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Weak-coupling superconductivity in a strongly correlated iron pnictide A. Charnukha1,2,3, K. W. Post1, S. Thirupathaiah2,4, D. Pro¨pper3, S. Wurmehl2, M. Roslova2,5, I. Morozov2,5, B. Bu¨chner2, A. N. Yaresko3, A. V. Boris3, S. V. Borisenko2 & D. N. Basov1 6 1 1PhysicsDepartment,UniversityofCalifornia–SanDiego,LaJolla,CA92093,USA,2LeibnizInstituteforSolidStateandMaterialsResearch,IFW, 0 01069Dresden,Germany,3MaxPlanckInstituteforSolidStateResearch,70569Stuttgart,Germany,4SolidStateandStructuralChemistryUnit, 2 IndianInstituteofScience,Bangalore–560012,India,5DepartmentofChemistry,MoscowStateUniversity,119991Moscow,Russia.†E-mail: n [email protected]. a J Iron-basedsuperconductorshavebeenfoundtoexhibitanintimateinterplayoforbital,spin,andlatticedegreesoffreedom,dramatically 9 affectingtheirlow-energyelectronicproperties,includingsuperconductivity. Albeittheprecisepairingmechanismremainsunidentified, 2 severalcandidateinteractionshavebeensuggestedtomediatethesuperconductingpairing,bothintheorbitalandinthespinchannel. Here,weemployopticalspectroscopy(OS),angle-resolvedphotoemissionspectroscopy(ARPES),abinitioband-structure,andEliashberg ] n calculationstoshowthatnearlyoptimallydopedNaFe0.978Co0.022Asexhibitssomeofthestrongestorbitallyselectiveelectroniccorrelations o inthefamilyofironpnictides.Unexpectedly,wefindthatthemassenhancementofitinerantchargecarriersinthestronglycorrelatedband c isdramaticallyreducedneartheΓpointandattributethiseffecttoorbitalmixinginducedbypronouncedspin-orbitcoupling. Embracing - thetruebandstructureallowsustodescribealllow-energyelectronicpropertiesobtainedinourexperimentswithremarkableconsistency r p anddemonstratethatsuperconductivityinthismaterialisratherweakandmediatedbyspinfluctuations. u Strong entanglement of various electronic and lattice degrees of freedom in the iron-based superconductors has become the s leitmotifofrecentcondensed-matterresearchandhasbeenidentifiedwithavastvarietyofexperimentalprobes1–4 andinterpreted t. theoretically5,6. ThisinherentcomplexityarisesfrommultiplepartiallyfilledFe-3dorbitalssimultaneouslycontributingtothelow- a energy quasiparticle dynamics and strongly affected by the Hund’s coupling correlations7. The orbitally selective nature of these m interactionsleadstoalikewiseorbitallyselectivebandwidthrenormalizationandrelativeenergyshiftofvariousbandswithrespect - to each other and the Fermi level due to the pronounced particle-hole asymmetry of the electronic structure8. Such non-trivial d interaction-inducedmodificationsresultinasingularFermi-surfacetopologythatisdramaticallydifferentfromthepredictionsof n o theoretical calculations in both the number and the binding energy of the bands crossing the Fermi level9,10, strongly affecting c low-energyelectronicpropertiesincludingsuperconductivity. [ Here,weshowthatinthenearlyoptimallydopedNaFe0.978Co0.022Ascompound,low-energyorbitallyselectiverenormalization ofthebandstructuredeviatesmarkedlyfromthegeneralexperimentalandtheoreticalrenormalizationtrendiniron-basedsupercon- 1 ductors11. WefindmorethantwicestrongerthanexpectedorbitallyselectiveelectroniccorrelationsintheFe-3d bandcrossing v xy 5 the Fermi level near the Γ point of the Brillouin zone, similarly to FeTe1−xSex12–14. However, in contrast to the observations in 9 thelattercompounds,themassenhancementinthestronglycorrelatedbandofNaFe0.978Co0.022Asisdrasticallyreducednearthe 1 Fermilevel,whereourrelativisticabinitiocalculationspredictorbitalmixingoftheFe-3dxy,3dxz,and3dyz orbitalstooccurdueto 8 spin-orbitcoupling,leadingtoapronouncedmodificationoflow-energyelectronicproperties. Asimultaneousdetailedanalysisof 0 theARPESandOSdatarevealsremarkableconsistencyintheextracteditinerantpropertiesofboththenormalandthesupercon- . ductingstate. Itallowsustoconcludethattheubiquitousdichotomybetweenthecoherentandincoherentfar-infraredquasiparticle 1 response observedin all iron-basedsuperconductors15 is notdominated by thedisparity inthe mobilities ofthe hole andelectron 0 chargecarriersbutratheroriginatesintheinelasticscatteringfromanintermediatebosonicexcitation. Finally,alloftheobserved 6 featuresinthefar-infraredconductivityinthesuperconductingandnormalstatecanbereproducedinaneffectivetwo-bandEliash- 1 bergmodelassumingrelativelyweaksuperconductingpairingwiths symmetrymediatedbylow-energyspinfluctuationswiththe : ± v frequencyandtemperaturedependenceobservedinthesamecompoundbyinelasticneutronscattering16. i X Theeffectofelectroniccorrelationsonthelow-energyelectronicstructureofNaFe0.978Co0.022AsisillustratedinFigs.1a–c. The generalbandstructureofNaFe Co Ashasbeenstudiedextensivelyandconsists,similarlytomostiron-basedsuperconductors, 1−x x r a ofthreeholebandsattheΓ(Z)pointoftheBrillouinzoneandtwoelectronbandsneartheMpointofthetwo-FeBrillouinzone17,18 (thedifferenceinthebandstructureattheΓandZpointsisminor,seeSupplementaryInformation). Bothofthesesetsofelectronic dispersionsareanalyzedinFigs.1a,b,respectively,andcomparedtothecorrespondingpredictionsofourband-structurecalculations showninFig.1c. InstarkcontrasttothepredictionofthetheoryinFig.1c,onlyoneholebandattheΓpointofNaFe Co As 0.978 0.022 crossestheFermilevel,theremainingtwoareshiftedtolowerbindingenergiesandterminatewithinabout20meVbelowtheFermi level. Theseinnerholebandshaveawell-definedparabolicshape,asillustratedbythefits(lowerwhiteandreddashedlines)tothe 1 Figure1| Low-energyelectronicpropertiesofNaFe0.978Co0.022As.a,b,Low-energyelectronicstructureofNaFe0.978Co0.022Asinthenormal stateneartheΓ(a,30K)andM(b,22K)pointsoftheBrillouinzonerecordedusing20eVand25eVphotonslinearlypolarizedperpendicularto andwithintheplaneofincidence,respectively.Thedispersionofallelectronicbandsobservedinexperiment(blacksolidlines)hasbeenobtained usingamulti-Lorentzianfitofthemomentum-distributioncurves. Effective-massrenormalizationindicatedinthepanelshasbeencalculatedby comparingthelow-energyparabolicfitstotheelectronicdispersionsextractedfromtheexperimentaldata(dashedlinesinpanelsa,b)withthoseto thecorrespondingelectronicbandspredictedtheoretically(dashedlinesinpanelc).c,Theoreticallypredictedlow-energyelectronicbandstructure ofNaFeAsintheΓ−M high-symmetrydirectionoftheBrillouinzone(blacksolidlines)andlow-energyparabolicfitstothedispersionsnear ΓandM(dashedlines). Thecolorsofthedashedlinescorrespondtothoseinpanelsa,b. PlasmafrequenciesofallbandscrossingtheFermi levelextractedfromexperimentaldataandpredictedbytheoryareshowninpanelsa–c.d,ElectronicbandstructureintheΓ−Mhigh-symmetry directionoftheBrillouinzoneneartheΓpointobtainedinarelativisticDFTcalculation(blacklines),whichexplicitlyaccountsforafinitespin- orbitcoupling(itscharacteristicenergyscaleisshownasbluehatchedarea). Theresultsofthecorrespondingnon-relativisticcalculationfrom panelcareshownforcomparison(greylines).e,Energydependenceoftheeffectivemassrenormalizationintheouter(blueopencircles),middle (greycircles),andinner(redcircles)holebandattheΓpointwithrespecttothecorrespondinglow-energyquasiparticlemassesextractedfrom thetheoreticallypredictedbandstructureinpanelcusingparabolicfits. Theenergyscaleaffectedbyspin-orbitinteractionisindicatedasablue hatched area. f,g, Real part of the optical conductivity (f) and the dielectric function (g) of NaFe0.978Co0.022As obtained in OS measurements (opencircles)alongwiththeresultsofaDrude-Lorentzdispersionanalysis(blueandredlines/shadedareasandgreenline/shadedareaforthetwo Drudetermsandthetotalcontributionofallinterbandtransitions,respectively;graysolidlinesindicatethesumofallterms). Theparametersof theitinerantchargecarrierresponseobtainedbymeansofthisanalysisaresummarizedinpanelg. experimental band dispersions extracted from momentum-distribution curves at various binding energies (black solid lines). The comparisonofthefittedeffectivemassestothetheoreticalbandstructureinFig.1crevealsarenormalizationbyafactorof4.3and 4.5fortheinnerandmiddleholebandsofFe-3d orbitalcharacter,respectively. TheouterholebandofFe-3d orbitalcharacter xz,yz xy in Fig. 1a shows a dramatic renormalization by a factor of more than 8 (blue dashed line), clearly demonstrating the existence of verystrongandorbitallyselectiveelectroniccorrelationsinNaFe Co As,similartoFeTe Se 12–14 (theslightasymmetry 0.978 0.022 1−x x ofthephotoemissionintensitydistributioninFig.1adoesnotaffectourconclusions,seeSupplementaryInformation).Suchastrong enhancementoftheeffectivequasiparticlemassisatoddswiththepredictedrenormalizationbyafactorofonly3to4,identifiedin combineddensity-functionalanddynamicmean-fieldtheorycalculations(DFT+DMFT)inRefs.11. Ouranalogousanalysisofthe experimentalbandstructureofNaFe Co AsattheMpointoftheBrillouinzone(Fig.1d)revealstwowell-definedparabolic 0.978 0.022 bandsofelectroncharacter,consistentwiththepredictionoftheoryinFig.1c,withaverydisparateeffective-massrenormalization ofabout2.2and5.7fortheinnerandouterelectronbands,respectively. Quite surprisingly, the outer hole band’s dispersion reveals a departure from a parabolic shape (blue dashed line in Fig. 1a) upon approaching the Fermi level, clearly absent in the calculated band structure. To quantify this non-parabolicity, we extract theenergy-dependenteffectivemassm(E)=h¯2k(E)dk/dE,whereh¯ isthePlanckconstant,k—quasiparticlewavevector,andE —quasiparticleenergy. Foraparabolicdispersionm(E)=const. Theresultingenergy-dependenteffectivemassrenormalization m (E)/m inallholebandsneartheΓpointoftheBrillouinzone(m fromFig.1c)isshowninFig.1e. Itisclearthatwhile exp LDA LDA thehigher-energy(outsideofthebluehatchedarea)effectivemassoftheouterholebandissimplyrenormalizedfromitstheoretical counterpartbyafactorof8,atlowenergiesthisisnotthecase. This dramatic reduction of the effective mass at lower binding energies cannot be attributed solely to the effect of high-energy electroniccorrelations, whichtypicallyleadtoanenhancementoftheeffectivemassovertheentireelectronicbandwidth. Inthe 2 Figure 2| Superconductivity in nearly optimally doped NaFe0.978Co0.022As. a, Relative change in the sample reflectance as a function of temperatureforseveralfrequenciesintheTHzspectralrange. Thetransitionintothesuperconductingstateisevidencedbyamarkedincreasein thesamplereflectancebelowTc≈18K(verticaldashedline).b,RealpartoftheitinerantTHzandfar-infraredconductivityofNaFe0.978Co0.022As inthesuperconductingstateat8K(bluesolidline)andnormalstateat20and30K(redandblacksolidlines,respectively). Theformationof Cooperpairsismanifestedinthemissingareaundertheconductivitycurveinthesuperconductingvsnormalstate(hatchedarea),whichamounts toaLondonpenetrationdepthof430nm. Opticalsuperconductingenergygap2∆isclearlyvisibleastheenergyatwhichtherealpartofthe opticalconductivityvanishes. Thefrequency-dependenceoftheopticalconductivityabovetheinitialonsetofabsorptioninthesuperconducting stateexhibitsaquasilinearcharacter,whichdefinesanadditionalenergyscale,E (forinterpretationseetext). Normalstateopticalconductivity 1 is recovered at about 16∆ (vertical dashed line). c, Comparison of the real part of the optical conductivity in the superconducting (8 K, gray opencircles)andnormal(20K,grayfilledcircles)stateobtainedexperimentallytotheresultsoftheoreticalcalculationsintheframeworkofan effectivetwo-bandEliashbergtheoryat8K(bluesolidline)and20K(redsolidline).Absorptionbelow2∆inthesuperconductingstateisdueto thermallyexcitedquasiparticles. Allparametersofthetheoryareindicatedinthepanel. Theinitialsharponsetofabsorptionat2∆isassistedby elasticimpurityscatteringwhilethequasilinearfrequencydependenceoftheopticalconductivityathigherenergiesresultsfromHolsteinprocesses (breakingofaCooperpairwithasimultaneouscreationofoneorseveralquantaofthemediatingboson).d,Thespectralfunctionofthemediating bosoninthenormal(25K)andsuperconducting(5K)stateusedinthecalculation(redandbluesolidlines,respectively)andtheimaginarypart ofthespinsusceptibilityobtainedusinginelasticneutronscatteringonthesamecompound(opencircles;datafromRef.16). Imaginarypartof thespinsusceptibilityinthesuperconductingstateclearlyexhibitsaresonancemodeat7.5meVandaspingap(SG)of5.6meV,approximately equaltotheopticalsuperconductingenergygap2∆inthismaterial. presenceoforbitallyselectiverenormalizationthesameistrueforeachbandofagivenorbitalcharacter. Ourabinitiocalculations (Fig. 1c) clearly show that the outer hole band has a well-defined 3d orbital character up to its termination. Recently, it has xy been demonstrated that spin-orbit coupling is not negligible in iron-based superconductors19. Provided that the hole bands of 3d and 3d character are almost degenerate at the Γ point of the Brillouin zone, as can be seen in Fig. 1c, the existence of a xy xz,yz sizablespin-orbitinteractionwouldleadtothemixingoftheorbitalcharacterinthesethreebandsandpotentiallyreducethemass renormalization in the outer 3d hole band due to a large admixture of more weakly renormalized 3d bands. The existence xy xz,yz ofsuchorbitalmixinghasbeenidentifiedpreviouslybasedonthepolarizationdependenceofthephotoemissionintensitynearthe Γ(Z)pointinRef.17. Giventhereductionoftheeffectivemassintheouterholebandduetoorbitalmixing,oneshouldexpecta corresponding enhancement of the effective mass in the middle and/or inner hole bands dueto the finite admixture of the heavier 3d orbital. Thiseffect,albeitrathersubtle,canneverthelessbeclearlyidentifiedinthesecondderivativeoftheexperimentaldata xy inFig.1auponcloseinspection(seeSupplementaryInformation). The aforementioned reduction of the effective mass due to orbital mixing does not rely on the existence of strong electronic correlations and should be observable already at the level of quasiparticle band masses. Indeed, Fig. 1d demonstrates that when spin-orbitcouplinginthismaterialistakenintoaccountinarelativisticabinitiocalculation(blacksolidlines),thedispersionofthe holebandsatlowenergiesshowsapronounceddeparturefromthatobtainedinthenon-relativisticcalculationpresentedinFig.1c (greysolidlines). Boththereductionoftheeffectivemassintheouterbandanditsenhancementinthemiddleandinnerbandsare apparent. Thecomplexmodificationofthelow-energyelectronicstructurewithrespecttotheoryobservedinourexperimenthasaprofound effectontheitinerantpropertiesofNaFe Co As. ItstronglyaffectstheanalysisandinterpretationoftheOSdataobtained 0.978 0.022 onthesamecompound, aswewilldemonstratebelow. TheitinerantquasiparticleresponsecanbeextractedfromtheOSdataby eliminatingthecontributionofallclearlyidentifiableinterbandtransitions(greenlinesinFigs.1f,g)fromtheopticalconductivity σ(ω) or, equivalently, dielectric function ε(ω)=1+4πiσ(ω)/ω (see also Supplementary Information). The resulting itinerant optical response σit(ω), or εit(ω), can be decomposed into a narrow (coherent) and a broad (incoherent) Drude-like contribution (blueandredlinesinFigs.1f,g). Suchadecompositionisrathercommonintheiron-basedsuperconductorsandhasbeenobserved inessentiallyallknownmaterialsofthisfamily15. Atthesametime,theelectronicbandstructureofNaFe Co Asfeatures 0.978 0.022 threebandscrossingtheFermilevel,indicatingtheexistenceofasegregationofallfreechargecarriersintotwoeffectiveelectronic subsystems: onewithalargeandtheotheronewithasmallscatteringrate(summarizedinFig.1g). It is tempting to assign the narrow Drude component to the combined response of charge carriers on the electron sheets of the Fermi surface (which in iron-based compounds have been found to have higher mobilities than hole carriers based on Hall and quantum-oscillationmeasurements20,21),andthebroadonetothecontributionofthecarriersontheholesheetoftheFermisurface. However,adirectcomparisonoftheplasmafrequenciesofthetwoDrudetermsextractedinouranalysisoftheopticalconductivity (Fig. 1g) to those obtained from the ARPES data (as shown in Figs. 1a,b and detailed in the supplementary information) reveals 3 that this assignment is incorrect: the plasma frequency of the hole sheet of the Fermi surface, ωhole =0.2 eV, is substantially pl (cid:113) smallerthanthetotalplasmafrequencyoftheelectronsheets,ωel = ωel,in+ωel,out=0.7eV. Thereverseassignment(broad pl,tot pl pl Drudecomponenttoelectronchargecarriers)cannotbereconciledwiththenegativeHallcoefficientobservedinthiscompound22. Additionally,asimpleestimateoftheelectronmeanfreepathduetoelasticimpurityscatteringasl =v /γ,wherev istheFermi 0 F F velocity and γ is the quasiparticle scattering rate obtained in our Drude-Lorentz analysis, leads to an unrealistic result. Taking v =0.6eVA˚ fortheelectronbandsinFig.1bandγ =0.1eVforthebroadDrudecomponentinFigs.1f,g,onearrivesatl =6A˚ F 0 orlessthantwounitcells. SuchasmallmeanfreepathishardtojustifyinanearlystoichiometricNaFe Co As. Asimilar 0.978 0.022 estimateassumingγ=0.1eVontheholepocket(v =0.15eVA˚)leadstol =1.5A˚,orlessthanoneunitcell. Analogousanalysis F 0 ofthebroadDrudecomponentintheopticalconductivityofoptimallydopedBaFe Co As previouslyextractedacomparable 1.85 0.15 2 mean free path assuming elastic scattering of holes23. These inconsistencies imply that the large scattering rate of the incoherent Drudecomponentdoesnotoriginateinthelowmobilityofoneofthecharge-carriertypebutratherresultsfrominelasticscattering of charge carriers (of either sign) from an intermediate boson. This conclusion is consistent with the association of the broad Drude component with electronic correlations based on the doping dependence of the optical conductivity in various iron-based compounds24,25. The strength of electronic correlations is frequently estimated by comparing the total itinerant spectral weight (area under the (cid:16) (cid:17)2 itinerantopticalconductivitycurve)SW =(cid:82)∞σit(Ω)dΩ= ωit,exp /8,whereωit,expisthetotalitinerantplasmafrequency,tothe 0 1 pl,tot pl,tot predictionsoftheoreticalband-structurecalculations26. Whileinparticle-hole–symmetricsingle-bandmaterialsthisapproachpro- videsagoodestimateofeffective-massrenormalizationandtherebycorrelations,iniron-basedsuperconductorstheexperimentally observedplasmafrequencyismodifiedfromitstheoreticalpredictionnotonlybyorbitallyselectivebandwidthrenormalizationbut alsointrinsic(seeSupplementaryInformation)bandshifts9,aprocessthatingeneralconservesneithertheFermiwavevectornor thenumberofbandscrossingtheFermilevel,dramaticallyaffectingthetotalplasmafrequency. Therefore,theassessmentofelec- troniccorrelationsinsuchcasescanonlybereliablycarriedoutbasedonthecomparisonofthecompletelow-energyexperimentally observedbandstructuretoitstheoreticallypredictedcounterpart. Fortunately, even in such complicated cases the spectral-weight analysis of the itinerant optical response bears fruit. It is well- known that the total spectral weight of any system (including optical absorption in the ultraviolet and x-ray spectral range) is constant and does not depend on the details of the band structure: SWtot =(cid:82)∞σtot(Ω)dΩ=4πne2/m (in CGS units), where n 0 e istheelectrondensity, eandm arethebareelectronchargeandmass, respectively. Quitesimilarly, theitinerantspectralweight e (devoidofallinterbandtransitions)isalsoconstant,withm substitutedbythequasiparticlebandmassincludingrenormalization e at energies larger than the plasma frequency. Any low-energy mass renormalization due to, e.g., coupling to phonons or other bosonic excitations will not affect this spectral weight as long as its characteristic energy is smaller than the plasma frequency of free charge carriers. On the other hand, the low-energy band structure and the plasma frequency extracted from it will be affectedbysuchrenormalization. Therefore,thecomparisonofthetotalitinerantplasmafrequencyobtainedfromOSandARPES data provides access to purely boson-exchange–induced effective mass renormalization even when it is not immediately apparent in the experimental band structure. In the present case of NaFe Co As this renormalization amounts to m /m = 0.978 0.022 OS ARPES (ωit,OS/ωARPES)2 =2.15 (see Fig. 1a,b,g). This is related to the strength of electron-boson couling λ via 1+λ =m /m , pl,tot pl,tot OS ARPES givingλ =1.15. Having established that only three out of five electronic bands predicted theoretically actually contribute to the itinerant carrier responseofNaFe Co Asandthatelectronsarecoupledtoanintermediatebosonwithacouplingstrengthofλ =1.15, we 0.978 0.022 nowturntotheanalysisofthesuperconductingstatethatdevelopsinthiselectronicstructure. Uptonow,thecharacterofsupercon- ductivity in optimally doped NaFe Co As has remained unclear, with both weak and strong superconducting pairing suggested 1−x x basedontheARPESmeasurementsofthesuperconductingenergygapinRefs.17,18,respectively. Thisuncertaintycanbeelim- inated based on the analysis of our bulk OS measurements in the far-infrared and THz spectral range, shown in Fig. 2. Panel 2a showsthetemperaturedependenceoftherelativechangeofthereflectancewithrespecttothatat30Kforseveralfrequenciesinthe lowestTHzspectralrange. Thenormal-statetrendforallfrequenciesissuddenlyreversednear18K,whichthusmustbeidentified with the superconducting transition temperature, consistent with the previous ARPES measurements on the same samples17. The analysis of the real part of the optical conductivity in the far-infrared and THz spectral range reveals the quintessential feature of Cooper pairing — the dramatic suppression of the optical conductivity, with the missing area δA between the normal and the L superconducting state at finite frequencies ω >0 (δA =(cid:82)16∆(σ20K(ω)−σ8K(ω))dω, hatched area in Fig. 2b) transferred into L 0+ 1 1 the coherent response of the condensate at ω =0 (Ref. 27). Our analysis shows that this missing area corresponds to a London √ penetrationdepthλ =c/ 8δA =430nm,inaremarkableagreementwithnuclear-magnetic–resonanceandmuon-spin–rotation L L measurementsonthismaterial28,29. The vanishing of the optical conductivity in the superconducting state (blue solid line in Fig. 2b) further identifies the optical superconductingenergygap2∆≈5.6meVandthecorrespondinggapratio2∆/k T ≈3.6,veryclosetotheweak-couplinglimitof B c theBardeen-Cooper-Schrieffertheoryofsuperconductivity27,30.Thesevaluesareinagoodagreementwiththoseextractedfromthe ARPESdataonthesamesinglecrystals17andtogetherprovidecompellingevidenceforrelativelyweak-couplingsuperconductivity inNaFe Co As. 0.978 0.022 Theonsetofabsorptionat2∆(bluesolidlineinFig.2b)isverysharpandhasaMattis-Bardeenshape,characteristicofaweakly coupled superconductor or that with large elastic impurity scattering31,32. Intriguingly, the frequency dependence of the optical conductivity beyond this initial increase is non-monotonic and reveals a quasilinear section, which deviates markedly from the Mattis-Bardeenshapeanddefinesanotherenergyscale,E .Suchaquasilinearfrequencybehaviorintheopticalconductivityofiron- 1 basedsuperconductorsisnotunprecedentedandhasbeenpreviouslyobservedintheresponseofoptimallydoped(Ba,K)Fe As 33,34 2 2 andattributedtotheboson-mediatedabsorptioninthecleanlimit(lowimpurityscattering)ofastronglycoupledsuperconductor35. 4 It is quite clear that the combination of such very different features characteristic of a weakly and strongly coupled as well as clean-anddirty-limitsuperconductorintheopticalresponseofthesamematerialnecessitatesacomparisonwithatheoreticalmodel thatencompassesalloftheselimitingbehaviors. TheEliashbergtheoryofsuperconductivityisperfectlysuitedtothistask. Thekey inputparameterofthetheoryisthespectrumofthebosonicexcitationthatmediatessuperconductingpairingandtheoverallelectron- bosoncouplingstrength.SpindynamicsinNaFe Co Ashasbeenshowntobesensitivetosuperconductivity,asmanifestedin 0.978 0.022 theformationofaresonancepeakintheimaginarypartofthespinsusceptibilitybelowT (Refs.16,36),whiletheelectron-phonon c interactionhasbeendemonstratedtobeinsufficienttoaccountfortheelevatedsuperconductingtransitiontemperatureofiron-based superconductors37. Therefore, we assume interband electron-electron interaction via the exchange of spin fluctuations with the experimentallyobtainedspectralshapeinthenormalandsuperconductingstate(Fig.2d)tomediatesuperconductingpairinginour model. InthepresenceofthedisparatefeaturesobservedintheopticalresponseofNaFe Co Asandaninterbandpairinginterac- 0.978 0.022 tion,thesimplest,minimal,modelwouldincorporatetwoeffectiveelectronicbands. Thetwo-bandEliashbergformalismemployed in our calculations has been detailed in Ref. 38. We assume the symmetry of the superconducting order parameter to be of the s -type. GiventhatthedensitiesofstatesofallbandscrossingtheFermilevelarecomparableandthatallARPESmeasurements ± findlittlevariationinthesizeofthesuperconductingenergygapwithinandbetweenthebands17,18,weassumetwoeffectivebands with isotropic superconducting energy gaps of the same magnitude and opposite sign, as well as equal densities of states. Elas- tic (impurity) interband scattering is neglected35. The plasma frequencies, intraband impurity scattering rates, and the coupling strengthbetweenthebandsarethefreeparametersofthemodeltunedtofittheopticalsuperconductingenergygap2∆=5.6meV, thesuperconductingtransitiontemperatureT =18K,andtheoverallshapeoftheopticalconductivityinthesuperconductingand c normalstate. TheiroptimalvaluesobtainedinthefitundertheaforementionedconstraintsareindicatedinFig.2c. Figure2cshowstheresultofourmodeling(solidlines)overlaidontheexperimentaldatainthesuperconducting(opencircles) andnormal(filledcircles)state. Itisimmediatelyevidentthatquantitativeagreementcanbeachievedfortheparametersgivenin thepanel. Quiteremarkably,ifnotunprecedentedly,allofthetransportparameters(theindividualplasmafrequenciesofthebands andtheireffectiveimpurityscatteringrates)areinaverygoodagreementwiththepropertiesofthetwoeffectiveitinerantelectronic subsystemsextractedintheDrudeanalysisoftheconductivitydatainFig.1g. Furthermore,theinterbandelectron-bosoncoupling strengthobtainedfromthefit(λ =λ =1.2)showsexcellentagreementwiththevalueobtainedfromthespectral-weightanalysis 12 21 above(λ =1.15). Ourtheoreticalanalysisoftheopticalconductivityintheframeworkofaneffectivetwo-bandEliashbergmodelthusreconciles all of the characteristic energy scales and spectral features observed in NaFe Co As. The sharp onset of absorption at 2∆ 0.978 0.022 isdominatedbythebandwithlargeimpurityscattering. EnergyscaleE canbetracedbacktotheonsetofabsorptioninaclean 1 superconductor via a Holstein-type process of breaking-up of a Cooper pair with a simultaneous creation of one spin-fluctuation quantum39,40. In our model the lowest energy cost of this process is 2∆+SG≈11.2 meV, where SG≈5.6 meV is the spin gap observed in the spin-fluctuation spectrum (see Fig. 2d), below which no spin fluctuations exist in the superconducting state. The quasilinearbehavioraboveE resultsfromthequasilinearshapeofthespin-fluctuationspectrumabovethespingap. 1 Theremarkableagreementbetweendifferentexperimentalprobesandtheoreticaltoolsemployedinthisworkdemonstratesthe importance of employing a realistic electronic band structure to interpret the low-energy electronic properties in such complex multiband systems as iron-based superconductors, if complete and consistent understanding of their properties is to be achieved. Ourobservation ofadramatic reductionof theeffectivemass inoneof theelectronicbands ofNaFe Co As, accompanied 0.978 0.022 byrelativelyweaksuperconductingpairing, underlinestheintimateinterplaybetweendifferentelectronicdegreesoffreedomand the importance of spin-orbit coupling for the ground-state properties of the iron-based superconductors. It further shows that the modification of the orbital character of the bands crossing the Fermi level by means of intrinsic or extrinsic strain may allow for unprecedentedcontroloflow-energyelectronicpropertiesofthesecompounds,includingsuperconductivity. Methods Angle-resolved photoemission measurements were performed using synchrotron radiation (“13–ARPES” end-station at BESSY) within the range of photon energies20-90eVandvariouspolarizationsoncleavedsurfacesofhigh-qualitysinglecrystalsofNaFe0.978Co0.022As. Theoverallenergyandangularresolution were∼5meVand0.3◦,respectively,forthelowtemperaturemeasurements. Optical-spectroscopymeasurementswerecarriedoutintheTHzandthefar-infraredspectralrangebymeansofthereflectancetechniqueandfromthefar-inrared totheultravioletspectralrangeusingspectroscopicellipsometry. Theair-sensitivesamplesofoptimallydopedNaFe0.978Co0.022Aswerecleavedbeforeevery measurementandloadedintothemeasurementchamberintheneutralatmosphereofargongas,withoutexposingthesampletoairatanytime. High-accuracy absolutemeasurementsofthesample’sreflectancewerecarriedoutusingthegold-overfillingtechnique. High-qualitysinglecrystalsofsuperconductingNaFe0.978Co0.022Asweresynthesizedbytheself-fluxtechniqueandwerecharacterizedbyx-raydiffraction, transport and magnetization measurements41. The latter revealed a superconducting transition temperature of about 18 K. The width of the superconducting transitionwasfoundtobelessthan1K,indicatingveryhighhomogeneityoftheinvestigatedsamples. BandstructurecalculationswereperformedfortheexperimentalcrystalstructureofNaFeAs(Ref.42)usingthePYLMTOcomputercode43. References 1. Yi,M.etal.Symmetry-breakingorbitalanisotropyobservedfordetwinnedBa(Fe1−xCox)2As2abovethespindensitywavetransition.Proc.Natl.Acad.Sci. 108,6878-6883(2011). 2. Chu,J.-H.,Kuo,H.-H.,Analytis,J.G.&Fisher,I.R.DivergentNematicSusceptibilityinanIronArsenideSuperconductor.Science337,710–712(2012). 3. Kim,Y.K.etal.ExistenceofOrbitalOrderanditsFluctuationinSuperconductingBa(Fe1−xCox)2As2SingleCrystalsRevealedbyX-rayAbsorptionSpec- troscopy.Phys.Rev.Lett.111,217001(2013). 4. Lu,X.etal.NematicspincorrelationsinthetetragonalstateofuniaxialstrainedBaFe2−xNixAs2.Science345,657–660(2014). 5. Fernandes,R.M.,Chubukov,A.V.&Schmalian,J.Whatdrivesnematicorderiniron-basedsuperconductors?.NaturePhys.10,97–104(2014). 6. Liang,S.,Moreo,A.&Dagotto,E.NematicStateofPnictidesStabilizedbyInterplaybetweenSpin,Orbital,andLatticeDegreesofFreedom.Phys.Rev.Lett. 111,047004(2013). 7. de’Medici,L.,Giovannetti,G.&Capone,M.SelectiveMottPhysicsasaKeytoIronSuperconductors.Phys.Rev.Lett.112,177001(2014). 5 8. Cappelluti, E. , Ortenzi, L. , Benfatto, L. & Pietronero, L. Fermi surface shrinking, band shifts and interband coupling in iron-based pnictides. Phys. C: Supercond.470,S508–S510(2010). 9. Charnukha,A.etal.Interaction-inducedsingularFermisurfaceinahigh-temperatureoxypnictidesuperconductor.Sci.Rep.5,10392(2015). 10. Zabolotnyy,V.B.etal.(π,π)electronicorderinironarsenidesuperconductors.Nature457,569–572(2009). 11. Yin,Z.P.,Haule,K.&Kotliar,G.Kineticfrustrationandthenatureofthemagneticandparamagneticstatesinironpnictidesandironchalcogenides.Nature Mater.10,932–935(2011). 12. Tamai,A.etal.StrongElectronCorrelationsintheNormalStateoftheIron-BasedFeSe0.42Te0.58SuperconductorObservedbyAngle-ResolvedPhotoemission Spectroscopy.Phys.Rev.Lett.104,097002(2010). 13. Liu,Z.K.etal.MeasurementofCoherentPolaronsintheStronglyCoupledAntiferromagneticallyOrderedIron-ChalcogenideFe1.02TeusingAngle-Resolved PhotoemissionSpectroscopy.Phys.Rev.Lett.110,037003(2013). 14. Maletz,J.etal.Unusualbandrenormalizationinthesimplestiron-basedsuperconductorFeSe1−x.Phys.Rev.B89,220506(2014). 15. Charnukha,A.Opticalconductivityofiron-basedsuperconductors.J.Phys.:Condens.Matter26,253203(2014). 16. Zhang,C.etal.Distinguishings± ands++ electronpairingsymmetriesbyneutronspinresonanceinsuperconductingNaFe0.935Co0.045As.Phys.Rev.B88, 064504(2013). 17. Thirupathaiah,S.etal.Weak-couplingsuperconductivityinelectron-dopedNaFe0.95Co0.05AsrevealedbyARPES.Phys.Rev.B86,214508(2012). 18. Liu,Z.-H.etal.UnconventionalsuperconductinggapinNaFe0.95Co0.05Asobservedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B84,064519 (2011). 19. Borisenko,S.etal.Directobservationofspin-orbitcouplinginiron-basedsuperconductors.arXiv:1409.8669(unpublished)(2014). 20. Fang,L.etal.Rolesofmultibandeffectsandelectron-holeasymmetryinthesuperconductivityandnormal-statepropertiesofBa(Fe1−xCox)2As2.Phys.Rev.B 80,140508(2009). 21. Coldea,A.I.etal.FermiSurfaceofSuperconductingLaFePODeterminedfromQuantumOscillations.Phys.Rev.Lett.101,216402(2008). 22. Wang,A.F.etal.AcrossoverinthephasediagramofNaFe1−xCoxAsdeterminedbyelectronictransportmeasurements.NewJ.Phys.15,043048(2013). 23. Tu,J.J.etal.OpticalpropertiesoftheironarsenicsuperconductorBaFe1.85Co0.15As2.Phys.Rev.B82,174509(2010). 24. Nakajima,M.etal.CrossoverfrombadtogoodmetalinBaFe2(As1−xPx)2inducedbyisovalentPsubstitution.Phys.Rev.B88,094501(2013). 25. Nakajima,M.etal.StrongElectronicCorrelationsinIronPnictides:ComparisonofOpticalSpectraforBaFe2As2-RelatedCompounds.J.Phys.Soc.Jpn.83, 104703(2014). 26. Basov,D.N.&Timusk,T.Electrodynamicsofhigh-Tcsuperconductors.Rev.Mod.Phys.77,721–779(2005). 27. Tinkham,M.IntroductionToSuperconductivity(McGraw-Hill,1995). 28. Oh,S.etal.SpinpairingandpenetrationdepthmeasurementsfromnuclearmagneticresonanceinNaFe0.975Co0.025As.Phys.Rev.B87,174517(2013). 29. Parker,D.R.etal.ControloftheCompetitionbetweenaMagneticPhaseandaSuperconductingPhaseinCobalt-DopedandNickel-DopedNaFeAsUsing ElectronCount.Phys.Rev.Lett.104,057007(2010). 30. Bardeen,J.,Cooper,L.N.&Schrieffer,J.R.MicroscopicTheoryofSuperconductivity.Phys.Rev.106,162–164(1957). 31. Mattis,D.C.&Bardeen,J.TheoryoftheAnomalousSkinEffectinNormalandSuperconductingMetals.Phys.Rev.111,412–417(1958). 32. Suhl,H.,Matthias,B.T.&Walker,L.R.Bardeen-Cooper-SchriefferTheoryofSuperconductivityintheCaseofOverlappingBands.Phys.Rev.Lett.3,552–554 (1959). 33. Li,G.etal.ProbingtheSuperconductingEnergyGapfromInfraredSpectroscopyonaBa0.6K0.4Fe2As2SingleCrystalwithTc=37K.Phys.Rev.Lett.101, 107004(2008). 34. Charnukha,A.etal.Superconductivity-inducedopticalanomalyinanironarsenide.NatureCommun.2,219(2011). 35. Charnukha,A.etal.EliashbergapproachtoinfraredanomaliesinducedbythesuperconductingstateofBa0.68K0.32Fe2As2 singlecrystals.Phys.Rev.B84, 174511(2011). 36. Wang, Z.etal.CloserelationshipbetweensuperconductivityandthebosonicmodeinBa0.6K0.4Fe2As2 andNa(Fe0.975Co0.025)As.NaturePhys.9, 42–48 (2012). 37. Boeri,L.,Dolgov,O.V.&Golubov,A.A.IsLaFeAsO1−xFxanelectron-phononsuperconductor?.Phys.Rev.Lett.101,026403(2008). 38. Efremov,D.V.,Golubov,A.A.&Dolgov,O.V.Manifestationsofimpurity-induceds±⇒s++transition:multibandmodelfordynamicalresponsefunctions. NewJ.Phys.15,013002(2013). 39. Nicol,E.J.,Carbotte,J.P.&Timusk,T.Opticalconductivityinhigh-Tcsuperconductors.Phys.Rev.B43,473–479(1991). 40. Moon, S.J.etal.InfraredMeasurementofthePseudogapofP-DopedandCo-DopedHigh-TemperatureBaFe2As2 Superconductors.Phys.Rev.Lett.109, 027006(2012). 41. Steckel,F.etal.Crystalgrowthandelectronicphasediagramof4d-dopedNa1−δFe1−xRhxAsincomparisonto3d-dopedNa1−δFe1−xCoxAs.Phys.Rev.B91, 184516(2015). 42. Parker,D.R.etal.Structure,antiferromagnetismandsuperconductivityofthelayeredironarsenideNaFeAs.Chem.Commun.2189–2191(2009). 43. Antonov, V., Harmon, B.&Yaresko, A.Electronicstructureandmagneto-opticalpropertiesofsolids(KluwerAcademicPublishers(Dordrecht, Boston, London),2004). Acknowledgements WewouldliketothankO.V.DolgovandA.A.GolubovforprovidingthecodeusedforthecalculationoftheopticalconductivityintheEliashbergformalismand B.Keimerforstimulatingdiscussions.A.C.acknowledgesfinancialsupportbytheAlexandervonHumboldtfoundation.ThisprojectwassupportedbytheGerman ScienceFoundationunderGrantNo. BO1912/2-2,throughtheEmmyNoetherProgrammeinprojectWU595/3-1andWU595/3-2(S.W.)andwithinSPP1458 (BU887/15-1).S.W.thankstheBMBFforsupportintheframeworkoftheERA.NetRUSproject(project01DJ12096,Fe-SuCo).S.T.appreciatesfinancialsupport byDepartmentofScienceandTechnologythroughINSPIRE-Facultyfellowship(GrantNo.IFA-14PH-86). WewouldliketothankA.Wolter-Giraud,F.Steckel, andC.Hessforsamplecharacterization. Authorcontributions A.C.,K.W.P.,S.T.,andD.P.carriedouttheexperiments.A.C.analyzedthedataandwrotethemanuscript.S.W.,M.R.,andI.M.carriedoutthesamplegrowthand characterization. A.N.Y.performedabinitiocalculations. B.B.,A.V.B.,S.V.B.,andD.N.B.supervisedtheproject. Allauthorsdiscussedtheresultsandreviewed themanuscript. Additionalinformation Competingfinancialinterests:Theauthorsdeclarenocompetingfinancialinterests. CorrespondenceshouldbeaddressedtoA.C.([email protected])andD.N.B.([email protected]). RequestsformaterialsshouldbeaddressedtoS.W. ([email protected]). 6 Supplementary information I. SPIN-ORBITCOUPLINGINTHELOW-ENERGYELECTRONICSTRUCTUREOFNaFe0.978Co0.022AsNEARTHEΓPOINT In order to confirm that the slight anisotropy of the photoemission intensity in the energy-momentum cut shown in Fig.1a of themaintextdoesnotaffecttheconclusionsofourstudywehavefittedtheleftandrightbranchesoftheouterband’sdispersion independently and compared these fits to the results of the simultaneous fit of both branches presented in the text. Only the data pointsathighenoughbindingenergies(unaffectedbythereductionintheeffectivemassduetothespin-orbitcoupling)wereused forallfits(redandgreenfilledcircles);theentiredispersionofthebandisshownforcompleteness(greyemptycircles). The results of this comparison are shown in Fig. S1a. The red and green solid lines are the parabolic dispersions obtained from the fit of the data points of the corresponding color (only the left and right branches of the parabola were used in the fit of the red and green data points, respectively). It is clear that the independent fit of the right (green solid line) branch gives results very similar to the simultaneous fit of both branches (blue solid line). The independent fit of the left branch deviates somewhat fromthesimultaneousfit,albeititprovidesonlyamarginalimprovementinthefit’sfigureofmerit. Toquantifytheeffectofthis uncertaintyontheextractedrenormalizationoftheeffectivemasswehavecalculatedthelatterusingtheformulagiveninthemain text,m(E)=h¯2k(E)dk/dE,independentlyfortheleftandrightbranches. Theresultingenergy-dependenteffectivemassisshown in Fig. S1b for the left (red open circles) and right (green open circles) branches of the dispersion along with their average (blue open circles) plotted in Fig.1e of the main text. It can be seen that even the lowest value of the renormalization corresponding to theindependentfitoftheleftbranchisstillsignificantlylargerthantherenormalizationofalltheotherbandsandthelargestinthe familyofthehigh-temperatureiron-pnictidesuperconductors. InviewoftheindependentfitsshowninFig.S1itismorelikelythat thetruevalueoftherenormalizationisclosertotheaveragethantothelowestvalue. Similarresultscanbeobtainedthroughthe analysisofquasiparticledispersioninthesymmetrized(withrespecttozerowavevector)data. FiguresS1c,ddemonstratetheflatteningofthemiddleholeband’sdispersion(whitearrows)nearitstopduetotheorbital-mixing effectinducedbythespin-orbitcoupling. II. INHERENTCHARACTEROFTHEORBITALLYSELECTIVEBANDSHIFTSINTHEELECTRONICSTRUCTUREOF NaFe Co As 0.978 0.022 Inthissectionwewouldliketobrieflysubstantiatethebulk-relatedcharacteroftheorbitallyselectivebandshiftsor,equivalently, disprove their surface-related origin. Orbitally selective band width renormalization and band shifts are generic to iron-based superconductors,havebeenobservedinessentiallyallmaterialsofthisfamily[S1–9],andsuggestedtoresultfromorbitalblocking inthepresenceofstrongHund’scoupling[S10]andapronouncedparticle-holeasymmetry[S11],respectively. Thisrenormalized andband-shiftedelectronicstructure,aswellasthesuperconductingenergygapthatdevelopsonit,observedviaARPEShasbeen 2 0 2 0 0 c d a 0 0 -2 0 ) -2 0 -2 0 V e (m-4 0 ergy - 4 0 -4 0 n E -6 0 -6 0 -6 0 b -8 0 -8 0 -8 0 -0 .3 0 .0 0 .3 0 3 6 9 1 2 -0 .3 0 .0 0 .3 -0 .3 0 .0 0 .3 M o m e n tu m ((cid:3)(cid:1)(cid:2)) m Gexp/m LDA M o m e n tu m ((cid:3)(cid:1)(cid:2)) M o m e n tu m ((cid:3)(cid:1)(cid:2)) FigureS1| Detailsofthelow-energyelectronicbandstructureofNaFe0.978Co0.022AsneartheΓpoint.a,Energydispersionoftheouterhole bandneartheΓpointoftheBrillouinzone(circles)extractedfromthemaximumofthequasiparticlepeakinthemomentum-distributioncurves overlaidwiththesimultaneousparabolicfitofboththeleftandrightbranches(bluesolidline)aswellasindependentparabolicfitsoftheleft(red solidline)andright(greensolidline)branches. Thedatausedforthefittingareshownasfilledcirclesofthecorrespondingcolor. Greyopen circlesshowtheenergydispersionuptotheFermilevel.b,Renormalizationoftheeffectivemassextractedindependentlyfromtheleft(redopen circles)andright(greenopencircles)branchesofthedispersionoftheouterholeband,aswellastheiraverage,asshowninFig.1eofthemain text.c,d,Energy-momentumcutalongtheΓ-MdirectionoftheBrillouinzoneplottedinFig.1aofthemaintext(panelc)andthesecondderivative ofthisphotoemissionintensitydistributiontakeninthedirectionofenergy(paneld). SolidanddashedlinesareasinFig.1aofthemaintext. Whitearrowsindicatetheflatteningoftheenergydispersionofthemiddleholebandduetoorbitalmixinginducedbyspin-orbitcoupling. 7 1 0 0 1 0 0 1 0 0 a b c 9 5 9 5 9 5 ) (% e c 9 0 9 0 9 0 n ta c fle 3 0 0 K 3 0 K d a ta 3 0 K d a ta e a s in m a in te x t a s in m a in te x t R 8 5 2 0 0 K 3 0 K 8 5 w w 8 5 g 1 0 0 K 2 0 K pl,2+ 1 0 % pl,2 2 x 2 5 0 K 1 0 K w -1 0 % w 0 .5 x g pl,2 pl,2 2 8 0 8 0 8 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) 1 0 0 1 0 0 d e 9 5 9 5 ) (% e c n 9 0 9 0 ta c efle 3 0 K d a ta 3 0 K d a ta R 8 5 wa s in+ 1m0 a% in w te x t 8 5 ga s+ i1n0 m% a gin te x t pl,1 pl,1 1 1 w -1 0 % w g -1 0 % g pl,1 pl,1 1 1 8 0 8 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) FigureS2|Detailsofthefar-infrareddataandanalysis.a,Photon-energydependenceofthefar-infraredreflectanceatvarioustemperatures.b– e, Analysis of the reflectance at 30 K (cyan solid line) in the framework of the two-Drude model (dotted lines). Black dotted line shows the reflectancecorrespondingtothebest-fitparametersofthetwoDrudeterms, asspecifiedinFig.1gofthemaintext. Redandbluedottedlines demonstratetheeffectofdetuningtheseparametersup(bluelines)ordown(redlines)fromthebest-fitvalues,asdetailedinthefigurelegends. Thehigh-frequencydielectricfunctionusedinthismodelwastakentobeε∞=60,determinedbythecontributionoftheinterbandtransitionsat higherenergies. found to agree remarkably well with many bulk-sensitive techniques, strongly suggesting that the electronic band structure of the surface layer in these compounds is reflective of that in the bulk. The only exception to this rule is the 1111 type of compounds, in which the presence of both bulk- and surface-related states in the photoemission signal has been found [S 12–21], making the extraction of the inherently bulk electronic structure challenging. Recently, a detailed ARPES work succeeded in disentangling the bulk and surface contributions to the photoemission signal and demonstrated that the bulk electronic structure features the sameorbitallyselectivebandwidthrenormalizationandbandshiftsasobservedinotherclassesofiron-basedsuperconductors[S 11], provingitsgenericandinherentcharacter. Finally, itiswell-knownthat111-typematerialscleavebetweenthetwolayersof the intercalant, which results in a non-polar surface. The equivalence of the bulk and surface electronic states has been further demonstratedinanexplicitdensity-functionalcalculation[S22]. III. DETAILSOFTHEFAR-INFRAREDDATAANDANALYSIS Herewewouldliketodemonstratethedegreeofuncertaintyintheextractedparametersofthefree-charge-carrierresponseshown inFig.1gthatthefinitesignal-to-noiseratioofandtheuncoveredlowest-frequencyrangeintheexperimentaldataallow. Wedoso bycomparingtheopticalresponsecorrespondingtothebestfitshowninFigs.1f,gwiththatderivedfromtheDrude-termparameters slightly detuned from those optimal values. In order to eliminate the integral transformation via Kramers-Kronig relations and toemphasizethefunctionalshapeofthereflectanceassumedintheextrapolationregionatlowestfrequenciesforKramers-Kronig analysis,wedemonstratethesetrendsintherawfar-infraredreflectancedata.Thelatterareshownfordifferenttemperaturesbetween 10Kand300KinFig.S2a. FiguresS2b–eshowthereflectanceobtainedinourexperimentasafunctionofphotonenergyat30K overlaid with that produced by assuming two Drude terms (ω ,γ ; ω ,γ ) with the parameters specified in the figure legends. pl,1 1 pl,2 2 Thehigh-frequencydielectricfunctionistakentobeε =60,determinedbythecontributionoftheinterbandtransitionsathigher ∞ energies. Thedefault(best-fit)parametersofthefree-charge-carrierresponsereferredtointhesepanelsarethosespecifiedinFig.1g ofthemaintext. 8 IV. DETERMINATIONOFBAND-SPECIFICPLASMAFREQUENCIESBASEDONARPESDATA InoptimallydopedNaFe Co AstheFermisurfaceconsistsofthreesheets: twoelectonlikeinthecornersoftheBrillouin 0.978 0.022 zone and one holelike at the center [S 23]. It is well-known and a generic feature of iron-based superconductors that the bands generatingtheelectronsheetsareonlyweaklydispersiveintheout-of-planedirection,givingrisetotwoquasi-cylindricalsheetsof theFermisurfacewithrelativelysmallcorrugations[S24]. Therefore,wecanapproximatethesetwosheetsbytwoidenticalideal cylinderswiththeirradiiequaltotheaverageofthelongandtheshorthalf-axisoftheellipsoidsgivingrisetothecorrugation. The electronicbandgeneratingtheholesheetoftheFermisurfacealsodispersesratherweaklyalongtheΓ-ZdirectionoftheBrillouin zone, as shown in Fig. S3: the Fermi wave vector of this band remains within 0.07–0.09 A˚−1 between Γ and Z. Therefore, the Fermi-surfacesheetgeneratedbythisbandcanlikewisebeapproximatedbyacylinderwitharadiusofabout0.08A˚−1. Thusthe taskofcalculatingtheplasmafrequencyhasbeenreducedtoatwo-dimensionalproblem. Ingeneral,theplasmafrequencyoffree chargecarrierscanbeobtainedfromthesemi-classicalexpressionforthedielectricfunction[S25]assumingtheintrabandcaseand lowtemperaturesandisgivenbythefollowingexpression(inSIunits): e2 (cid:90) (cid:20)dE (cid:21)2 ω2 = ∑ nk δ(E −E )d3k, (1) pl,σ 8π3h¯2ε0 n dkσ nk F whereσ =x,y,zenumeratesthecoordinateaxes,nisthebandindex,δ(x)isDirac’sdeltafunction,E istheenergydispersionof nk thenthband, E istheFermienergy, eistheelectroncharge, h¯ isthereducedPlanckconstant, andε isthevacuumpermittivity. F 0 Assuming our two-dimensional approach and the tetragonal symmetry of NaFe Co As, ω =0 and ω =ω =ω . 0.978 0.022 pl,z pl,x pl,y pl Thusonlyonequantityω needstobecalculatedforeachband. Inthetwo-dimensionalcaseandforanisotropicparabolicband pl withaneffectivebandmassm [E =h¯2k2/(2m )]Eq.1canberewrittenasasimpleandfamiliarexpression: eff k eff N (E )e2 ω2 = 2D F , (2) pl m ε eff 0 where N (E )= kF2 2π is the density of states at the Fermi level for an isotropic parabolic band in two dimensions, k is the 2D F (2π)2 c F Fermiwavevector,andcistheout-of-planelatticeconstant.Thusthecalculationoftheband-specificplasmafrequenciesisreduced tothedeterminationoftheFermiwavevectorandthequasiparticleeffectivemassforeachband, whichcaneasilybedonebased onthephotoemissionintensitydistributionsneartheFermilevelpresentedinFigs.1a,b. Asalreadymentionedaboveandshownin Fig.S3, theFermiwavevectoroftheholebandisabout0.08A˚−1, anditseffectivemassisfoundtobe3.83m (wherem isthe e e bareelectronmass),whichresultsinaplasmafrequencyofωhole,1=0.23eV. TheFermiwavevectorsandeffectivemassesofthe pl electronbandsattheM-pointare0.086A˚−1,0.92m and0.153A˚−1,2.34m fortheinnerandtheouterband,respectively. These e e valuesresultinalmostidenticalplasmafrequenciesofωel,in=0.5eVandωel,out=0.56eV,respectively. pl pl 4 5 e V 2 0 4 3 e V 4 1 e V 3 9 e V 3 7 e V 1 5 .) 3 5 e V . u 3 3 e V rb (a 3 1 e V ity1 0 2 9 e V FigureS3|Out-of-planedispersionofthehole s ten 2 7 e V ba ndalongtheΓ-ZdirectionintheBrillouin In zone. Momentum-distribution curves (MDCs) 2 5 e V at near-normal photoemission (0 momentum 5 2 3 e V corresponds to normal emission) averaged in 2 1 e V a 5 meV energy window around the Fermi level for various energies of incident photons. 1 9 e V The data were recorded in the normal state of 1 7 e V NaFe Co Asat27K. TheMDCsaredis- 0 0.95 0.05 placedverticallybyaconstantof1.5.Blackver- ticallinesindicatethepositionoftheFermiwave -0 .2 -0 .1 0 .0 0 .1 0 .2 vectorextractedasthemaximumofthequasipar- M o m e n tu m ((cid:3)(cid:1)(cid:2)) ticlepeakforeveryMDC. 9 References S1. Borisenko,S.V.etal.SuperconductivitywithoutNestinginLiFeAs.Phys.Rev.Lett.105,067002(2010). S2. Sudayama,T.etal.Doping-DependentandOrbital-DependentBandRenormalizationinBa(Fe1−xCox)2As2Superconductors.J.Phys.Soc.Jpn.80,113707 (2011). S3. Ding,H.etal.ElectronicstructureofoptimallydopedpnictideBa0.6K0.4Fe2As2:acomprehensiveangle-resolvedphotoemissionspectroscopyinvestigation. J.Phys.:Condens.Matter23,135701(2011). S4. Cui,S.T.etal.EvolutionofthebandstructureofsuperconductingNaFeAsfromoptimallydopedtoheavilyoverdopedCosubstitutionusingangle-resolved photoemissionspectroscopy.Phys.Rev.B86,155143(2012). S5. Yi,M.etal.ObservationofTemperature-InducedCrossovertoanOrbital-SelectiveMottPhaseinAxFe2−ySe2(A=K,Rb)Superconductors.Phys.Rev.Lett. 110,067003(2013). S6. Maletz,J.etal.Unusualbandrenormalizationinthesimplestiron-basedsuperconductorFeSe1−x.Phys.Rev.B89,220506(2014). S7. Lee,G.etal.OrbitalSelectiveFermiSurfaceShiftsandMechanismofHighTc SuperconductivityinCorrelatedAFeAs(A=Li,Na).Phys.Rev.Lett.109, 177001(2012). S8. Evtushinsky,D.V.etal.Strongelectronpairingattheiron3dxz,yzorbitalsinhole-dopedBaFe2As2superconductorsrevealedbyangle-resolvedphotoemission spectroscopy.Phys.Rev.B89,064514(2014). S9. Brouet,V.etal.LargeTemperatureDependenceoftheNumberofCarriersinCo-DopedBaFe2As2.Phys.Rev.Lett.110,167002(2013). S10. Yin,Z.P.,Haule,K.&Kotliar,G.Kineticfrustrationandthenatureofthemagneticandparamagneticstatesinironpnictidesandironchalcogenides.Nature Mater.10,932–935(2011). S11. Charnukha,A.etal.Interaction-inducedsingularFermisurfaceinahigh-temperatureoxypnictidesuperconductor.Sci.Rep.5,10392(2015). S12. Lu,D.H.etal.Electronicstructureoftheiron-basedsuperconductorLaOFeP.Nature455,81–84(2008). S13. Liu,H.-Y.etal.PseudogapandSuperconductingGapinSmFeAs(O1−xFx)SuperconductorfromPhotoemissionSpectroscopy.Chin.Phys.Lett.25,3761 (2008). S14. Kondo,T.etal.MomentumDependenceoftheSuperconductingGapinNdFeAsO0.9F0.1SingleCrystalsMeasuredbyAngleResolvedPhotoemissionSpec- troscopy.Phys.Rev.Lett.101,147003(2008). S15. Liu,C.etal.Electronicpropertiesofironarsenichightemperaturesuperconductorsrevealedbyangleresolvedphotoemissionspectroscopy(ARPES).Phys. C:Supercond.469,491–497(2009). S16. Lu,D.etal.ARPESstudiesoftheelectronicstructureofLaOFe(P,As).Phys.C:Supercond.469,452–458(2009). S17. Liu,H.etal.UnusualElectronicStructureandObservationofDispersionKinkinCeFeAsOParentCompoundofFeAs-basedSuperconductors.Phys.Rev. Lett.105,027001(2010). S18. Liu,C.etal.Surface-drivenelectronicstructureinLaFeAsOstudiedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B82,075135(2010). S19. Yang,L.X.etal.SurfaceandbulkelectronicstructuresofLaFeAsOstudiedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B82,104519(2010). S20. Yang,L.etal.ElectronicstructureofSmOFeAs.J.Phys.Chem.Solids72,460–464(2011). S21. Nishi,I.etal.Angle-resolvedphotoemissionspectroscopystudyofPrFeAsO0.7:ComparisonwithLaFePO.Phys.Rev.B84,014504(2011). S22. Lankau,A.etal.AbsenceofsurfacestatesforLiFeAsinvestigatedusingdensityfunctionalcalculations.Phys.Rev.B82,184518(2010). S23. Thirupathaiah,S.etal.Weak-couplingsuperconductivityinelectron-dopedNaFe0.95Co0.05AsrevealedbyARPES.Phys.Rev.B86,214508(2012). S24. Mazin,I.I.&Schmalian,J.Pairingsymmetryandpairingstateinferropnictides:Theoreticaloverview.Phys.C469,614–627(2009). S25. Yu,P.Y.&Cardona,M.FundamentalsofSemiconductors(Berlin:Springer,2005). 10

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Preview Weak-coupling superconductivity in a strongly correlated iron pnictide

Weak-coupling superconductivity in a strongly correlated iron pnictide A. Charnukha1,2,3, K. W. Post1, S. Thirupathaiah2,4, D. Pro¨pper3, S. Wurmehl2, M. Roslova2,5, I. Morozov2,5, B. Bu¨chner2, A. N. Yaresko3, A. V. Boris3, S. V. Borisenko2 & D. N. Basov1 6 1 1PhysicsDepartment,UniversityofCalifornia–SanDiego,LaJolla,CA92093,USA,2LeibnizInstituteforSolidStateandMaterialsResearch,IFW, 0 01069Dresden,Germany,3MaxPlanckInstituteforSolidStateResearch,70569Stuttgart,Germany,4SolidStateandStructuralChemistryUnit, 2 IndianInstituteofScience,Bangalore–560012,India,5DepartmentofChemistry,MoscowStateUniversity,119991Moscow,Russia.†E-mail: n [email protected]. a J Iron-basedsuperconductorshavebeenfoundtoexhibitanintimateinterplayoforbital,spin,andlatticedegreesoffreedom,dramatically 9 affectingtheirlow-energyelectronicproperties,includingsuperconductivity. Albeittheprecisepairingmechanismremainsunidentified, 2 severalcandidateinteractionshavebeensuggestedtomediatethesuperconductingpairing,bothintheorbitalandinthespinchannel. Here,weemployopticalspectroscopy(OS),angle-resolvedphotoemissionspectroscopy(ARPES),abinitioband-structure,andEliashberg ] n calculationstoshowthatnearlyoptimallydopedNaFe0.978Co0.022Asexhibitssomeofthestrongestorbitallyselectiveelectroniccorrelations o inthefamilyofironpnictides.Unexpectedly,wefindthatthemassenhancementofitinerantchargecarriersinthestronglycorrelatedband c isdramaticallyreducedneartheΓpointandattributethiseffecttoorbitalmixinginducedbypronouncedspin-orbitcoupling. Embracing - thetruebandstructureallowsustodescribealllow-energyelectronicpropertiesobtainedinourexperimentswithremarkableconsistency r p anddemonstratethatsuperconductivityinthismaterialisratherweakandmediatedbyspinfluctuations. u Strong entanglement of various electronic and lattice degrees of freedom in the iron-based superconductors has become the s leitmotifofrecentcondensed-matterresearchandhasbeenidentifiedwithavastvarietyofexperimentalprobes1–4 andinterpreted t. theoretically5,6. ThisinherentcomplexityarisesfrommultiplepartiallyfilledFe-3dorbitalssimultaneouslycontributingtothelow- a energy quasiparticle dynamics and strongly affected by the Hund’s coupling correlations7. The orbitally selective nature of these m interactionsleadstoalikewiseorbitallyselectivebandwidthrenormalizationandrelativeenergyshiftofvariousbandswithrespect - to each other and the Fermi level due to the pronounced particle-hole asymmetry of the electronic structure8. Such non-trivial d interaction-inducedmodificationsresultinasingularFermi-surfacetopologythatisdramaticallydifferentfromthepredictionsof n o theoretical calculations in both the number and the binding energy of the bands crossing the Fermi level9,10, strongly affecting c low-energyelectronicpropertiesincludingsuperconductivity. [ Here,weshowthatinthenearlyoptimallydopedNaFe0.978Co0.022Ascompound,low-energyorbitallyselectiverenormalization ofthebandstructuredeviatesmarkedlyfromthegeneralexperimentalandtheoreticalrenormalizationtrendiniron-basedsupercon- 1 ductors11. WefindmorethantwicestrongerthanexpectedorbitallyselectiveelectroniccorrelationsintheFe-3d bandcrossing v xy 5 the Fermi level near the Γ point of the Brillouin zone, similarly to FeTe1−xSex12–14. However, in contrast to the observations in 9 thelattercompounds,themassenhancementinthestronglycorrelatedbandofNaFe0.978Co0.022Asisdrasticallyreducednearthe 1 Fermilevel,whereourrelativisticabinitiocalculationspredictorbitalmixingoftheFe-3dxy,3dxz,and3dyz orbitalstooccurdueto 8 spin-orbitcoupling,leadingtoapronouncedmodificationoflow-energyelectronicproperties. Asimultaneousdetailedanalysisof 0 theARPESandOSdatarevealsremarkableconsistencyintheextracteditinerantpropertiesofboththenormalandthesupercon- . ductingstate. Itallowsustoconcludethattheubiquitousdichotomybetweenthecoherentandincoherentfar-infraredquasiparticle 1 response observedin all iron-basedsuperconductors15 is notdominated by thedisparity inthe mobilities ofthe hole andelectron 0 chargecarriersbutratheroriginatesintheinelasticscatteringfromanintermediatebosonicexcitation. Finally,alloftheobserved 6 featuresinthefar-infraredconductivityinthesuperconductingandnormalstatecanbereproducedinaneffectivetwo-bandEliash- 1 bergmodelassumingrelativelyweaksuperconductingpairingwiths symmetrymediatedbylow-energyspinfluctuationswiththe : ± v frequencyandtemperaturedependenceobservedinthesamecompoundbyinelasticneutronscattering16. i X Theeffectofelectroniccorrelationsonthelow-energyelectronicstructureofNaFe0.978Co0.022AsisillustratedinFigs.1a–c. The generalbandstructureofNaFe Co Ashasbeenstudiedextensivelyandconsists,similarlytomostiron-basedsuperconductors, 1−x x r a ofthreeholebandsattheΓ(Z)pointoftheBrillouinzoneandtwoelectronbandsneartheMpointofthetwo-FeBrillouinzone17,18 (thedifferenceinthebandstructureattheΓandZpointsisminor,seeSupplementaryInformation). Bothofthesesetsofelectronic dispersionsareanalyzedinFigs.1a,b,respectively,andcomparedtothecorrespondingpredictionsofourband-structurecalculations showninFig.1c. InstarkcontrasttothepredictionofthetheoryinFig.1c,onlyoneholebandattheΓpointofNaFe Co As 0.978 0.022 crossestheFermilevel,theremainingtwoareshiftedtolowerbindingenergiesandterminatewithinabout20meVbelowtheFermi level. Theseinnerholebandshaveawell-definedparabolicshape,asillustratedbythefits(lowerwhiteandreddashedlines)tothe 1 Figure1| Low-energyelectronicpropertiesofNaFe0.978Co0.022As.a,b,Low-energyelectronicstructureofNaFe0.978Co0.022Asinthenormal stateneartheΓ(a,30K)andM(b,22K)pointsoftheBrillouinzonerecordedusing20eVand25eVphotonslinearlypolarizedperpendicularto andwithintheplaneofincidence,respectively.Thedispersionofallelectronicbandsobservedinexperiment(blacksolidlines)hasbeenobtained usingamulti-Lorentzianfitofthemomentum-distributioncurves. Effective-massrenormalizationindicatedinthepanelshasbeencalculatedby comparingthelow-energyparabolicfitstotheelectronicdispersionsextractedfromtheexperimentaldata(dashedlinesinpanelsa,b)withthoseto thecorrespondingelectronicbandspredictedtheoretically(dashedlinesinpanelc).c,Theoreticallypredictedlow-energyelectronicbandstructure ofNaFeAsintheΓ−M high-symmetrydirectionoftheBrillouinzone(blacksolidlines)andlow-energyparabolicfitstothedispersionsnear ΓandM(dashedlines). Thecolorsofthedashedlinescorrespondtothoseinpanelsa,b. PlasmafrequenciesofallbandscrossingtheFermi levelextractedfromexperimentaldataandpredictedbytheoryareshowninpanelsa–c.d,ElectronicbandstructureintheΓ−Mhigh-symmetry directionoftheBrillouinzoneneartheΓpointobtainedinarelativisticDFTcalculation(blacklines),whichexplicitlyaccountsforafinitespin- orbitcoupling(itscharacteristicenergyscaleisshownasbluehatchedarea). Theresultsofthecorrespondingnon-relativisticcalculationfrom panelcareshownforcomparison(greylines).e,Energydependenceoftheeffectivemassrenormalizationintheouter(blueopencircles),middle (greycircles),andinner(redcircles)holebandattheΓpointwithrespecttothecorrespondinglow-energyquasiparticlemassesextractedfrom thetheoreticallypredictedbandstructureinpanelcusingparabolicfits. Theenergyscaleaffectedbyspin-orbitinteractionisindicatedasablue hatched area. f,g, Real part of the optical conductivity (f) and the dielectric function (g) of NaFe0.978Co0.022As obtained in OS measurements (opencircles)alongwiththeresultsofaDrude-Lorentzdispersionanalysis(blueandredlines/shadedareasandgreenline/shadedareaforthetwo Drudetermsandthetotalcontributionofallinterbandtransitions,respectively;graysolidlinesindicatethesumofallterms). Theparametersof theitinerantchargecarrierresponseobtainedbymeansofthisanalysisaresummarizedinpanelg. experimental band dispersions extracted from momentum-distribution curves at various binding energies (black solid lines). The comparisonofthefittedeffectivemassestothetheoreticalbandstructureinFig.1crevealsarenormalizationbyafactorof4.3and 4.5fortheinnerandmiddleholebandsofFe-3d orbitalcharacter,respectively. TheouterholebandofFe-3d orbitalcharacter xz,yz xy in Fig. 1a shows a dramatic renormalization by a factor of more than 8 (blue dashed line), clearly demonstrating the existence of verystrongandorbitallyselectiveelectroniccorrelationsinNaFe Co As,similartoFeTe Se 12–14 (theslightasymmetry 0.978 0.022 1−x x ofthephotoemissionintensitydistributioninFig.1adoesnotaffectourconclusions,seeSupplementaryInformation).Suchastrong enhancementoftheeffectivequasiparticlemassisatoddswiththepredictedrenormalizationbyafactorofonly3to4,identifiedin combineddensity-functionalanddynamicmean-fieldtheorycalculations(DFT+DMFT)inRefs.11. Ouranalogousanalysisofthe experimentalbandstructureofNaFe Co AsattheMpointoftheBrillouinzone(Fig.1d)revealstwowell-definedparabolic 0.978 0.022 bandsofelectroncharacter,consistentwiththepredictionoftheoryinFig.1c,withaverydisparateeffective-massrenormalization ofabout2.2and5.7fortheinnerandouterelectronbands,respectively. Quite surprisingly, the outer hole band’s dispersion reveals a departure from a parabolic shape (blue dashed line in Fig. 1a) upon approaching the Fermi level, clearly absent in the calculated band structure. To quantify this non-parabolicity, we extract theenergy-dependenteffectivemassm(E)=h¯2k(E)dk/dE,whereh¯ isthePlanckconstant,k—quasiparticlewavevector,andE —quasiparticleenergy. Foraparabolicdispersionm(E)=const. Theresultingenergy-dependenteffectivemassrenormalization m (E)/m inallholebandsneartheΓpointoftheBrillouinzone(m fromFig.1c)isshowninFig.1e. Itisclearthatwhile exp LDA LDA thehigher-energy(outsideofthebluehatchedarea)effectivemassoftheouterholebandissimplyrenormalizedfromitstheoretical counterpartbyafactorof8,atlowenergiesthisisnotthecase. This dramatic reduction of the effective mass at lower binding energies cannot be attributed solely to the effect of high-energy electroniccorrelations, whichtypicallyleadtoanenhancementoftheeffectivemassovertheentireelectronicbandwidth. Inthe 2 Figure 2| Superconductivity in nearly optimally doped NaFe0.978Co0.022As. a, Relative change in the sample reflectance as a function of temperatureforseveralfrequenciesintheTHzspectralrange. Thetransitionintothesuperconductingstateisevidencedbyamarkedincreasein thesamplereflectancebelowTc≈18K(verticaldashedline).b,RealpartoftheitinerantTHzandfar-infraredconductivityofNaFe0.978Co0.022As inthesuperconductingstateat8K(bluesolidline)andnormalstateat20and30K(redandblacksolidlines,respectively). Theformationof Cooperpairsismanifestedinthemissingareaundertheconductivitycurveinthesuperconductingvsnormalstate(hatchedarea),whichamounts toaLondonpenetrationdepthof430nm. Opticalsuperconductingenergygap2∆isclearlyvisibleastheenergyatwhichtherealpartofthe opticalconductivityvanishes. Thefrequency-dependenceoftheopticalconductivityabovetheinitialonsetofabsorptioninthesuperconducting stateexhibitsaquasilinearcharacter,whichdefinesanadditionalenergyscale,E (forinterpretationseetext). Normalstateopticalconductivity 1 is recovered at about 16∆ (vertical dashed line). c, Comparison of the real part of the optical conductivity in the superconducting (8 K, gray opencircles)andnormal(20K,grayfilledcircles)stateobtainedexperimentallytotheresultsoftheoreticalcalculationsintheframeworkofan effectivetwo-bandEliashbergtheoryat8K(bluesolidline)and20K(redsolidline).Absorptionbelow2∆inthesuperconductingstateisdueto thermallyexcitedquasiparticles. Allparametersofthetheoryareindicatedinthepanel. Theinitialsharponsetofabsorptionat2∆isassistedby elasticimpurityscatteringwhilethequasilinearfrequencydependenceoftheopticalconductivityathigherenergiesresultsfromHolsteinprocesses (breakingofaCooperpairwithasimultaneouscreationofoneorseveralquantaofthemediatingboson).d,Thespectralfunctionofthemediating bosoninthenormal(25K)andsuperconducting(5K)stateusedinthecalculation(redandbluesolidlines,respectively)andtheimaginarypart ofthespinsusceptibilityobtainedusinginelasticneutronscatteringonthesamecompound(opencircles;datafromRef.16). Imaginarypartof thespinsusceptibilityinthesuperconductingstateclearlyexhibitsaresonancemodeat7.5meVandaspingap(SG)of5.6meV,approximately equaltotheopticalsuperconductingenergygap2∆inthismaterial. presenceoforbitallyselectiverenormalizationthesameistrueforeachbandofagivenorbitalcharacter. Ourabinitiocalculations (Fig. 1c) clearly show that the outer hole band has a well-defined 3d orbital character up to its termination. Recently, it has xy been demonstrated that spin-orbit coupling is not negligible in iron-based superconductors19. Provided that the hole bands of 3d and 3d character are almost degenerate at the Γ point of the Brillouin zone, as can be seen in Fig. 1c, the existence of a xy xz,yz sizablespin-orbitinteractionwouldleadtothemixingoftheorbitalcharacterinthesethreebandsandpotentiallyreducethemass renormalization in the outer 3d hole band due to a large admixture of more weakly renormalized 3d bands. The existence xy xz,yz ofsuchorbitalmixinghasbeenidentifiedpreviouslybasedonthepolarizationdependenceofthephotoemissionintensitynearthe Γ(Z)pointinRef.17. Giventhereductionoftheeffectivemassintheouterholebandduetoorbitalmixing,oneshouldexpecta corresponding enhancement of the effective mass in the middle and/or inner hole bands dueto the finite admixture of the heavier 3d orbital. Thiseffect,albeitrathersubtle,canneverthelessbeclearlyidentifiedinthesecondderivativeoftheexperimentaldata xy inFig.1auponcloseinspection(seeSupplementaryInformation). The aforementioned reduction of the effective mass due to orbital mixing does not rely on the existence of strong electronic correlations and should be observable already at the level of quasiparticle band masses. Indeed, Fig. 1d demonstrates that when spin-orbitcouplinginthismaterialistakenintoaccountinarelativisticabinitiocalculation(blacksolidlines),thedispersionofthe holebandsatlowenergiesshowsapronounceddeparturefromthatobtainedinthenon-relativisticcalculationpresentedinFig.1c (greysolidlines). Boththereductionoftheeffectivemassintheouterbandanditsenhancementinthemiddleandinnerbandsare apparent. Thecomplexmodificationofthelow-energyelectronicstructurewithrespecttotheoryobservedinourexperimenthasaprofound effectontheitinerantpropertiesofNaFe Co As. ItstronglyaffectstheanalysisandinterpretationoftheOSdataobtained 0.978 0.022 onthesamecompound, aswewilldemonstratebelow. TheitinerantquasiparticleresponsecanbeextractedfromtheOSdataby eliminatingthecontributionofallclearlyidentifiableinterbandtransitions(greenlinesinFigs.1f,g)fromtheopticalconductivity σ(ω) or, equivalently, dielectric function ε(ω)=1+4πiσ(ω)/ω (see also Supplementary Information). The resulting itinerant optical response σit(ω), or εit(ω), can be decomposed into a narrow (coherent) and a broad (incoherent) Drude-like contribution (blueandredlinesinFigs.1f,g). Suchadecompositionisrathercommonintheiron-basedsuperconductorsandhasbeenobserved inessentiallyallknownmaterialsofthisfamily15. Atthesametime,theelectronicbandstructureofNaFe Co Asfeatures 0.978 0.022 threebandscrossingtheFermilevel,indicatingtheexistenceofasegregationofallfreechargecarriersintotwoeffectiveelectronic subsystems: onewithalargeandtheotheronewithasmallscatteringrate(summarizedinFig.1g). It is tempting to assign the narrow Drude component to the combined response of charge carriers on the electron sheets of the Fermi surface (which in iron-based compounds have been found to have higher mobilities than hole carriers based on Hall and quantum-oscillationmeasurements20,21),andthebroadonetothecontributionofthecarriersontheholesheetoftheFermisurface. However,adirectcomparisonoftheplasmafrequenciesofthetwoDrudetermsextractedinouranalysisoftheopticalconductivity (Fig. 1g) to those obtained from the ARPES data (as shown in Figs. 1a,b and detailed in the supplementary information) reveals 3 that this assignment is incorrect: the plasma frequency of the hole sheet of the Fermi surface, ωhole =0.2 eV, is substantially pl (cid:113) smallerthanthetotalplasmafrequencyoftheelectronsheets,ωel = ωel,in+ωel,out=0.7eV. Thereverseassignment(broad pl,tot pl pl Drudecomponenttoelectronchargecarriers)cannotbereconciledwiththenegativeHallcoefficientobservedinthiscompound22. Additionally,asimpleestimateoftheelectronmeanfreepathduetoelasticimpurityscatteringasl =v /γ,wherev istheFermi 0 F F velocity and γ is the quasiparticle scattering rate obtained in our Drude-Lorentz analysis, leads to an unrealistic result. Taking v =0.6eVA˚ fortheelectronbandsinFig.1bandγ =0.1eVforthebroadDrudecomponentinFigs.1f,g,onearrivesatl =6A˚ F 0 orlessthantwounitcells. SuchasmallmeanfreepathishardtojustifyinanearlystoichiometricNaFe Co As. Asimilar 0.978 0.022 estimateassumingγ=0.1eVontheholepocket(v =0.15eVA˚)leadstol =1.5A˚,orlessthanoneunitcell. Analogousanalysis F 0 ofthebroadDrudecomponentintheopticalconductivityofoptimallydopedBaFe Co As previouslyextractedacomparable 1.85 0.15 2 mean free path assuming elastic scattering of holes23. These inconsistencies imply that the large scattering rate of the incoherent Drudecomponentdoesnotoriginateinthelowmobilityofoneofthecharge-carriertypebutratherresultsfrominelasticscattering of charge carriers (of either sign) from an intermediate boson. This conclusion is consistent with the association of the broad Drude component with electronic correlations based on the doping dependence of the optical conductivity in various iron-based compounds24,25. The strength of electronic correlations is frequently estimated by comparing the total itinerant spectral weight (area under the (cid:16) (cid:17)2 itinerantopticalconductivitycurve)SW =(cid:82)∞σit(Ω)dΩ= ωit,exp /8,whereωit,expisthetotalitinerantplasmafrequency,tothe 0 1 pl,tot pl,tot predictionsoftheoreticalband-structurecalculations26. Whileinparticle-hole–symmetricsingle-bandmaterialsthisapproachpro- videsagoodestimateofeffective-massrenormalizationandtherebycorrelations,iniron-basedsuperconductorstheexperimentally observedplasmafrequencyismodifiedfromitstheoreticalpredictionnotonlybyorbitallyselectivebandwidthrenormalizationbut alsointrinsic(seeSupplementaryInformation)bandshifts9,aprocessthatingeneralconservesneithertheFermiwavevectornor thenumberofbandscrossingtheFermilevel,dramaticallyaffectingthetotalplasmafrequency. Therefore,theassessmentofelec- troniccorrelationsinsuchcasescanonlybereliablycarriedoutbasedonthecomparisonofthecompletelow-energyexperimentally observedbandstructuretoitstheoreticallypredictedcounterpart. Fortunately, even in such complicated cases the spectral-weight analysis of the itinerant optical response bears fruit. It is well- known that the total spectral weight of any system (including optical absorption in the ultraviolet and x-ray spectral range) is constant and does not depend on the details of the band structure: SWtot =(cid:82)∞σtot(Ω)dΩ=4πne2/m (in CGS units), where n 0 e istheelectrondensity, eandm arethebareelectronchargeandmass, respectively. Quitesimilarly, theitinerantspectralweight e (devoidofallinterbandtransitions)isalsoconstant,withm substitutedbythequasiparticlebandmassincludingrenormalization e at energies larger than the plasma frequency. Any low-energy mass renormalization due to, e.g., coupling to phonons or other bosonic excitations will not affect this spectral weight as long as its characteristic energy is smaller than the plasma frequency of free charge carriers. On the other hand, the low-energy band structure and the plasma frequency extracted from it will be affectedbysuchrenormalization. Therefore,thecomparisonofthetotalitinerantplasmafrequencyobtainedfromOSandARPES data provides access to purely boson-exchange–induced effective mass renormalization even when it is not immediately apparent in the experimental band structure. In the present case of NaFe Co As this renormalization amounts to m /m = 0.978 0.022 OS ARPES (ωit,OS/ωARPES)2 =2.15 (see Fig. 1a,b,g). This is related to the strength of electron-boson couling λ via 1+λ =m /m , pl,tot pl,tot OS ARPES givingλ =1.15. Having established that only three out of five electronic bands predicted theoretically actually contribute to the itinerant carrier responseofNaFe Co Asandthatelectronsarecoupledtoanintermediatebosonwithacouplingstrengthofλ =1.15, we 0.978 0.022 nowturntotheanalysisofthesuperconductingstatethatdevelopsinthiselectronicstructure. Uptonow,thecharacterofsupercon- ductivity in optimally doped NaFe Co As has remained unclear, with both weak and strong superconducting pairing suggested 1−x x basedontheARPESmeasurementsofthesuperconductingenergygapinRefs.17,18,respectively. Thisuncertaintycanbeelim- inated based on the analysis of our bulk OS measurements in the far-infrared and THz spectral range, shown in Fig. 2. Panel 2a showsthetemperaturedependenceoftherelativechangeofthereflectancewithrespecttothatat30Kforseveralfrequenciesinthe lowestTHzspectralrange. Thenormal-statetrendforallfrequenciesissuddenlyreversednear18K,whichthusmustbeidentified with the superconducting transition temperature, consistent with the previous ARPES measurements on the same samples17. The analysis of the real part of the optical conductivity in the far-infrared and THz spectral range reveals the quintessential feature of Cooper pairing — the dramatic suppression of the optical conductivity, with the missing area δA between the normal and the L superconducting state at finite frequencies ω >0 (δA =(cid:82)16∆(σ20K(ω)−σ8K(ω))dω, hatched area in Fig. 2b) transferred into L 0+ 1 1 the coherent response of the condensate at ω =0 (Ref. 27). Our analysis shows that this missing area corresponds to a London √ penetrationdepthλ =c/ 8δA =430nm,inaremarkableagreementwithnuclear-magnetic–resonanceandmuon-spin–rotation L L measurementsonthismaterial28,29. The vanishing of the optical conductivity in the superconducting state (blue solid line in Fig. 2b) further identifies the optical superconductingenergygap2∆≈5.6meVandthecorrespondinggapratio2∆/k T ≈3.6,veryclosetotheweak-couplinglimitof B c theBardeen-Cooper-Schrieffertheoryofsuperconductivity27,30.Thesevaluesareinagoodagreementwiththoseextractedfromthe ARPESdataonthesamesinglecrystals17andtogetherprovidecompellingevidenceforrelativelyweak-couplingsuperconductivity inNaFe Co As. 0.978 0.022 Theonsetofabsorptionat2∆(bluesolidlineinFig.2b)isverysharpandhasaMattis-Bardeenshape,characteristicofaweakly coupled superconductor or that with large elastic impurity scattering31,32. Intriguingly, the frequency dependence of the optical conductivity beyond this initial increase is non-monotonic and reveals a quasilinear section, which deviates markedly from the Mattis-Bardeenshapeanddefinesanotherenergyscale,E .Suchaquasilinearfrequencybehaviorintheopticalconductivityofiron- 1 basedsuperconductorsisnotunprecedentedandhasbeenpreviouslyobservedintheresponseofoptimallydoped(Ba,K)Fe As 33,34 2 2 andattributedtotheboson-mediatedabsorptioninthecleanlimit(lowimpurityscattering)ofastronglycoupledsuperconductor35. 4 It is quite clear that the combination of such very different features characteristic of a weakly and strongly coupled as well as clean-anddirty-limitsuperconductorintheopticalresponseofthesamematerialnecessitatesacomparisonwithatheoreticalmodel thatencompassesalloftheselimitingbehaviors. TheEliashbergtheoryofsuperconductivityisperfectlysuitedtothistask. Thekey inputparameterofthetheoryisthespectrumofthebosonicexcitationthatmediatessuperconductingpairingandtheoverallelectron- bosoncouplingstrength.SpindynamicsinNaFe Co Ashasbeenshowntobesensitivetosuperconductivity,asmanifestedin 0.978 0.022 theformationofaresonancepeakintheimaginarypartofthespinsusceptibilitybelowT (Refs.16,36),whiletheelectron-phonon c interactionhasbeendemonstratedtobeinsufficienttoaccountfortheelevatedsuperconductingtransitiontemperatureofiron-based superconductors37. Therefore, we assume interband electron-electron interaction via the exchange of spin fluctuations with the experimentallyobtainedspectralshapeinthenormalandsuperconductingstate(Fig.2d)tomediatesuperconductingpairinginour model. InthepresenceofthedisparatefeaturesobservedintheopticalresponseofNaFe Co Asandaninterbandpairinginterac- 0.978 0.022 tion,thesimplest,minimal,modelwouldincorporatetwoeffectiveelectronicbands. Thetwo-bandEliashbergformalismemployed in our calculations has been detailed in Ref. 38. We assume the symmetry of the superconducting order parameter to be of the s -type. GiventhatthedensitiesofstatesofallbandscrossingtheFermilevelarecomparableandthatallARPESmeasurements ± findlittlevariationinthesizeofthesuperconductingenergygapwithinandbetweenthebands17,18,weassumetwoeffectivebands with isotropic superconducting energy gaps of the same magnitude and opposite sign, as well as equal densities of states. Elas- tic (impurity) interband scattering is neglected35. The plasma frequencies, intraband impurity scattering rates, and the coupling strengthbetweenthebandsarethefreeparametersofthemodeltunedtofittheopticalsuperconductingenergygap2∆=5.6meV, thesuperconductingtransitiontemperatureT =18K,andtheoverallshapeoftheopticalconductivityinthesuperconductingand c normalstate. TheiroptimalvaluesobtainedinthefitundertheaforementionedconstraintsareindicatedinFig.2c. Figure2cshowstheresultofourmodeling(solidlines)overlaidontheexperimentaldatainthesuperconducting(opencircles) andnormal(filledcircles)state. Itisimmediatelyevidentthatquantitativeagreementcanbeachievedfortheparametersgivenin thepanel. Quiteremarkably,ifnotunprecedentedly,allofthetransportparameters(theindividualplasmafrequenciesofthebands andtheireffectiveimpurityscatteringrates)areinaverygoodagreementwiththepropertiesofthetwoeffectiveitinerantelectronic subsystemsextractedintheDrudeanalysisoftheconductivitydatainFig.1g. Furthermore,theinterbandelectron-bosoncoupling strengthobtainedfromthefit(λ =λ =1.2)showsexcellentagreementwiththevalueobtainedfromthespectral-weightanalysis 12 21 above(λ =1.15). Ourtheoreticalanalysisoftheopticalconductivityintheframeworkofaneffectivetwo-bandEliashbergmodelthusreconciles all of the characteristic energy scales and spectral features observed in NaFe Co As. The sharp onset of absorption at 2∆ 0.978 0.022 isdominatedbythebandwithlargeimpurityscattering. EnergyscaleE canbetracedbacktotheonsetofabsorptioninaclean 1 superconductor via a Holstein-type process of breaking-up of a Cooper pair with a simultaneous creation of one spin-fluctuation quantum39,40. In our model the lowest energy cost of this process is 2∆+SG≈11.2 meV, where SG≈5.6 meV is the spin gap observed in the spin-fluctuation spectrum (see Fig. 2d), below which no spin fluctuations exist in the superconducting state. The quasilinearbehavioraboveE resultsfromthequasilinearshapeofthespin-fluctuationspectrumabovethespingap. 1 Theremarkableagreementbetweendifferentexperimentalprobesandtheoreticaltoolsemployedinthisworkdemonstratesthe importance of employing a realistic electronic band structure to interpret the low-energy electronic properties in such complex multiband systems as iron-based superconductors, if complete and consistent understanding of their properties is to be achieved. Ourobservation ofadramatic reductionof theeffectivemass inoneof theelectronicbands ofNaFe Co As, accompanied 0.978 0.022 byrelativelyweaksuperconductingpairing, underlinestheintimateinterplaybetweendifferentelectronicdegreesoffreedomand the importance of spin-orbit coupling for the ground-state properties of the iron-based superconductors. It further shows that the modification of the orbital character of the bands crossing the Fermi level by means of intrinsic or extrinsic strain may allow for unprecedentedcontroloflow-energyelectronicpropertiesofthesecompounds,includingsuperconductivity. Methods Angle-resolved photoemission measurements were performed using synchrotron radiation (“13–ARPES” end-station at BESSY) within the range of photon energies20-90eVandvariouspolarizationsoncleavedsurfacesofhigh-qualitysinglecrystalsofNaFe0.978Co0.022As. Theoverallenergyandangularresolution were∼5meVand0.3◦,respectively,forthelowtemperaturemeasurements. Optical-spectroscopymeasurementswerecarriedoutintheTHzandthefar-infraredspectralrangebymeansofthereflectancetechniqueandfromthefar-inrared totheultravioletspectralrangeusingspectroscopicellipsometry. Theair-sensitivesamplesofoptimallydopedNaFe0.978Co0.022Aswerecleavedbeforeevery measurementandloadedintothemeasurementchamberintheneutralatmosphereofargongas,withoutexposingthesampletoairatanytime. High-accuracy absolutemeasurementsofthesample’sreflectancewerecarriedoutusingthegold-overfillingtechnique. High-qualitysinglecrystalsofsuperconductingNaFe0.978Co0.022Asweresynthesizedbytheself-fluxtechniqueandwerecharacterizedbyx-raydiffraction, transport and magnetization measurements41. The latter revealed a superconducting transition temperature of about 18 K. The width of the superconducting transitionwasfoundtobelessthan1K,indicatingveryhighhomogeneityoftheinvestigatedsamples. BandstructurecalculationswereperformedfortheexperimentalcrystalstructureofNaFeAs(Ref.42)usingthePYLMTOcomputercode43. References 1. Yi,M.etal.Symmetry-breakingorbitalanisotropyobservedfordetwinnedBa(Fe1−xCox)2As2abovethespindensitywavetransition.Proc.Natl.Acad.Sci. 108,6878-6883(2011). 2. Chu,J.-H.,Kuo,H.-H.,Analytis,J.G.&Fisher,I.R.DivergentNematicSusceptibilityinanIronArsenideSuperconductor.Science337,710–712(2012). 3. Kim,Y.K.etal.ExistenceofOrbitalOrderanditsFluctuationinSuperconductingBa(Fe1−xCox)2As2SingleCrystalsRevealedbyX-rayAbsorptionSpec- troscopy.Phys.Rev.Lett.111,217001(2013). 4. Lu,X.etal.NematicspincorrelationsinthetetragonalstateofuniaxialstrainedBaFe2−xNixAs2.Science345,657–660(2014). 5. Fernandes,R.M.,Chubukov,A.V.&Schmalian,J.Whatdrivesnematicorderiniron-basedsuperconductors?.NaturePhys.10,97–104(2014). 6. Liang,S.,Moreo,A.&Dagotto,E.NematicStateofPnictidesStabilizedbyInterplaybetweenSpin,Orbital,andLatticeDegreesofFreedom.Phys.Rev.Lett. 111,047004(2013). 7. de’Medici,L.,Giovannetti,G.&Capone,M.SelectiveMottPhysicsasaKeytoIronSuperconductors.Phys.Rev.Lett.112,177001(2014). 5 8. Cappelluti, E. , Ortenzi, L. , Benfatto, L. & Pietronero, L. Fermi surface shrinking, band shifts and interband coupling in iron-based pnictides. Phys. C: Supercond.470,S508–S510(2010). 9. Charnukha,A.etal.Interaction-inducedsingularFermisurfaceinahigh-temperatureoxypnictidesuperconductor.Sci.Rep.5,10392(2015). 10. Zabolotnyy,V.B.etal.(π,π)electronicorderinironarsenidesuperconductors.Nature457,569–572(2009). 11. Yin,Z.P.,Haule,K.&Kotliar,G.Kineticfrustrationandthenatureofthemagneticandparamagneticstatesinironpnictidesandironchalcogenides.Nature Mater.10,932–935(2011). 12. Tamai,A.etal.StrongElectronCorrelationsintheNormalStateoftheIron-BasedFeSe0.42Te0.58SuperconductorObservedbyAngle-ResolvedPhotoemission Spectroscopy.Phys.Rev.Lett.104,097002(2010). 13. Liu,Z.K.etal.MeasurementofCoherentPolaronsintheStronglyCoupledAntiferromagneticallyOrderedIron-ChalcogenideFe1.02TeusingAngle-Resolved PhotoemissionSpectroscopy.Phys.Rev.Lett.110,037003(2013). 14. Maletz,J.etal.Unusualbandrenormalizationinthesimplestiron-basedsuperconductorFeSe1−x.Phys.Rev.B89,220506(2014). 15. Charnukha,A.Opticalconductivityofiron-basedsuperconductors.J.Phys.:Condens.Matter26,253203(2014). 16. Zhang,C.etal.Distinguishings± ands++ electronpairingsymmetriesbyneutronspinresonanceinsuperconductingNaFe0.935Co0.045As.Phys.Rev.B88, 064504(2013). 17. Thirupathaiah,S.etal.Weak-couplingsuperconductivityinelectron-dopedNaFe0.95Co0.05AsrevealedbyARPES.Phys.Rev.B86,214508(2012). 18. Liu,Z.-H.etal.UnconventionalsuperconductinggapinNaFe0.95Co0.05Asobservedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B84,064519 (2011). 19. Borisenko,S.etal.Directobservationofspin-orbitcouplinginiron-basedsuperconductors.arXiv:1409.8669(unpublished)(2014). 20. Fang,L.etal.Rolesofmultibandeffectsandelectron-holeasymmetryinthesuperconductivityandnormal-statepropertiesofBa(Fe1−xCox)2As2.Phys.Rev.B 80,140508(2009). 21. Coldea,A.I.etal.FermiSurfaceofSuperconductingLaFePODeterminedfromQuantumOscillations.Phys.Rev.Lett.101,216402(2008). 22. Wang,A.F.etal.AcrossoverinthephasediagramofNaFe1−xCoxAsdeterminedbyelectronictransportmeasurements.NewJ.Phys.15,043048(2013). 23. Tu,J.J.etal.OpticalpropertiesoftheironarsenicsuperconductorBaFe1.85Co0.15As2.Phys.Rev.B82,174509(2010). 24. Nakajima,M.etal.CrossoverfrombadtogoodmetalinBaFe2(As1−xPx)2inducedbyisovalentPsubstitution.Phys.Rev.B88,094501(2013). 25. Nakajima,M.etal.StrongElectronicCorrelationsinIronPnictides:ComparisonofOpticalSpectraforBaFe2As2-RelatedCompounds.J.Phys.Soc.Jpn.83, 104703(2014). 26. Basov,D.N.&Timusk,T.Electrodynamicsofhigh-Tcsuperconductors.Rev.Mod.Phys.77,721–779(2005). 27. Tinkham,M.IntroductionToSuperconductivity(McGraw-Hill,1995). 28. Oh,S.etal.SpinpairingandpenetrationdepthmeasurementsfromnuclearmagneticresonanceinNaFe0.975Co0.025As.Phys.Rev.B87,174517(2013). 29. Parker,D.R.etal.ControloftheCompetitionbetweenaMagneticPhaseandaSuperconductingPhaseinCobalt-DopedandNickel-DopedNaFeAsUsing ElectronCount.Phys.Rev.Lett.104,057007(2010). 30. Bardeen,J.,Cooper,L.N.&Schrieffer,J.R.MicroscopicTheoryofSuperconductivity.Phys.Rev.106,162–164(1957). 31. Mattis,D.C.&Bardeen,J.TheoryoftheAnomalousSkinEffectinNormalandSuperconductingMetals.Phys.Rev.111,412–417(1958). 32. Suhl,H.,Matthias,B.T.&Walker,L.R.Bardeen-Cooper-SchriefferTheoryofSuperconductivityintheCaseofOverlappingBands.Phys.Rev.Lett.3,552–554 (1959). 33. Li,G.etal.ProbingtheSuperconductingEnergyGapfromInfraredSpectroscopyonaBa0.6K0.4Fe2As2SingleCrystalwithTc=37K.Phys.Rev.Lett.101, 107004(2008). 34. Charnukha,A.etal.Superconductivity-inducedopticalanomalyinanironarsenide.NatureCommun.2,219(2011). 35. Charnukha,A.etal.EliashbergapproachtoinfraredanomaliesinducedbythesuperconductingstateofBa0.68K0.32Fe2As2 singlecrystals.Phys.Rev.B84, 174511(2011). 36. Wang, Z.etal.CloserelationshipbetweensuperconductivityandthebosonicmodeinBa0.6K0.4Fe2As2 andNa(Fe0.975Co0.025)As.NaturePhys.9, 42–48 (2012). 37. Boeri,L.,Dolgov,O.V.&Golubov,A.A.IsLaFeAsO1−xFxanelectron-phononsuperconductor?.Phys.Rev.Lett.101,026403(2008). 38. Efremov,D.V.,Golubov,A.A.&Dolgov,O.V.Manifestationsofimpurity-induceds±⇒s++transition:multibandmodelfordynamicalresponsefunctions. NewJ.Phys.15,013002(2013). 39. Nicol,E.J.,Carbotte,J.P.&Timusk,T.Opticalconductivityinhigh-Tcsuperconductors.Phys.Rev.B43,473–479(1991). 40. Moon, S.J.etal.InfraredMeasurementofthePseudogapofP-DopedandCo-DopedHigh-TemperatureBaFe2As2 Superconductors.Phys.Rev.Lett.109, 027006(2012). 41. Steckel,F.etal.Crystalgrowthandelectronicphasediagramof4d-dopedNa1−δFe1−xRhxAsincomparisonto3d-dopedNa1−δFe1−xCoxAs.Phys.Rev.B91, 184516(2015). 42. Parker,D.R.etal.Structure,antiferromagnetismandsuperconductivityofthelayeredironarsenideNaFeAs.Chem.Commun.2189–2191(2009). 43. Antonov, V., Harmon, B.&Yaresko, A.Electronicstructureandmagneto-opticalpropertiesofsolids(KluwerAcademicPublishers(Dordrecht, Boston, London),2004). Acknowledgements WewouldliketothankO.V.DolgovandA.A.GolubovforprovidingthecodeusedforthecalculationoftheopticalconductivityintheEliashbergformalismand B.Keimerforstimulatingdiscussions.A.C.acknowledgesfinancialsupportbytheAlexandervonHumboldtfoundation.ThisprojectwassupportedbytheGerman ScienceFoundationunderGrantNo. BO1912/2-2,throughtheEmmyNoetherProgrammeinprojectWU595/3-1andWU595/3-2(S.W.)andwithinSPP1458 (BU887/15-1).S.W.thankstheBMBFforsupportintheframeworkoftheERA.NetRUSproject(project01DJ12096,Fe-SuCo).S.T.appreciatesfinancialsupport byDepartmentofScienceandTechnologythroughINSPIRE-Facultyfellowship(GrantNo.IFA-14PH-86). WewouldliketothankA.Wolter-Giraud,F.Steckel, andC.Hessforsamplecharacterization. Authorcontributions A.C.,K.W.P.,S.T.,andD.P.carriedouttheexperiments.A.C.analyzedthedataandwrotethemanuscript.S.W.,M.R.,andI.M.carriedoutthesamplegrowthand characterization. A.N.Y.performedabinitiocalculations. B.B.,A.V.B.,S.V.B.,andD.N.B.supervisedtheproject. Allauthorsdiscussedtheresultsandreviewed themanuscript. Additionalinformation Competingfinancialinterests:Theauthorsdeclarenocompetingfinancialinterests. CorrespondenceshouldbeaddressedtoA.C.([email protected])andD.N.B.([email protected]). RequestsformaterialsshouldbeaddressedtoS.W. ([email protected]). 6 Supplementary information I. SPIN-ORBITCOUPLINGINTHELOW-ENERGYELECTRONICSTRUCTUREOFNaFe0.978Co0.022AsNEARTHEΓPOINT In order to confirm that the slight anisotropy of the photoemission intensity in the energy-momentum cut shown in Fig.1a of themaintextdoesnotaffecttheconclusionsofourstudywehavefittedtheleftandrightbranchesoftheouterband’sdispersion independently and compared these fits to the results of the simultaneous fit of both branches presented in the text. Only the data pointsathighenoughbindingenergies(unaffectedbythereductionintheeffectivemassduetothespin-orbitcoupling)wereused forallfits(redandgreenfilledcircles);theentiredispersionofthebandisshownforcompleteness(greyemptycircles). The results of this comparison are shown in Fig. S1a. The red and green solid lines are the parabolic dispersions obtained from the fit of the data points of the corresponding color (only the left and right branches of the parabola were used in the fit of the red and green data points, respectively). It is clear that the independent fit of the right (green solid line) branch gives results very similar to the simultaneous fit of both branches (blue solid line). The independent fit of the left branch deviates somewhat fromthesimultaneousfit,albeititprovidesonlyamarginalimprovementinthefit’sfigureofmerit. Toquantifytheeffectofthis uncertaintyontheextractedrenormalizationoftheeffectivemasswehavecalculatedthelatterusingtheformulagiveninthemain text,m(E)=h¯2k(E)dk/dE,independentlyfortheleftandrightbranches. Theresultingenergy-dependenteffectivemassisshown in Fig. S1b for the left (red open circles) and right (green open circles) branches of the dispersion along with their average (blue open circles) plotted in Fig.1e of the main text. It can be seen that even the lowest value of the renormalization corresponding to theindependentfitoftheleftbranchisstillsignificantlylargerthantherenormalizationofalltheotherbandsandthelargestinthe familyofthehigh-temperatureiron-pnictidesuperconductors. InviewoftheindependentfitsshowninFig.S1itismorelikelythat thetruevalueoftherenormalizationisclosertotheaveragethantothelowestvalue. Similarresultscanbeobtainedthroughthe analysisofquasiparticledispersioninthesymmetrized(withrespecttozerowavevector)data. FiguresS1c,ddemonstratetheflatteningofthemiddleholeband’sdispersion(whitearrows)nearitstopduetotheorbital-mixing effectinducedbythespin-orbitcoupling. II. INHERENTCHARACTEROFTHEORBITALLYSELECTIVEBANDSHIFTSINTHEELECTRONICSTRUCTUREOF NaFe Co As 0.978 0.022 Inthissectionwewouldliketobrieflysubstantiatethebulk-relatedcharacteroftheorbitallyselectivebandshiftsor,equivalently, disprove their surface-related origin. Orbitally selective band width renormalization and band shifts are generic to iron-based superconductors,havebeenobservedinessentiallyallmaterialsofthisfamily[S1–9],andsuggestedtoresultfromorbitalblocking inthepresenceofstrongHund’scoupling[S10]andapronouncedparticle-holeasymmetry[S11],respectively. Thisrenormalized andband-shiftedelectronicstructure,aswellasthesuperconductingenergygapthatdevelopsonit,observedviaARPEShasbeen 2 0 2 0 0 c d a 0 0 -2 0 ) -2 0 -2 0 V e (m-4 0 ergy - 4 0 -4 0 n E -6 0 -6 0 -6 0 b -8 0 -8 0 -8 0 -0 .3 0 .0 0 .3 0 3 6 9 1 2 -0 .3 0 .0 0 .3 -0 .3 0 .0 0 .3 M o m e n tu m ((cid:3)(cid:1)(cid:2)) m Gexp/m LDA M o m e n tu m ((cid:3)(cid:1)(cid:2)) M o m e n tu m ((cid:3)(cid:1)(cid:2)) FigureS1| Detailsofthelow-energyelectronicbandstructureofNaFe0.978Co0.022AsneartheΓpoint.a,Energydispersionoftheouterhole bandneartheΓpointoftheBrillouinzone(circles)extractedfromthemaximumofthequasiparticlepeakinthemomentum-distributioncurves overlaidwiththesimultaneousparabolicfitofboththeleftandrightbranches(bluesolidline)aswellasindependentparabolicfitsoftheleft(red solidline)andright(greensolidline)branches. Thedatausedforthefittingareshownasfilledcirclesofthecorrespondingcolor. Greyopen circlesshowtheenergydispersionuptotheFermilevel.b,Renormalizationoftheeffectivemassextractedindependentlyfromtheleft(redopen circles)andright(greenopencircles)branchesofthedispersionoftheouterholeband,aswellastheiraverage,asshowninFig.1eofthemain text.c,d,Energy-momentumcutalongtheΓ-MdirectionoftheBrillouinzoneplottedinFig.1aofthemaintext(panelc)andthesecondderivative ofthisphotoemissionintensitydistributiontakeninthedirectionofenergy(paneld). SolidanddashedlinesareasinFig.1aofthemaintext. Whitearrowsindicatetheflatteningoftheenergydispersionofthemiddleholebandduetoorbitalmixinginducedbyspin-orbitcoupling. 7 1 0 0 1 0 0 1 0 0 a b c 9 5 9 5 9 5 ) (% e c 9 0 9 0 9 0 n ta c fle 3 0 0 K 3 0 K d a ta 3 0 K d a ta e a s in m a in te x t a s in m a in te x t R 8 5 2 0 0 K 3 0 K 8 5 w w 8 5 g 1 0 0 K 2 0 K pl,2+ 1 0 % pl,2 2 x 2 5 0 K 1 0 K w -1 0 % w 0 .5 x g pl,2 pl,2 2 8 0 8 0 8 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) 1 0 0 1 0 0 d e 9 5 9 5 ) (% e c n 9 0 9 0 ta c efle 3 0 K d a ta 3 0 K d a ta R 8 5 wa s in+ 1m0 a% in w te x t 8 5 ga s+ i1n0 m% a gin te x t pl,1 pl,1 1 1 w -1 0 % w g -1 0 % g pl,1 pl,1 1 1 8 0 8 0 0 2 0 4 0 6 0 0 2 0 4 0 6 0 P h o to n e n e rg y (m e V ) P h o to n e n e rg y (m e V ) FigureS2|Detailsofthefar-infrareddataandanalysis.a,Photon-energydependenceofthefar-infraredreflectanceatvarioustemperatures.b– e, Analysis of the reflectance at 30 K (cyan solid line) in the framework of the two-Drude model (dotted lines). Black dotted line shows the reflectancecorrespondingtothebest-fitparametersofthetwoDrudeterms, asspecifiedinFig.1gofthemaintext. Redandbluedottedlines demonstratetheeffectofdetuningtheseparametersup(bluelines)ordown(redlines)fromthebest-fitvalues,asdetailedinthefigurelegends. Thehigh-frequencydielectricfunctionusedinthismodelwastakentobeε∞=60,determinedbythecontributionoftheinterbandtransitionsat higherenergies. found to agree remarkably well with many bulk-sensitive techniques, strongly suggesting that the electronic band structure of the surface layer in these compounds is reflective of that in the bulk. The only exception to this rule is the 1111 type of compounds, in which the presence of both bulk- and surface-related states in the photoemission signal has been found [S 12–21], making the extraction of the inherently bulk electronic structure challenging. Recently, a detailed ARPES work succeeded in disentangling the bulk and surface contributions to the photoemission signal and demonstrated that the bulk electronic structure features the sameorbitallyselectivebandwidthrenormalizationandbandshiftsasobservedinotherclassesofiron-basedsuperconductors[S 11], provingitsgenericandinherentcharacter. Finally, itiswell-knownthat111-typematerialscleavebetweenthetwolayersof the intercalant, which results in a non-polar surface. The equivalence of the bulk and surface electronic states has been further demonstratedinanexplicitdensity-functionalcalculation[S22]. III. DETAILSOFTHEFAR-INFRAREDDATAANDANALYSIS Herewewouldliketodemonstratethedegreeofuncertaintyintheextractedparametersofthefree-charge-carrierresponseshown inFig.1gthatthefinitesignal-to-noiseratioofandtheuncoveredlowest-frequencyrangeintheexperimentaldataallow. Wedoso bycomparingtheopticalresponsecorrespondingtothebestfitshowninFigs.1f,gwiththatderivedfromtheDrude-termparameters slightly detuned from those optimal values. In order to eliminate the integral transformation via Kramers-Kronig relations and toemphasizethefunctionalshapeofthereflectanceassumedintheextrapolationregionatlowestfrequenciesforKramers-Kronig analysis,wedemonstratethesetrendsintherawfar-infraredreflectancedata.Thelatterareshownfordifferenttemperaturesbetween 10Kand300KinFig.S2a. FiguresS2b–eshowthereflectanceobtainedinourexperimentasafunctionofphotonenergyat30K overlaid with that produced by assuming two Drude terms (ω ,γ ; ω ,γ ) with the parameters specified in the figure legends. pl,1 1 pl,2 2 Thehigh-frequencydielectricfunctionistakentobeε =60,determinedbythecontributionoftheinterbandtransitionsathigher ∞ energies. Thedefault(best-fit)parametersofthefree-charge-carrierresponsereferredtointhesepanelsarethosespecifiedinFig.1g ofthemaintext. 8 IV. DETERMINATIONOFBAND-SPECIFICPLASMAFREQUENCIESBASEDONARPESDATA InoptimallydopedNaFe Co AstheFermisurfaceconsistsofthreesheets: twoelectonlikeinthecornersoftheBrillouin 0.978 0.022 zone and one holelike at the center [S 23]. It is well-known and a generic feature of iron-based superconductors that the bands generatingtheelectronsheetsareonlyweaklydispersiveintheout-of-planedirection,givingrisetotwoquasi-cylindricalsheetsof theFermisurfacewithrelativelysmallcorrugations[S24]. Therefore,wecanapproximatethesetwosheetsbytwoidenticalideal cylinderswiththeirradiiequaltotheaverageofthelongandtheshorthalf-axisoftheellipsoidsgivingrisetothecorrugation. The electronicbandgeneratingtheholesheetoftheFermisurfacealsodispersesratherweaklyalongtheΓ-ZdirectionoftheBrillouin zone, as shown in Fig. S3: the Fermi wave vector of this band remains within 0.07–0.09 A˚−1 between Γ and Z. Therefore, the Fermi-surfacesheetgeneratedbythisbandcanlikewisebeapproximatedbyacylinderwitharadiusofabout0.08A˚−1. Thusthe taskofcalculatingtheplasmafrequencyhasbeenreducedtoatwo-dimensionalproblem. Ingeneral,theplasmafrequencyoffree chargecarrierscanbeobtainedfromthesemi-classicalexpressionforthedielectricfunction[S25]assumingtheintrabandcaseand lowtemperaturesandisgivenbythefollowingexpression(inSIunits): e2 (cid:90) (cid:20)dE (cid:21)2 ω2 = ∑ nk δ(E −E )d3k, (1) pl,σ 8π3h¯2ε0 n dkσ nk F whereσ =x,y,zenumeratesthecoordinateaxes,nisthebandindex,δ(x)isDirac’sdeltafunction,E istheenergydispersionof nk thenthband, E istheFermienergy, eistheelectroncharge, h¯ isthereducedPlanckconstant, andε isthevacuumpermittivity. F 0 Assuming our two-dimensional approach and the tetragonal symmetry of NaFe Co As, ω =0 and ω =ω =ω . 0.978 0.022 pl,z pl,x pl,y pl Thusonlyonequantityω needstobecalculatedforeachband. Inthetwo-dimensionalcaseandforanisotropicparabolicband pl withaneffectivebandmassm [E =h¯2k2/(2m )]Eq.1canberewrittenasasimpleandfamiliarexpression: eff k eff N (E )e2 ω2 = 2D F , (2) pl m ε eff 0 where N (E )= kF2 2π is the density of states at the Fermi level for an isotropic parabolic band in two dimensions, k is the 2D F (2π)2 c F Fermiwavevector,andcistheout-of-planelatticeconstant.Thusthecalculationoftheband-specificplasmafrequenciesisreduced tothedeterminationoftheFermiwavevectorandthequasiparticleeffectivemassforeachband, whichcaneasilybedonebased onthephotoemissionintensitydistributionsneartheFermilevelpresentedinFigs.1a,b. Asalreadymentionedaboveandshownin Fig.S3, theFermiwavevectoroftheholebandisabout0.08A˚−1, anditseffectivemassisfoundtobe3.83m (wherem isthe e e bareelectronmass),whichresultsinaplasmafrequencyofωhole,1=0.23eV. TheFermiwavevectorsandeffectivemassesofthe pl electronbandsattheM-pointare0.086A˚−1,0.92m and0.153A˚−1,2.34m fortheinnerandtheouterband,respectively. These e e valuesresultinalmostidenticalplasmafrequenciesofωel,in=0.5eVandωel,out=0.56eV,respectively. pl pl 4 5 e V 2 0 4 3 e V 4 1 e V 3 9 e V 3 7 e V 1 5 .) 3 5 e V . u 3 3 e V rb (a 3 1 e V ity1 0 2 9 e V FigureS3|Out-of-planedispersionofthehole s ten 2 7 e V ba ndalongtheΓ-ZdirectionintheBrillouin In zone. Momentum-distribution curves (MDCs) 2 5 e V at near-normal photoemission (0 momentum 5 2 3 e V corresponds to normal emission) averaged in 2 1 e V a 5 meV energy window around the Fermi level for various energies of incident photons. 1 9 e V The data were recorded in the normal state of 1 7 e V NaFe Co Asat27K. TheMDCsaredis- 0 0.95 0.05 placedverticallybyaconstantof1.5.Blackver- ticallinesindicatethepositionoftheFermiwave -0 .2 -0 .1 0 .0 0 .1 0 .2 vectorextractedasthemaximumofthequasipar- M o m e n tu m ((cid:3)(cid:1)(cid:2)) ticlepeakforeveryMDC. 9 References S1. Borisenko,S.V.etal.SuperconductivitywithoutNestinginLiFeAs.Phys.Rev.Lett.105,067002(2010). S2. Sudayama,T.etal.Doping-DependentandOrbital-DependentBandRenormalizationinBa(Fe1−xCox)2As2Superconductors.J.Phys.Soc.Jpn.80,113707 (2011). S3. Ding,H.etal.ElectronicstructureofoptimallydopedpnictideBa0.6K0.4Fe2As2:acomprehensiveangle-resolvedphotoemissionspectroscopyinvestigation. J.Phys.:Condens.Matter23,135701(2011). S4. Cui,S.T.etal.EvolutionofthebandstructureofsuperconductingNaFeAsfromoptimallydopedtoheavilyoverdopedCosubstitutionusingangle-resolved photoemissionspectroscopy.Phys.Rev.B86,155143(2012). S5. Yi,M.etal.ObservationofTemperature-InducedCrossovertoanOrbital-SelectiveMottPhaseinAxFe2−ySe2(A=K,Rb)Superconductors.Phys.Rev.Lett. 110,067003(2013). S6. Maletz,J.etal.Unusualbandrenormalizationinthesimplestiron-basedsuperconductorFeSe1−x.Phys.Rev.B89,220506(2014). S7. Lee,G.etal.OrbitalSelectiveFermiSurfaceShiftsandMechanismofHighTc SuperconductivityinCorrelatedAFeAs(A=Li,Na).Phys.Rev.Lett.109, 177001(2012). S8. Evtushinsky,D.V.etal.Strongelectronpairingattheiron3dxz,yzorbitalsinhole-dopedBaFe2As2superconductorsrevealedbyangle-resolvedphotoemission spectroscopy.Phys.Rev.B89,064514(2014). S9. Brouet,V.etal.LargeTemperatureDependenceoftheNumberofCarriersinCo-DopedBaFe2As2.Phys.Rev.Lett.110,167002(2013). S10. Yin,Z.P.,Haule,K.&Kotliar,G.Kineticfrustrationandthenatureofthemagneticandparamagneticstatesinironpnictidesandironchalcogenides.Nature Mater.10,932–935(2011). S11. Charnukha,A.etal.Interaction-inducedsingularFermisurfaceinahigh-temperatureoxypnictidesuperconductor.Sci.Rep.5,10392(2015). S12. Lu,D.H.etal.Electronicstructureoftheiron-basedsuperconductorLaOFeP.Nature455,81–84(2008). S13. Liu,H.-Y.etal.PseudogapandSuperconductingGapinSmFeAs(O1−xFx)SuperconductorfromPhotoemissionSpectroscopy.Chin.Phys.Lett.25,3761 (2008). S14. Kondo,T.etal.MomentumDependenceoftheSuperconductingGapinNdFeAsO0.9F0.1SingleCrystalsMeasuredbyAngleResolvedPhotoemissionSpec- troscopy.Phys.Rev.Lett.101,147003(2008). S15. Liu,C.etal.Electronicpropertiesofironarsenichightemperaturesuperconductorsrevealedbyangleresolvedphotoemissionspectroscopy(ARPES).Phys. C:Supercond.469,491–497(2009). S16. Lu,D.etal.ARPESstudiesoftheelectronicstructureofLaOFe(P,As).Phys.C:Supercond.469,452–458(2009). S17. Liu,H.etal.UnusualElectronicStructureandObservationofDispersionKinkinCeFeAsOParentCompoundofFeAs-basedSuperconductors.Phys.Rev. Lett.105,027001(2010). S18. Liu,C.etal.Surface-drivenelectronicstructureinLaFeAsOstudiedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B82,075135(2010). S19. Yang,L.X.etal.SurfaceandbulkelectronicstructuresofLaFeAsOstudiedbyangle-resolvedphotoemissionspectroscopy.Phys.Rev.B82,104519(2010). S20. Yang,L.etal.ElectronicstructureofSmOFeAs.J.Phys.Chem.Solids72,460–464(2011). S21. Nishi,I.etal.Angle-resolvedphotoemissionspectroscopystudyofPrFeAsO0.7:ComparisonwithLaFePO.Phys.Rev.B84,014504(2011). S22. Lankau,A.etal.AbsenceofsurfacestatesforLiFeAsinvestigatedusingdensityfunctionalcalculations.Phys.Rev.B82,184518(2010). S23. Thirupathaiah,S.etal.Weak-couplingsuperconductivityinelectron-dopedNaFe0.95Co0.05AsrevealedbyARPES.Phys.Rev.B86,214508(2012). S24. Mazin,I.I.&Schmalian,J.Pairingsymmetryandpairingstateinferropnictides:Theoreticaloverview.Phys.C469,614–627(2009). S25. Yu,P.Y.&Cardona,M.FundamentalsofSemiconductors(Berlin:Springer,2005). 10

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