Table Of ContentRamanscattering from the CaC superconductor inthe presence ofdisorder
6
A. Mialitsin1, J.S. Kim2, R.K. Kremer2 and G. Blumberg1
1DepartmentofPhysicsandAstronomy,RutgersUniversity,Piscataway,NewJersey08854-8019, USA
2Max-Planck-Institut fu¨r Festko¨rperforschung, 70569 Stuttgart, Germany
9
(Dated:January2,2009)
0
0 PolarizedRamanscatteringhasbeenperformedonCaC6superconductor.WeidentifytwoofthethreeRaman
2 activeEg phononmodesat440and1508cm−1expectedfortheR3mspacegroupofCaC6. Thesefirstorder
n scatteringmodesappear alongwiththeDandGbandsaround1300cm−1 and1600cm−1 thataresimilarin
a origintothecorrespondingbandsinplaingraphite.TheintensitiesoftheDandGbandsinCaC6correlatewith
J degreeofdisorder. TheDbandarisesfromthedoubleresonantRamanscatteringprocess;itsfrequencyshifts
2 asafunctionof excitationenergywith 35cm−1/eV.Thedoubleresonant Ramanscatteringprobesphonon
∼
excitationswithfinitewavevectorq. Weestimatethecharacteristicspacingofstructuraldefectstobeonthe
] scaleofabout100A˚ bycomparingtheintensityoftheDbandandthe1508cm−1EgmodeinCaC6tocalibrated
i intensityratioofanalogousbandsindisorderedgraphites.Asharpsuperconductingcoherencepeakat24cm−1
c
s isobservedbelowTc.
-
l
r PACSnumbers: 71.20.Tx,74.25.Gz,74.25.Kc,78.30.-j
t
m
. I. INTRODUCTION Fractional contribution of Ca atoms at the corners of
t
a theunitcelladdsuptooneatomperunitcell.
m
Examples of superconductivity in graphite interca- CaC6 and its parent graphene structure are intu-
- lated with alkali metals have been known for several itively comparable. Introducing Ca atoms inbetween
d
n decades1. More recently the occurrence of supercon- the carbon sheets lowers the symmetry of the D6h
o ductivity in graphite intercalation compounds (GICs) spacegroupofgraphenetotheD53d spacegroup. This
c has been linked to the partial occupation of the inter- leads to a unit cell in CaC6 with a hexagonal cross-
[ layerbandinthose intercalatedstructuresthatdisplay section area in the ab-plane that is three times larger
1 the superconductingphasetransition2,3. Experimental than that of graphene, and a corresponding Brillouin
v studies of superconductivity in GICs were limited to zone (BZ) that is three times smaller. The BZ of
3 very low temperatures, since previously known GIC graphene and CaC6 are rotated by 30◦ in respect to
9 superconductors, like KC8 or LiC2, display low su- each other, thus when the graphene BZ is folded into
2 perconducting transition temperatures under ambient thatofCaC6 theequivalentKandK′ pointsfallback
0
. conditions. The synthesis of CaC6, with a surpris- ontotheΓpoint. Whencomparingthephonondisper-
1 ingly high superconductingtransition temperature4 of sionofgrapheneandCaC6 the21phononbranchesin
0 11.5K, has spurred new research in the area of GIC CaC6 can be derivedapproximatelyfrom 6 graphene
9 superconductivity. Inadditiontoencouragingnewex- phononbranchesfoldedintothesmallerCaC6 BZ,re-
0
periments, this development calls for expanding the- sultingin3×6=18branches,inadditiontothethree
:
v oretical models to explain its high Tc. CaC6 further phononbranchesfromtheCasublattice.
Xi meritsspecialattentionamongsimplegraphitederived Accordingtofirstprinciplescalculations7,8,lowfre-
compoundsbecauseitillustrateshowthepropertiesof quency Ca vibrations and carbon out-of-plane vibra-
r
a graphene sheets are altered by the change in crystal tions both contribute almost equally to most of the
symmetry and in electronic band structure due to in- electron-phonon coupling responsible for the Cooper
teractionwiththeCasublattice. pairsbinding. Contrarytothisfinding,however,based
TheCaC6 structureisshowninFig.1a. Itbelongs onevidencefromisotopeeffectmeasurements9 itwas
to the space group Nr.166 (R3m) with an AgBgCg the Ca phonons that have been found to be primar-
stacking sequence which sets it apart from all other ilyresponsibleforthemediationofsuperconductivity.
known 1st stage GIC compounds5,6. Here g stands Latticevibrationshavealsobeenthefocusofspectro-
for the hexagonalgraphene planes stacked in a prim- scopic investigations: a Raman study directed at the
itive fashion (as opposed to staggered plane stacking zone center phonon modes10 and an inelastic X-ray
of graphite). The unitcellis rhombohedraland spans (IXR) scattering study aimed at low-energy phonon
threeintercalateplanes. Itsinversioncenterliesinthe branches11.
middle of the graphitic hexagon in the median plane. TheRamanstudyhasrecordedaRamanactiveband
2
a b roomformoreindepthCaC6 phononstudies.
Double resonant Raman scattering14 (DRRS) is a
process that involves light scattering mediated by
phonon excitations with a quasi-momentum greater
than zero15. DRRS allows to access selected points
in the phonondispersion away from the Γ point. Ra-
man bands associated with DRRS occur in the pres-
enceofstructuraldefectswhicharenecessarytoensure
quasi-momentum conservation15. In fact the phonon
dispersionofgraphitehasbeeninvestigatedbymeans
of DRRS in considerable detail16. The so-called D
band, a disorder induced feature appearing between
1300cm−1 and 1400cm−1 in graphite is also seen
in CaC6 Raman spectra in the same frequencyrange;
FIG.1:(coloronline)CrystalstructureofCaC6.a)Thelay- however, the underlying mechanism behind DRRS in
erednatureofthecompoundwiththeintercalantsandwiched CaC6 hasnotbeendescribed.Thedispersivebehavior
betweenthehostgraphiteplanesisshownina4times4super of the D band10 in CaC6 is a fingerprint signature of
cell. b)viewontheCaC6 structurefromthetop. Thinlines DRRS. In the context of DRRS and disorder, Hlinka
indicatethetwo-foldrotationalaxisC2andthemirrorplanes et al.10 have highlightedthe rapid sample degradation
σ. Thethree-foldrotationalaxisthatcoincideswiththesix-
in air. Itis apparentthatthe interpretationofspectro-
foldrotation-reflectionaxisgoesverticallythroughthepaper
scopicdataisaffectedbysamplequalityandage.
atthepoint of theintersectionof theC2 axesinthecentral
hexagon.BluecoloredCaatomsframedbysquaresareabove
Whilethebodyofworkdescribingsuperconductiv-
thegraphenelayerandthegreencoloredonesbelow.
ityinCaC6 isquitesubstantial,therearediscrepancies
in the estimations of the magnitude of the SC gap by
meansoftunnelingspectroscopies. Theaccountsvary
at 1500cm−1 that has been assigned to the high- from2∆=21.8cm−1 (Ref.17)to37.1cm−1 (Ref.18).
frequency E vibration by a rough Raman shift co-
incidence wigth the theoretical prediction8. Since the TheformervalueputssuperconductivityinCaC6 into
aweakcouplingregimewhilethelatterraisesthepos-
frequency of this band is measured to be higher than
sibility of strong coupling. A third scanning tunnel-
1447cm−1 correspondingtothezonecentermodepre-
ing spectroscopy study (Ref.19) provides an interme-
dictedbya’frozen-phonon’densityfunctionalcalcula- diate value of 25.8cm−1. This issue has been ad-
tion, ithasbeenattemptedto explainthisdiscrepancy
dressed in Ref.20 by proposing a distribution of gaps
bynon-adiabaticbehavior12. Non-adiabaticeffectsare around the average value of 26.3cm−1 as calculated
assumed to become importantwhen a relatively short
fromfirstprinciples(SCDFT).Anopticalinvestigation
lattice vibrationperiodisaccompaniedbya relatively
ofreflectanceofCaC6 infarinfrared21alsosuggestsa
longelectronscatteringtime13. InsuchacasetheBorn
distributionofgapsaroundtheabovevalue.
Oppenheimerapproximation(BOA),whichassertsthat
electronsremaininthegroundstateatalltimesinthe In this work we study CaC6 crystals by polarized
process of the lattice vibration, is not applicable any Ramanspectroscopy. WeobserveexpectedRamanac-
more and excitations of the electron cloud to higher tiveE vibrationalmodesat440and1508cm−1. The
g
states as a consequence of electron-phonon coupling disorderinducedDbandappears∼150-200cm−1 be-
needtobeconsidered. low the latter E mode, accompanied by weaker dis-
g
The IXR study has traced two acoustic branches orderrelated bands. We measureRaman spectra with
and one optical Ca sublattice branch along the Γ−L multiple excitations to highlight the dispersive nature
andΓ−Xdirectionsfindinggoodagreementwithpre- of the D band in the DRRS process. The prominent
dictions by Calandra and Mauri8 barring a slight sys- presence of the D bandfurther enablesexplorationof
tematicunderestimationofcalculatedbandfrequencies structural defects in the investigated samples. Elec-
throughoutthe dispersion. The energywindow of the tronicRamanscatteringrevealsasharpsuperconduct-
X-raystudyhasbeenlimitedtoenergiesupto40meV ingpairbreakingpeakappearingat24cm−1 belowT .
c
and in both works some of the predicted modes have We assess how the degree of disorder correlates with
been absent in experimental data. This leaves ample thesuperconductingproperties.
3
II. EXPERIMENTAL noted as follows: T3 - translation, C3 - three-fold ro-
tation around the axis perpendicular to the graphene
The high-quality CaC6 crystals were synthesized plane, C2 - two-fold rotation around the axes lying
by reacting highly oriented pyrolytic graphite (Ad- in the graphene plane, I - inversion, S6 - six-fold
vanced Ceramics, Grade : ZYA) with a molten alloy rotation-reflectionaroundtheaxisperpendiculartothe
ofLiandCaat350◦Cforseveralweeks7. Theresult- grapheneplane, σd - diagonalmirrorplanes bisecting
ingc-orientedpolycrystallinesampleswerecharacter- theangleenclosedbytheC2axes.Withtheknowledge
ized by X-ray diffraction, and susceptibility measure- ofthecharacterstableΓvibisreducedtothedirectsum
ments. The samples for the Raman study were care-
fully selected to have almost pure CaC6 phase with Γvib =A1g⊕A1u⊕2A2g⊕3A2u⊕3Eg⊕4Eu . (1)
a minimal amount (< 5%) of impurity LiCx phase, One set of A2u⊕Eu irreduciblerepresentationscorre-
and to show a very sharp superconducting transition spondstothetranslationaldegreesoffreedom(T and
z
(∆Tc(10%− 90%) = 0.1 K) with the onset at Tc = Txy) and thus is allocated to the acoustic branches.
11.4K. Further details on the characterization of the A second pair of A2u⊕ Eu irreducible representa-
samplescanbefoundinRef.6. Becauseofthesensitiv- tions is attributed to the mutual shift of the Ca and
ityofthelustroussamplesurfacetomoisturecontained C sublattices10 comprising the three lowest optical
inair,thesampleshavebeenmanipulatedandmounted phononbranches(seeFig.4c). Modesassociatedwith
in Argon atmosphere. The samples were then trans- CamovementarenotRamanactive.
ferredtoandcleavedinaHe-filledgloveboxthatwas Polarized Raman spectra recorded at 5K from the
enclosingthecontinuousflowHe-cryostat.Thefreshly CaC6 ab-plane are displayed in Fig.2. It shows Ra-
cleavedspecimenwerethenimmediatelycooledto5K man bands observedwith the 476nm excitation up to
andholdbelow20Katalltimesforthedurationofthe the Raman shift of 1700cm−1. The two juxtaposed
measurement. datasetshavebeenobtainedindifferentscatteringcon-
To perform Raman scattering from the ab-plane of figurations.TheRLgeometrywithcircularlypolarized
bulk CaC6 we have used a Kr+ laser for a range of lightofoppositechiralityfortheincidentandscattered
excitationwavelengthswith2mWpowerfocusedtoa beamsselectsRamanmodesoftheE symmetry. The
g
50x100µmspot, anOxfordInstrumentscryostatfor data set collected in RL features a total of six modes
sampletemperaturecontroldownto3K,andacustom in the accessed energyrange. The RR geometrywith
triple-stagespectrometer.Wehaveemployedcircularly incidentandscatteredlightofthesamechiralityselects
polarized light with the optical configurations select- modesoftheA1g⊕A2g symmetries. Thedatasetcol-
ing either the same or opposite chirality. The former lected in RR features four bands. Depending on the
andthelatterarerespectivelyreferredtoasRight-Right presencethemodesinjusttheE orinbothsymmetry
g
(RR) and Right-Left (RL) configurations. The circu- channelswecategorizetheobservedfeaturesaspolar-
larly polarizedconfigurationsallowto recordsymme- ized,partiallypolarizedanddepolarized.
try resolved Raman spectra. For the D3d point group Resolving polarization is helpful in identifying the
theEgsymmetryisselectedintheRLscatteringgeom- modes.WenoticethattoalargeextenttheRRpolariza-
etryandtheA1g⊕A2g symmetriesintheRRsetup22. tionspectrumfollowstheRLspectrum,withtheexcep-
Thesymmetrychannelscorrespondtoirreduciblerep- tionofthemodesataround1100,1500and1600cm−1
resentationsofdistinctivelatticevibrationmodes. and the low energypeak related to superconductivity.
UnderlyingtheRamanpeaksthereisabroaddepolar-
izedcontinuumthatisphenomenologicallymodeledby
III. RAMANACTIVEMODES abroadfeaturepeakingataround800cm−1 ontopofa
linearslope.Wedeterminefrequenciesofthephononic
Theatomsintheunitcellthatremainunaffectedby RamanbandsintheRLpolarizationbyafittoasuper-
symmetryoperationsofthespacegroupdeterminethe positionofRamanoscillators23andthecontinuum:
characters of the vibrational representation Γ . For
vib
A ω γ ω
CaC6 wefindtherespectivecharacterstobe: χ′′ =X(ω2−ωi2)2i +i (γ ω)2 +cont. , (2)
D53d T3 2C3 3C2 I 2S6 3σd i i i
Γ 21 0 -3 -3 0 1 whereA , γ andω are the amplitude, the line width
vib i i i
andtheRamanshiftoftherespectivepeaks. Thefitted
Thesymmetryelements(illustratedbyFig.1b)arede- peakparametersarelistedinTableI.
4
50 The experimentally measured frequency of the E3
Right-Left (Eg) vs. Eg3 mode at 5K deviates from the calculated one by 4%g.
Right-Right (A1g+A2g)
40 geometry with l = 476 nm E1isfoundtomatchthefrequencyof434cm−1 deter-
L g
] D
u. G minedfromfirst principlescalculations8 more closely
el. 30 T = 5 K withadifferenceofonly1.5%. Thequestionhowand
r
[ if the renormalization of zone center modes frequen-
''
cccc 20 cies should scale with mode frequency in the context
SC D* offirst-principlescalculationsbeyondBOAisopenfor
E1
g discussion.
10
E1* AsnotedabovetheintensitiesoftheEg modesvary
g
strongly. The method of zone folding that is com-
0
0 200 400 600 1200 1400 1600 monly used to qualitatively evaluate the phonon dis-
persions of intercalate compounds1 is helpful to dis-
Raman shift [cm-1] cussthisfact. TheE1 andtheE2 modescanbeunder-
g g
stoodasturnedonbyzone-foldingofthepristineprim-
FIG.2: (color online) PolarizedRamanspectra fromCaC6 itivegraphitephonondispersion24. Inthiscontext,the
at 5K. RR and RL polarizations obtained with the 476nm E1 modeisexpectedtobeweak25reflectingtheobser-
excitation. Symbolsdisplayexperimentaldata. Bluecircles g
vationthat the modulationof the carbonlayersby Ca
interconnected withadashedlinecorrespond totheRLge-
ometryandgreencirclescorrespondtotheRRgeometry.The atomsisweak. ThehighfrequencyE3g modeofCaC6
solidlineisafittoEg databysuperpositionof fiveRaman (D53d space group) is deduced from the E2g vibration
oscillators on a broad continuum. The region between 600 ingraphene37(D6h)andthusistheonlytruenotzone-
and1100cm−1 isfeaturelessandhasbeencroppedout. folded graphitic intra-layer Raman active mode. Ac-
cordinglytheE3modedominatestheRamanspectrum
g
intheE symmetrychannel.
g
Only the 1508cm−1 mode is foundto be fully po- The mode corresponding to E3g is observed to be
larized (present in the E symmetry channel and en- downshifted in many GICs, sometimes displaying an
g
tirely absent in A1g⊕A2g). This mode is identified asymmetric shape attributed to Fano type interac-
as the high frequency doubly degenerate carbon in- tionwiththeelectronicbackground(see Ref-s25,26 for
plane stretching E3g mode (Fig.2 inset). The much RbCxandKCx).WhilethefrequencyoftheE3gphonon
weaker modeat440cm−1 appearsto be partially po- isclearlydownshiftedinCaC6 whencomparedtothe
parentgraphitemode(seeFig.5aandc)weobserveno
larized.ThereisasharppeakpresentintheE symme-
g
asymmetryandfitthemodewithaconventionalRaman
trychannelsuperimposedonabroaderfeatureappear-
oscillator.
ing in both polarizations. By examining the phonon
dispersion7,8(Fig.4c),weidentifytheadditionalinten- The energy region where the E2g mode is expected
sityinRLasthelowestRamanactiveE1 modewhich (1100cm−1) displays a depolarized feature. We be-
g
we measure at 440cm−1. The origin of depolarized lieve that we observea disorder inducedband instead
modes, which we associate with DRRS (see section oftheactualzonecentermode.TheRamanactiveA1g
mode expected around 1380cm−1 is not observed.
IV), is different from that of polarized modes, which
OurassignmentofRamanbandsissummarizedinTa-
arezonecentermodesvisibleduetofirstorderRaman
bleI. We attribute two of the observedRaman modes
scattering, and is going to be discussed in section IV.
WewilldiscussthegraphitelikeGbandat1600cm−1 at440cm−1 andat1508cm−1 tofundamentallattice
vibrations.WeassigntheDandD∗featurestodisorder
thatispartiallypolarizedinsectionVI.
inducedbands. TheG bandis attributedto deinterca-
latedregions.
TABLEI: Fitparameters for theCaC6 Raman spectrum at
T =5KinRLpolarizationexcitedwithλL=476nm. IV. DOUBLERESONANCERAMANSCATTERING
fitparameters peaks E1 D∗ D E3 G
\ g g
ωi[1/cm] 440 1120 1332 1508 1582 BesidesthefundamentalRamanfrequencies,spectra
γi[1/cm] 36 44 100 86 32 ofCaC6 exhibitfeatureswell knownfromdisordered
Ai[rel.u. 10−3/cm] 0.45 0.62 22.1 29.0 4.2 graphites10. These features are commonly labeled as
×
5
50 toattributetheobservedDbandtobespecificallydue
l lll = 476 nm vs. 647 nm (Eg) E3 T = 5 K
L g totheDRRSin CaC6, excludingthescenariothatwe
40 mightbeobservingthegraphiticDbandfromdeinter-
D(647nm) D(476nm)
G
calatedregions.
]
rel. u. 30 x 2.5 graTphheensec-hdeemrievefdorelDecRtrRoSnicinbaCnadCs6.T(hFeirge.4isaa)sienqvuoelnvcees
'' [ 20 offourstepstothisprocess: (1)Followingtheabsorp-
cccc D* tionofthephoton,anelectron-holepairisexcitedasa
resultofarealinter-bandtransition. Thiseventoccurs
10
at the band wave vector k in the BZ, where the inter-
x 2.5
band separation energy matches the excitation energy
0 asindicatedbya solid verticalarrow(ABforthe blue
1100 1200 1300 1400 1500 1600
laserline). Ifconsideringhigh-symmetrydirectionsin
Raman shift [cm-1]
the CaC6 band structure, the inter-bandtransition for
visiblelightisonlypossibleatthewavevectorkinthe
FIG.3:(coloronline)CaC6 RamanspectrumintheEgsym- Γ−TdirectionoftherhombohedralBZ39. Thisiswhy
metry channel excited with the 476nm laser line (blue cir- wechosetheelectronicbandstructureandthephonon
cles) vs. 647nm (red triangles). The vertical scale of the
dispersion along Γ−T to approximate our calculation
647nm excitation spectrum has been adjusted for the E3
g oftheDRRSeffectinCaC6. (2)Next,theelectronen-
modetobedisplayedwiththesamerelativeintensity.
countersan intra-bandtransition in which it is inelas-
tically scattered by a phonon of a finite wave vector
qoppositetothedirectionofthesoliddiagonalarrow
D and G bands and are identified by the rough fre- (BC,forthebluelaserlight)thatillustratestheelectron
quencyregionswheretheyappear: around1300cm−1 transition.(3)Theelectroniselasticallyscatteredback
fortheDbandandaround1600cm−1 fortheGband. acrosstheBZ(CD)byadefectto(4)recombine(DA)
The D band is indicative of disorder in form of scat- with the hole in the valence band by emission of the
tering centers as found in polycrystalline samples27, Ramanshiftedphoton.
inhighly-orientedpyrolyticgraphite(HOPG)samples Fig.4a reveals two possible ways to inelastically
close to edges28 and in irradiated graphite29. The G scattertheelectroninstep2oftheDRRSprocess: (a)
bandingraphiteandgrapheneisattributedto thefirst AcrosstheTpointintotheneighboringBZbetweenthe
order Raman band arising from the E2g phonon, an twononequivalentΓpoints,namelyintheΓ−T−Γ′
in-planehexagoncompressingvibration. Infew-layer direction (which is referred to as inter-valley scatter-
graphenethepositionoftheGbanddependsondoping ing), or (b) across the Γ point between the right and
of graphenesheets and on surface charges30,31,32. We left branches of the conduction band parabola inside
shalldiscusstheoriginoftheDandGband(shownin thesameBZ(whichisreferredtoasintra-valleyscat-
Fig-s2and3)inthissection. tering).TheDbandfrequencyisdeterminedbyfinding
The DRRS processcouplesto the disorderinduced the phonon energy in the phonon dispersion that cor-
D bandmakingpointsof the phonondispersionaway respondsto the length of the phononwave vector |q|,
fromtheBZcenteraccessiblebyRamanscattering.By which is set by the second DRRS transition by either
employingtwoexcitationwavelengthswemeasuretwo intra-valleyorinter-valleyscattering.
suchpointsbymeansoftheDbandRamanshift.More Fig.4b displays allowed DRRS frequencies as a
pointsinthephonondispersionofCaC6 willbetraced function of excitation energy. We call this function a
with the help of other (weaker) disorder induced Ra- double resonance curve; there is one curve for each
manbands38. Fig.3 showshowtheDbandshiftsfrom phonon branch and the set of the double resonance
1308cm−1 to 1332cm−1 accordingto the excitation curves is unique for any material. The double reso-
energychangefrom647nmto476nm. Thistranslates nance curve is obtained in two steps: (i) We examine
to a frequency shift rate of 35cm−1/eV in the visi- the CaC6 band structure and match the laser excita-
blelightrangeofexcitationenergiesinagreementwith tion energy to the electron wave vector k where the
data presented in Fig.1 of Ref.10. The observed fre- electron-hole pair creation can be accommodated by
quencyshiftrate ofthe D bandin CaC6 isspecific to a corresponding energy separation between the elec-
thiscompoundandislessthanthe50cm−1 frequency tronic bands. This allows us to find the length of the
shift rate of the D band in graphite33,34 which allows phonon wave vector q involved in the inelastic scat-
6
2 1600
G
1 E Y B C a -1m]1400 bD**DEg3 Eg 111343053802 c A2u+AE1gg 1200pho
Energy [eV] --021 gCraaCph6ene derDivedA baXnds Raman shift [c11024680000000000 EDg*1* EEgg 1414200 AEE2guu+++AAAEEE122uggugu 4800000 non energy [cm]-1
T ' G T G ' 0 1 2 3 4 c X G T
k excitation energy [eV] k
FIG.4:(coloronline)DoubleresonanceRamanscatteringinCaC6.a)SchemeoftheDRRSprocessbasedongraphenderived
electronic bands inCaC6. Thesolidvertical arrowsshow thefirst resonant transition. Thesoliddiagonal arrows show the
second resonant transition in which the electron is scattered inelastically by phonons of finite wave vector q. The dashed
horizontal linesindicatedefect-inducedelasticrecoiloftheelectron. Theverticaldashedlinesdepictthefinalelectron-hole
recombination. Both possible scattering scenarios: inter-valley (via T) and intra-valley (via Γ) are displayed. b) The solid
linesshowdoubleresonancecurves: allowedDRRSshiftsafunctionofexcitationenergy. Linesinblackarederivedfrom’E’
branchesandlinesingreyfrom’A’branches. DRRScurvesderivedfromgraphenelikephononbranches(E32g andA2g)are
drawnwithboldsolidlines. Allother(zonefolded)curvesaredrawneitherwithsimplesolidlineswhenderivedfromeven
’g’modesorwithhair-linesforodd’u’modes.TheobservedRamanpeaksaremarkedbysymbolsattherespectiveexcitation
energies.Thepeakat1450cm−1 isadoptedfromRef.10.c)ThemeasuredD,D∗,D∗∗andE1∗-bandspositionsaremappedin
g
theCaC6 phonondispersion(adoptedfromRef.8)withcoloredandfirstorderRamanactiveEgmodeswithwhitecircles.
tering step of the DRRS. (ii) We read off the phonon circles. Considering the D band frequency range, its
energy ω in the phonon dispersion that corresponds strong intensity and blue-shiftof the D band with ex-
q
totheq-sobtainedinthepreviousstepforallpossible citation energy, the DRRS characteristic displayed by
excitationenergiesforselectedphononbranches. the D band correspondswell to the double resonance
curvederivedfrom the lower E3 phononbranch. The
g
Theconclusionisthree-fold: experimentalpointsare belowthecalculatedcurveby
(1) For CaC6 there exists an activation threshold for approximately50cm−1. WeconcludethattheDband
thedisorderinducedDRRSprocessat1.1eVwherethe inCaC6 originatesfromthelowerE3g branch.
graphene derived conduction band crosses the Fermi
level. ThisisindifferencetoDRRSingraphitewhere The D band is depolarized because phase informa-
the first transition can in principle occur at arbitrary tion of the incoming photon is lost in the process of
smallexcitationenergiesasaresultofinter-bandtran- intra-bandrelaxationalscattering. Thisis trueforany
sitionsbetweentheDiracconesintheproximityofthe DRRS induced band and thus two other depolarized
KpointsofthehexagonalBZ. features: at 1120cm−1 and at 440cm−1 (labeled D∗
(2) Because of the symmetry of the band structure andE1∗) maybe interpretedas resultingfromDRRS.
g
the inter-valley and intra-valley scattering yield the Thesemodesaremarkedbysmallsymbolsattheirre-
sameDRRSfrequenciesintheapproximationthatthe spectivefrequenciesinFig.4bandc. WefindthatE1∗
g
lengthofthephononicwavevectorq(whichisthehy- isreadilyassociatedwiththeupperE1 phononbranch
g
pothenuseofthetrianglesBEDandBDC)isestimated thatismostlyflatinthevisibleenergyregion. D∗ can
bythehorizontallinesDEorDC40. arisefromthelowerE2 phononbranch. Itis60cm−1
g
(3) The slope of the double resonance curves is pos- belowthecalculateddoubleresonancecurve. Thiser-
itive for all three graphene derived phonon branches ror while substantial is of the same order as the error
(thick solid lines) in the visible light range. Thus we for the D band and appears to confirm what seems to
expect a positive (blue) shift of the D band when the beanoverestimationofthephononfrequenciesinthe
excitationenergyisincreasedfrom647nmto476nm. Γ−T direction close to the edge of the BZ. Finally,
The frequencies of observed Raman peaks are shown we can treat the 1450cm−1 band that has been ob-
bysymbolsinFig.4b. ThepositionoftheDbandfor served in Ref.10 in CaC6 samples exposed to air the
the employed laser wavelengths is indicated by filled sameway. Thisband(labeledD∗∗ andrepresentedby
7
a small circle at 2.41eV in Fig.4b) can be allocated VI. THEEFFECTOFINTERCALANTDISORDER
tothehighestdoubleresonancecurveoriginatingfrom
theupperE3branch.Indeed,examinationofFig.1bof
g Reactivitywithairhumidityposesasignificantchal-
Ref.10 shows that the the 1450cm−1 feature appears
lengetoexperimentalinvestigationofCaC6. Previous
onlyalongaverystrongDbandandisabsentinspec- spectroscopic work on lattice dynamics10 shows that
tra from freshly cleavedsamples where the D band is
Raman scattering is in particular sensitive to sample
weak. Consequentlythispeakcannotbeattributedto agingwith the characteristicE3 modedisappearingin
g
aRamanactivemodebutisadisorderinducedDRRS
less than half an hour upon air exposure. X-ray re-
band. The same argumentholdsalso for the D∗ band flectionstudydoesnotshowcomparablesensitivity11.
visible in Fig.3 of Ref.10. It confirms our interpreta-
This makes Raman scattering a preferred method to
tionofD∗ asduetoDRRS.
probesurfacedegradation. Whenanimperfectspoton
The frequencies of disorder induced bands can be the samplesurface isevaluatedor whenthe sampleis
plotted in the phonon dispersion diagram yielding a exposed to humidity in air the graphite-like D and G
measurement for points of the phonon dispersion in- bandsappearinthespectrum.
side the BZ. The electronic band separation is in res- The disorder induced D band in graphite is associ-
onance with the red laser excitation of λL = 647nm atedwithtwomaincategoriesofdefects.First,crystal-
(1.917eV) at 0.55|ΓT| and with the blue excitation lite edges or domain boundaries27,28, and second, de-
λL = 476.4nm (2.604eV) at 0.66|ΓT|, here |ΓT| fects introduced by ion irradiation29 that can be un-
is the extension of the BZ in the respective direction. derstoodasstrayCoulombpotentialsimplantedinthe
Thecorrespondingresonanttransitionpairs(ωph,qph) crystal lattice. While comparison of the D and G
are plotted for the frequencies of the disorder bands band features in graphite to the D and G bands in
ωp∗h in Fig.4c. From these experimentally measured CaC6 canonlybequalitativeduetodifferenceincrys-
pointsof phonondispersionwe concludethat the cal- talstructure, someanalogiesto bothtypesof disorder
culationfromfirstprinciplesasperformedinRef.8un- are observed. For polycrystalline graphites the rela-
derestimatestheenergyoftheE3gzonecentermode,but tiveRamanintensityratiooftheDbandtotheGband
tendstooverestimatetheenergyofhighfrequencyEg I(D)/I(G) has empirically been found to increase lin-
branchesclosetotheedgeofBZintheΓ−Tdirection. earlywiththeinversecrystallitesize27.
SubstitutingI(G)oftheRef.27calibrationwithI(E3)
g
wefindfromFig.3theratioI(D)/I(E3)≈ 0.65,which
g
V. SUPERCONDUCTINGGAPBYELECTRONIC infersahypotheticalaveragedomainsize41 La(CaC6)
∼ 100A˚.Thisvalueiscomparablewiththemeanfree
RAMANSCATTERING
path of ∼ 500A˚ along the ab-plane estimated from
the residual resistivity of ∼ 1µΩcm. Additionally,
Below Tc low energy electronic Raman scattering this ’scale of disorder’ is of the same magnitude as
exhibitsasharpSCcoherencepeakintheEg symme- the superconducting coherence length ξ ∼ 300A˚ as
trychannelat24cm−1 (Fig.2andFig.5c). Theposi- measuredbyscanningtunnelingmicroscopy19. Asim-
tionofthecoherencepeak(∼3.0kBTc)isin-between ilar I(D)/I(G) intensity ratio is observed in annealed
the values 2∆ab = 21.8cm−1 reported from direc- HOPG samples irradiated with 11B ions29 at a flux
tional point contact spectroscopy17, where ’ab’ refers rateof5×1015cm−2. IntercalatedCaionswhendis-
tothedirectionofthecurrentflow,and25.8cm−1 de- placedfromtheirtriangularpatternintheperfectcrys-
terminedbySTMmeasurements19. talline order will have the effect of implanted stray
The FWHM ∼12cm−1 of the coherence peak ob- Coulomb potentials in CaC6 and will display a Ra-
tainedbyfocusingthelaseronafew’high-quality’ar- mansignaturethatcorrespondstothemicro-crystallite
easofthecleavedsurfaceisofthesamemagnitudeas regime described in Ref.29. This regime that is acti-
thewidthofthestep intheincreaseofreflectancebe- vated for ion fluences above 1 × 1015 ions/cm2 may
low2∆observedinRef.21andcorrespondstotherange be described as an intermediate state between the or-
oftheanisotropicgapdistributionsuggestedinRef.20. dered and amorphousstates when regions of disorder
ButthecharacteristicwidthoftheSCcoherencepeak begintocoalesce/percolateformingislandsofordered
andimpurityrelatedbroadeningwillalsocontributeto regionssurroundedby disorder. Thisstate is reported
the observedline widthputtinglimitsonpossible gap tobemetastableingraphiteastheordercanberestored
distributions. byannealing. Thelinewidthofthepartiallypolarized
8
l lll = 647.1 nm
L
crystal 1 G CaC x 0.15 crystal 2 G SC (5 K) vs. crystal 3
20 CaC vs. graphite 6 normal state (20 K)
6 G E3
Kish Graphite g
x 0.75 E3
.] 15 g G
u T (CaC) = 5 K
6
el. T (graphite) = 300 K
r 10
[
''
c
5
a b c
0
0 100 1500 1600 0 100 1500 1600 0 100 1500 1600
Raman shift [cm-1]
FIG. 5: (color online) The relative intensities of the E3 mode (when present) and the G band in Raman spectra taken with
g
the647nmexcitationinRLgeometry fromdifferent samples. a) NoSCsignatureisobserved incrystal 1, theE3 mode is
g
absentalso. ThepinksolidlineshowstheRLpolarizedspectrumfromkishgraphitewithitsE2g peakat1579cm−1. (b)The
intensitiesofthetheCaC6 GbandandtheE3g modeincrystal2relateapproximatelyas2:1. Thesuperconductingcoherence
peakat24cm−1 ispresentbutisweakandbroad. c)TheGbandandE3 intensitiesincrystal3relateapproximatelyas1:2.
g
ThestrongE3modeandasharpprominentSCcoherencepeakareatthesameRamanshiftsasinpanel(b).
g
G band in our CaC6 sample (γG = 32cm−1) also shifts the unique E3g phononic mode of CaC6 is ab-
correspondstothemicro-crystalliteregimeofgraphite sent with only the G band contributing to the Raman
damagedbyionimplantation. intensity. We therefore suggest that down to the skin
Ingeneral,asharppairbreakingpeakisobservedby depth the CaC6 structure is disturbed from its rhom-
Raman in s-type superconductorsin the clean limit35. bohedralformbyCadeintercalation. We comparethe
The relative intensity of the SC pair breakingpeak to CaC6 GbandtothegraphiticGbandrecordedfroma
thebackgroundallowsevaluationoftheSCproperties. kish graphite sample to find that in the deintercalated
Thereisadistributionofresultsrangingfromabsence CaC6 theGbandisupshiftedincomparisontosimple
ofanySCfeaturesintheRamanspectrum(Fig.5a)to graphite.Thismightreflectremnantdopingby’surviv-
asharp,wellpronouncedSCcoherencepeak(Fig.5c). ing’disorderedCaatomsbutshouldnotbeinterpreted
Broadening and vanishing of the SC coherence peak asasignofelectron-phononcouplinginCaC6 aswith-
isattributedtodifferentdegreesofdisordercausedby out the E3g mode at 1508cm−1 it is not an ordered
possible Li-ion contamination, Ca deintercalation or CaC6 structure any more. Sample 2 (Fig.5b) shows
agingofthecleavedsurface.Theshownspectrarepre- weaksuperconductivitywithabroadSCpairbreaking
sentthebestresultsobtainedfromasetofspotsidenti- peakontopofunderlyingbackgroundintensity.Inthis
fiedbyavisualscanoftherespectivecrystalssurfaces. case we do observe the E3g mode with about half the
In Fig.5 we show that the relative ratio of the E3 intensityofthatoftheGband.Theinvestigatedregion
g ofsample2issuperconductingbutcanbedescribedas
modeintensitytothatoftheGbandcorrelateswiththe
low quality. The respective shapes and relative inten-
widthandintensityoftheSCcoherencepeak.Weeval-
sities of recorded electronic/phononic Raman modes
uateRamanscatteringinthelowenergywindowupto
150cm−1 totracetheSCsignatureandinthehighen- arecharacteristicofcontamination.Sample3(Fig.5c)
ergywindowbetween1450cm−1 and1700cm−1 for displays a sharp SC pair breaking peak, its rhombo-
hedralstructure is intact with the E3 mode more than
the phononic signature. Both measurements are per- g
two times stronger than the G band. We characterize
formedonthesamespotofthecleavedsurfaceandin
thissampleashighquality/lowcontaminationcrystal.
the samecoolingcycle. Sample1 (Fig.5a)displaysa
Insummary,forsamplequalityevaluationpurposethe
smooth, close to linear slope at low energiesshowing
no SC peak at all. Correspondingly, at high Raman relativeintensityofthe E3g modetothe CaC6 G band
9
indicatesifthesampleinquestionissuperconducting. sulting from disordered and partially non-intercalated
TheE3 modemustbepresentforsuperconductivityto regions. The dispersive behavior of the D band as a
g
occurandthegreateritsintensityrelativetotheGband function of excitation energy is a signature of double
arisingfromdeintercalatedregionsthegreaterportion resonant Raman scattering in CaC6. We have calcu-
ofthesampleissuperconducting. lateddoubleresonancecurvesforallphononbranches.
OnthebasisofthiscalculationwehaveassignedtheD
bandtoresultfromthelowerE branchalongtheΓ−T
g
VII. CONCLUSION line of the CaC6 phonondispersion. By using differ-
ent laser excitations we have measured points in the
InconclusionwehaveinvestigatedpolarizedRaman phonondispersionatfinitewavevectors. Fromanalo-
spectra from CaC6 samples with different degree of giestostudiesofdisorderedgraphitestheinvestigated
disorder. Thebestoftheexaminedsamplesexhibitsa CaC6 samplesarebestdescribedasbeinginamicro-
clearsignatureofsuperconductivityintheformofaSC crystalliteregimewithdomainboundaries∼100A˚.
coherencepeakat24cm−1. Wehaveusedthissample We thank F. Mauri and I. Mazin for discussion.
torecorddetailedfirstorderRamanscatteringspectra. AM acknowledgessupportby RutgersUniversity, the
InthesespectrawehaveidentifiedtwofundamentalE Alcatel-LucentFoundationandtheGermanAcademic
g
modesandadditionalgraphitelike D andGbandsre- ExchangeService.
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37 TheB2g outofplanegraphenevibrationbecomesanA2g specttothatofgraphite,resultingina70A˚ √3 120A˚
× ≈
vibrationinCaC6.Botharesilentmodes. estimateforLa(CaC6).
38 We observe these weak disorder modes only with the
476nmexcitation.Thesemodesareapparentlybelowthe
