 20 25 30
otherwiserotationally-stackedmultilayergraphenestruc-
Magnetic Field (T)
ture and enable spectroscopic studies of unperturbed
FIG.2: (coloronline) Fanchart: PointsmarkedwithRoman
graphene bilayers. The “electronic quality” of these bi-
letters,havingacharacteristic√B-dependence,correspondto
layers is comparable or even better than that of the bi-
inter-LLtransitionsinelectrically isolatedgraphenesheets.13
layers obtained by exfoliation or by epitaxial growth on
Points denoted by index n represent inter-band inter-LL
the Si-terminatedsurfaceofSiC.34,35 This way,wecould
tsrcahnemsitaitoincsalliyn tshheowgnrapinhetnheebinilsaeyte.r TL−hen(−funl−l1g)ra→yLlnin+e1s(ns)h,oaws tracethe inter-bandinter-LLtransitionsinthe graphene
expected energies of transitions in the graphene monolayer bilayer for the first time, and thus supply data com-
for vF =1.02 106 m.s−1,full black lines correspond topre- plementary to the cyclotron resonance absorption (i.e.,
×
dictedpositionsoftheabsorptionlinesinthegraphenebilayer intra-band inter-LL transitions) measured on the exfoli-
(only parameters γ0 =3150 meV and γ1 =385 meV consid- ated bilayer by Henriksen et al.12 We could also clearly
ered). The dashed lines denote theoretical positions of two visualize the departure of Landau levels in the graphene
trigonal-warping-induced transitions in the graphene bilayer
bilayer from the linearity in B, which clearly sets limits
L0(−4) →L4(0) and L0(−7) →L7(0). for the parabolic approximation of electronic bands in
this material.
(the crossing occurs at a very sharp angle, which brings
a significant uncertainty). These transitions are allowed
only due to the presence of the trigonal warping of the Acknowledgments
electronic bands, which mixes levels L with m differ-
m
| |
ing by an integer multiple of 3, see Ref. 30. The ratio of We acknowledge also funding received from EC-
the oscillator strength of the L0(−4) L4(0) transition EuroMagNetII under Contract No. 228043, from the
→
to that of the brightn=1 transitioncanbe estimated42 Keck Foundation and from the Partner University Fund
as (25/108)(γ γ /γ )2(l /~v )2 0.02 at B = 25 T. at the Embassy of France. This work has been sup-
3 1 0 B F
≃
The L0(−4) L4(0) transition is therefore not expected ported by the Projects No. 395/NPICS- FR/2009/0,
→
to be seen in the experiment unless some other, pos- No. MSM0021620834, GACR No. P204/10/1020 and
sibly resonant, admixture mechanism is taken into ac- No. MTKD-CT-2005-029671,furthermorebyGrantsNo.
count. Coupling between L0(−4) L4(0) and n = 1 670/N-ESF-EPI/2010/0, No. 671/NESF-EPI/2010/0,
→
transitions should be quite strong as the observed“anti- and No. GRA/10/E006 within the ESF EuroGraphene
crossing splitting” is of about 20 meV. programme (EPIGRAT).
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