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Ramanscattering 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 rotation 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 inelastically 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 different 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. 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Klein and S.B. Dierker, Phys. Rev. B 29, 4976 41 With6Catomsintheab-crosssectionoftheCa|C6−uni|t (1984). cell vs.2atoms intheprimitivecell of agraphene layer 36 R.NarulaandS.Reich,Phys.Rev.B78,165422(2008). thelinearcharacteristiclengthinCaC6 scalesas√3inre- 37 TheB2g outofplanegraphenevibrationbecomesanA2g specttothatofgraphite,resultingina70A˚ √3 120A˚ × ≈ vibrationinCaC6.Botharesilentmodes. estimateforLa(CaC6). 38 We observe these weak disorder modes only with the 476nmexcitation.Thesemodesareapparentlybelowthe