High-temperature superconductivity from fine-tuning of Fermi-surface singularities in iron oxypnictides

8.6 MB·

by  A. Charnukha

High-temperature superconductivity from fine-tuning
of Fermi-surface singularities in iron oxypnictides
A. Charnukha1,2,†, D. V. Evtushinsky1, C. E. Matt3,4, N. Xu3,5, M. Shi3, B. Bu¨chner1, N. D. Zhigadlo4,
B. Batlogg4 & S. V. Borisenko1
6
1 1LeibnizInstituteforSolidStateandMaterialsResearch,IFW,D-01069Dresden,Germany,2PhysicsDepartment,UniversityofCalifornia–San
0 Diego,LaJolla,CA92093,USA,3SwissLightSource,PaulScherrerInstitut,CH-5232VilligenPSI,Switzerland,4LaboratoryforSolidStatePhysics,
2 ETHZurich,CH-8093Zurich,Switzerland,5InstituteofCondensedMatterPhysics,E´colePolytechniqueFe´de´raledeLausanne,CH-1015Lausanne,

n Switzerland.†E-mail:[email protected].
a
J
Inthefamilyoftheiron-basedsuperconductors,theREFeAsO-typecompounds(withREbeingarare-earthmetal)exhibitthehighestbulk
1
1 superconductingtransitiontemperatures(Tc)upto55Kandthusholdthekeytotheelusivepairingmechanism. Recently, ithasbeen
demonstratedthattheintrinsicelectronicstructureofSmFe0.92Co0.08AsO(Tc=18K)ishighlynontrivialandconsistsofmultipleband-edge
] singularitiesincloseproximitytotheFermilevel.However,itremainsunclearwhetherthesesingularitiesaregenerictotheREFeAsO-type
n materials and if so, whether their exact topology is responsible for the aforementioned record Tc. In this work, we use angle-resolved
o photoemissionspectroscopy(ARPES)toinvestigatetheinherentelectronicstructureoftheNdFeAsO0.6F0.4compoundwithatwicehigher
c
- Tc=38K. WefindasimilarlysingularFermisurfaceandfurtherdemonstratethatthedramaticenhancementofsuperconductivityinthis
r compoundcorrelatescloselywiththefine-tuningofoneoftheband-edgesingularitiestowithinafractionofthesuperconductingenergy
p
gap ∆ below the Fermi level. Our results provide compelling evidence that the band-structure singularities near the Fermi level in the
u
iron-basedsuperconductorsmustbeexplicitlyaccountedforinanyattempttounderstandthemechanismofsuperconductingpairingin
s
thesematerials.
.
t Aftersevenyearsofintensiveresearch,themechanismofsuperconductivityintheiron-basedsuperconductorsremainsunknown.
a
m TheobservationoftheFermi-surfacetopologydrasticallydifferentfromtheearlypredictionsoftheabinitiocalculationsinsome
compounds[1–4]hascastdoubtonthetheoreticaldescriptionofsuperconductivitybasedonthissimplifiedpictureandnecessitates
-
the adoption of the true Fermi surface, a paradigm shift that is now beginning to occur [5, 6]. In this view, the identification of
d
n essentialelectronicfeaturesbearingdirectlyonthesuperconductingpairingmechanismisofvitalimportance. Recentobservation
o of a highly nontrivial electronic structure in SmFe0.92Co0.08AsO shaped by multiple band-edge singularities in the vicinity of the
c Fermi level (EF) implies, should it prove to be generic for the 1111-type compounds, that very small changes on the order of
[ tens of meV can potentially lead to drastic changes in the Fermi-surface topology and strongly affect the superconducting state.

WeemployARPEStoshowthatthebulkelectronicstructureofNdFeAsO F is,atfirstsight,virtuallyidenticaltothatofsister
1 0.6 0.4
SmFe Co AsOwithatwicelowerT ,withoneessentialdifference:thetopoftheholebandlocatedat≈6meVabovetheFermi
v 0.92 0.08 c
level in SmFe Co AsO (Ref. 4) sinks to 2.3 meV below the Fermi level, entirely eliminating the Fermi surface at the center
6 0.92 0.08
8 of the Brillouin zone. And yet this band remains within the reach of superconducting pairing interaction and, intriguingly, hosts
6 a superconducting energy gap of 10.5 meV — almost 10 times larger than that in SmFe0.92Co0.08AsO (Ref. 4). This observation
2 suggeststhatthe“fine-tuning”oftheaforementionedholebanddramaticallyenhancessuperconductivityinNdFeAsO0.6F0.4.
0 AtypicalphotoemissionintensitydistributionattheFermilevelinNdFeAsO0.6F0.4isshowninFigs.1a,b. Itisdominatedbytwo
. largecircularsheetsoftheFermisurfaceattheΓpointoftheBrillouinzoneandacomplexpropellerlikestructuresurroundedby
1
anothercircularsheetattheMpoint. Ithasbeenshowninseveralworks[7–16],particularlyinref.4,thatalllargecircularfeatures
0
(two at the Γ and one at the M point) are extrinsic and can be traced back to the polar cleaved surface of the crystal. Below we
6
1 provideadditionalcompellingevidencethatthisisindeedthecase.
: Withthelargecircularfeatureseliminatedtheelectroniclandscapethatremainsisclearlynontrivial. Toexamineitindetail,we
v
show several energy-momentum cuts (EMCs) obtained along the dashed lines in Figs. 1a,b. Figure 1c reveals the photoemission
i
X intensitydistributionalongthehigh-symmetryM–Γ–Mdirection. Thesurface-relatedbandsthatgeneratethelargecircularfeatures
inFigs.1a,bareshownwithwhitearrowshereandinsubsequentpanelsofthisfigure. AttheΓpoint,anotherholebandathigher
r
a bindingenergiesisevidentandispartofthebulkelectronicstructure, aswillbesubstantiatedinwhatfollows. AttheM point, a
very heavy hole band is clearly visible. This band gives rise to the blades of the propellerlike structure in Figs. 1a,b, as has been
showninsomeoftheearlierstudies[4,13]. Below, aweakelectronbandisvisiblewithadditionalbandsunderneathit. Inref.4
ithasbeenarguedthatthisentireintensitydistributionispresentalreadyintheabinitioLDAcalculationsatmuchhigherbinding
energiesthanfoundinexperimentandispulledtotheFermilevelbyelectronicinteractions,asisshownschematicallyinFig.1d.
Itiswell-knownthatthephotoemissionmatrixelementsdependstronglyonthepolarizationofincidentlight.Therefore,weshow
an energy-momentum cut along the same high-symmetry direction but obtained with the circular polarization in Fig. 1e. Indeed,
1
Fig.1. a,b,Constant-energymapsobtainedbyintegratingthephotoemissionintensitywithin15meVaroundE ,recordedatT =1Kusing
F
60eVphotonswithlinearhorizontal(a)andcircular(b)polarization. Whitedottedsquareshowsthe2-FeBrillouinzone.c,Energy-momentum
cut (EMC) along the line shown in a. White arrows in panels c,g–i indicate the surface-related bands giving rise to the large circular features
aroundΓandM ina,b.d,Schematicillustrationoftheeffectofhigh-energyelectroniccorrelationsontheabinitiobandstructure,asreported
inref.4.e–i, EMCsalongthelinesshownina,b.e, TheintensitydistributionnearΓshowsthebulkelectronicstructuremoreclearly: ahole
bandterminatingnearE togetherwithanotherbroadholelikedispersivefeatureat56meVbelowE (seepanelsh,i). Theexpectedconnection
F F
betweenthebulk-relatedfeaturesatΓandM(d)isclearlyseenandindicatedwithadashedlineandblackarrows.f,g,EMCsneartheMpoint.
Dashedlinesinfshowthepredictionofabinitiocalculationsrenormalizedbyafactorof1.8andshiftedtowardsE ,seepaneldandref.4.White
F
line and arrows in g indicate an additional electron band distinct from the complex structure in f and producing the circular feature around M
ina,b.h,i,EMCsnearΓat1Kand50K,respectively. Inh,aholebandjustbelowE (upperdashedline)andtwomorebandsterminatingat
F
56meVbindingenergy(lowerdashedlines;seesupplementaryinformationforconclusiveevidenceforthetwo-bandcharacterofthisfeature)are
indicated. Panelishowsthenormal-statedispersionoftheupperbulkholebandextractedfromthefitofmomentum-distributioncurves(white
circles)andaparabolicfittothisdispersion(blacksolidline). Thelatterprovidesthelocationofthebandedgeat2.3meVbelowE . Alldashed
F
andsolidlinesareschematicunlessstatedotherwise.
thisfigurerevealsadditionalkeyfeatures: theelectronbandsattheM pointaremuchmoreprominentandanadditionalintensity
spot just below the Fermi level is visible, which comes from a higher-lying electron band, consistent with the band structure in
Fig. 1d. The photoemission intensity at the Γ point now reveals a hole band just below the Fermi level as well as the additional
intensity distribution with holelike dispersion at higher binding energies, already pointed out in Fig. 1c. We show that the latter
intensitydistributioncomprisestwodifferentbandsdegenerateattheΓpoint(seesupplementaryinformation),consistentwiththe
theoretically predicted bulk electronic structure renormalized by a factor of about 1.8 as illustrated schematically in Fig. 1d. One
canclearlyseethattheupperbandisconnectedtotheheavyholebandattheM point(asshownwithblackarrowsandadashed
curve,displacedupwardsnottoconcealtheweakphotoemissionsignal). Thisobservationisessentialasitprovesthatthethreehole
bandsattheΓpointandthepropellerstructureattheMpointarepartofthesameelectronicstructureandareentirelydistinctfrom
thesurfacerelatedbandsmentionedabove. Figure1ffurthershowsthatthebandstructureattheM pointagreesremarkablywell
withthepredictionofabinitiocalculationsprovidedthatthelatterisrenormalizedbythesamefactorof1.8asthebandstructure
aroundtheΓpoint. Italsoindicatesthatalbeittheholebandsgivingrisetothebladesofthepropellerlikestructureintheintensity
mapsinFigs.1a,b(integratedinawindowof±15meVaroundtheFermilevel)terminateintheimmediatevicinityoftheFermi
level,theydonotcrossitand,therefore,donotcontributetotheFermisurfaceofNdFeAsO F .
0.6 0.4
2
Fig.2. a,CropofFig.1a.b–d,EMCsalongthedashedlinesinpanela.Alldatawererecordedat1Kusingalinearpolarizationand30eV(b,d)
or60eV(c)photonenergy. Normal-state(at50K)counterpartoftheEMCind,obtainedunderthesameconditions,isshowninFig.1i.e–h,
NormalizedEDCsintegratedinthemomentumwindowsshownasdashedrectanglesinpanelsb–d. AllfitswereobtainedusingtheDynes–like
modelforintegratedEDCs,asdescribedinthetext.i,j,TemperaturedependenceofthenormalizedEDCsine,g. Thedashedlinesinjindicate
(lefttoright)thelocationofthequasiparticlecoherencepeakE ,leadingedgeofthesuperconductingcomponentat1K,andE .k,Ratio(blue
0 F
open circles) of the normalized EDCs obtained in the superconducting (1 K) and normal (50 K) state in g, and its first derivative (black solid
line;shiftedupby0.7andmultipliedby5forclarity). Verticaldashedlines(lefttoright)markthelocationofE andE . Theformerisfurther
0 F
clearlyvisibleasthezeroofthefirstderivative(intersectionoftheleftverticalandlowerhorizontaldashedlines). Thenormalcomponentshown
inpanelgproducesaninflectionpointinthederivativeandhasitsleadingedge(minimumofthederivative)locatedatE . Itcouldoriginatein
F
afinitecontributiontothephotoemissionsignalfromoutsidethesamplesurface,giventhesmallsizeofthesinglecrystals(seeMethods).l,m,
Temperaturedependenceof|E |and∆I definedinpanelk(bluecircles)andoftheM-pointsuperconductinggap∆(extractedfromthedata
0 peak
inb,e,i)(redcircles). BlacksolidlineisthetemperaturedependenceexpectedintheBardeen-Cooper-Schrieffertheoryofsuperconductivityfor
∆=5meVandTc=38K. Anaccuratedescriptionofthetemperaturedependenceofthesesuperconductingfeatureswouldrequireconsistently
takingintoaccounttheexistenceofmultiplecoupledbandsandtheproximityoftheiredgestotheFermilevel.
Bytakinganenergy-momentumcutat45◦withrespecttotheorientationoftheblades,asshowninFig.1g,werevealtheelectron
bandthatgivesrisetothelargecircularfeatureattheMpointinFigs.1a,b.Itcanbeseenthatthiselectronbandismuchheavierthan
thatshowninFig.1f. Inref.4ithasbeenshownthattheelectronicstructureproducingthepropellerlikeconstructattheM point
doesnothaveanyintensityinthisdirectionandthusthisheavyelectronbandisnotapartofitandmustbeextrinsic. Therefore,
the only bulk band in NdFeAsO F that does clearly cross the Fermi level and generates a well-defined Fermi surface is the
0.6 0.4
shallowelectronbandattheMpointoftheBrillouinzone,consistentwiththepredominantlyelectron,asopposedtohole,transport
observedinthismaterial[17]. WethusarriveattheinherentelectronicstructureofNdFeAsO F fullyconsistentwiththatshown
0.6 0.4
inFig.1dandsurprisinglysimilartothatofSmFe Co AsO(ref.4).
0.92 0.08
Todeterminethefinedifferencesbetweenthesetwocompoundswithverydifferentsuperconductingtransitiontemperatureswe
investigate the electronic structure more closely. Figure 1h shows an energy-momentum cut at an angle to the Γ–M direction, as
indicated in Fig. 1a. All the relevant features discussed above are now more immediately evident. The white arrows indicate the
extrinsicsurfacestates.Thedashedlines,ontheotherhand,showthebulkholebandsidentifiedabove.Onecanclearlyseetheupper
hole band in the immediate vicinity of the Fermi level crossing the inner surface-related band as well as the intensity distribution
duetothelowertwobandsterminatingat∼50meVbelowtheFermilevel. Thebandedgesofthesethreebandsdonotshowany
observable dispersion in the out-of-plane direction of the Brillouin zone (see supplementary information), confirming the highly
two-dimensional character of the electronic structure of the 1111-type compounds predicted theoretically [18, 19]. To determine
3
thepreciselocationofthebandedgeclosesttotheFermilevel(andthusdirectlyaffectingtheitinerantproperties)weextractthe
dispersion of the corresponding band in the normal state (at 50 K) in Fig. 1i from a fit of the momentum-distribution curves. A
parabolicfittothedetermineddispersionshowsthatthisbandterminatesatonly2.3meVbelowtheFermilevelandthusdoesnot
generateaFermisurface.
Given that the overall bulk electronic structure of NdFeAsO F is so strikingly similar to that of SmFe Co AsO, and
0.6 0.4 0.92 0.08
yet their superconducting transition temperatures differ by a factor of 2, it is crucial to compare the effect of the fine differences
on the superconducting pairing. To that end, we have studied the temperature dependence of the electronic structure around the
Γ and M points of the Brillouin zone. Three representative energy-momentum cuts in the directions shown with dashed lines in
Fig. 2a are displayed in Figs. 2b–d. In order to determine the superconducting energy gap accurately by accounting for the finite
experimentalresolutionweusetheexpressionderivedinRef.3. Thevalueofthesuperconductingenergygapisextractedbyfitting
the momentum-integrated EDCs in the momentum windows indicated in Figs. 2b–d as white dashed rectangles with the Dynes
functionmultipliedbytheFermifunctionandconvolvedwiththeresolutionfunction:
(cid:20) (cid:12)(cid:12) ω+iΣ(cid:48)(cid:48)(cid:12)(cid:12)(cid:21)
IEDC(ω)= f(ω,T)(cid:12)(cid:12)Re E (cid:12)(cid:12) ⊗Rω(δE), (1)
(cid:112)
where E = (ω+iΣ(cid:48)(cid:48))2−∆2, ω is the binding energy with reversed sign, T is the temperature, Σ(cid:48)(cid:48) is the imaginary part of the
self-energy,∆isthesuperconductingenergygap,andδE istheexperimentalresolution. Themomentumresolutiondropsoutfrom
thisexpressionduetomomentumintegration. TheresultsofthefitareshowninFigs.2e-hforthemiddleandoneofthebladesof
thepropellerlikestructureattheMpoint,holebandterminatinginthevicinityoftheFermilevelattheΓpoint,aswellastheouter
surface-relatedbandattheΓpoint,respectively.Thesuperconductingenergygapatthecenterofthepropellerlikestructureamounts
to 5 meV and thus has a gap ratio 2∆/k T of about 3.2, comparable to that on the corresponding feature of SmFe Co AsO
B c 0.92 0.08
(≈3.3) (ref. 4) and close to the BCS value 3.52. The detailed temperature dependence of this superconducting gap, extracted by
fitting the data in Fig. 2i, is shown with red open circles in Fig. 2m and appears to deviate from the behavior expected from the
conventionalBardeen-Cooper-Schrieffertheoryofsuperconductivity(blacksolidline).
Unlike the energy-distribution curves recorded in the middle of the propellerlike structure, those obtained on one of the blades
(Figs.2candf)exhibitpronouncedfinite-bandeffects, manifestedinthestrongdeviationofthenormal-statedatainFig.2ffrom
theFermi-Diracdistribution. InsuchacaseEq.1cannotbeusedandthefullmodelingofafinitebandmustbeemployed[3]. The
correspondingfinite-bandfitsoftheexperimentaldata(opencircles)inthenormalandsuperconductingstate(solidlines)areshown
inFig.2fandsuggesttheabsenceofthesuperconductinggaponthisfeatureoftheelectronicstructure,which,ashasbeenargued
above,doesnotproduceanyFermisurface.
Quitesurprisingly,theholebandterminatingat2.3meVbelowtheFermilevelandthuslikewisenotproducinganyFermisurface,
isfoundtohostasuperconductingenergygapof10.5meV,withagapratioof6.65,significantlylargerthanthecorrespondingratio
inSmFe Co AsO(≈2.1).Interestingly,thisvalueisveryclosetothelargestgapratioof∼6.8observedintheoptimallydoped
0.92 0.08
Ba K Fe As compoundwiththesameT ≈38KasNdFeAsO F [3,20]. Eventhoughtheextractionofthesuperconducting
1−x x 2 2 c 0.6 0.4
gaponthisfeatureissomewhatcomplicatedbythepresenceofasizablenon-superconducting(normal)component, asshownby
theshadedareainFig.2gandfurthersubstantiatedinFig.2k,thepresenceofalargesuperconductinggapisdirectlyevidentinthe
rawdatapresentedinFigs.2d,g,j: thesuperconductivity-inducedcoherencepeakislocatedat13meVbelowtheFermileveland
the leading edge of the superconducting component — at about 7 meV below the Fermi level (it is well-known that the leading-
edge shift tends to underestimate the value of the superconducting gap). Both features vanish at the superconducting transition
temperature,ascanbeseeninFig.2j. ThetemperaturedependenceofthebindingenergyE andamplitudeofthecoherencepeak
0
∆I ,extractedfromtheexperimentaldataandtheirderivativeasindicatedinFig.2k,arepresentedinFigs.2l,m. Itisclearthat
peak
while ∆I (blue open circles in Fig. 2m) closely mimics the temperature dependence of the superconducting gap found in the
peak
middle of the propellerlike structure at the M point of the Brillouin zone (red open circles in Fig. 2), the binding energy of the
coherencepeakshowsnegligibletemperaturedependence,suggestingfilling-in,ratherthanclosing,ofthesuperconductingenergy
gapattheΓpoint.
Finally,andinstarkcontrasttopreviousstudies,theoutersurface-relatedbandinoursamplesshowsnosignofthesuperconduct-
ingenergygap,asshowninFig.2h,providingfurthercompellingevidencefortheextrinsiccharacterofthisfeature. Theabsence
or strong suppression of the proximity effect between the bulk and the surface layer of NdFeAsO F is remarkable, albeit not
0.6 0.4
unprecedented[21],andrequiresfurtherinvestigation.
Theproximityofband-edgesingularitiestotheFermilevelsimultaneouslyattheΓandMpointsoftheBrillouinzone,connected
bytheubiquitousintheiron-basedsuperconductors(π,π)Q-vector,indicatesthatnestingmayplayanimportantroleinthelow-
energyelectrodynamicsofthismaterial. Atthesametime,thesizablevalueofthesuperconductingenergygaponthefeaturesof
theelectronicstructurebothattheΓandMpointsimpliesthatthecondition∆/E (cid:28)1,where∆isthesuperconductingenergygap
F
and E is the Fermi energy, required for the Migdal approximation of the conventional theories of superconductivity is violated.
F
Thissuggeststhatamoregeneraltheoryisnecessaryforanadequatedescriptionofthesuperconductingpropertiesofthisandlikely
othercompoundsoftheiron-basedfamily[22,23].
Our observation of the dramatic enhancement of the superconducting energy gap in NdFeAsO F given the band structure
0.6 0.4
almostidenticaltothatofSmFe Co AsOisstriking.Itleavesonewithonlytwoalternatives:eitherthesuperconductingpairing
0.92 0.08
doesnotdependontheexactshapeoftheFermisurfaceatall,oritmustbeextremelysensitivetoveryfinechangesinthelow-energy
electronic structure of the iron oxypnictides. The former case is indeed possible and realized in conventional superconductors, in
which the exact shape of the Fermi surface is largely irrelevant, given the same density of states at the Fermi level [24], and the
superconductingpairingdrivenbyamediatornotbelongingtotheelectronicsysteminwhichsuperconductivityoccurs,i.e.phonons.
However,ithasbeenshownearlyonthatthesheerstrengthoftheelectron-phononcouplingisinsufficienttoexplaintheelevated
4
superconductingtransitiontemperaturesintheironoxypnictides[25,26]. Thedensityofstatesoftwo-dimensionalparabolicbands
(whichisthecaseinNdFeAsO F ,asdemonstratedinthiswork)isexpectedtobeconstantuptotheirrespectivebandedgesand
0.6 0.4
thuswouldbeverysimilarneartheFermilevelinNdFeAsO F andSmFe Co AsO. Therefore,oneappearstobeleftwith
0.6 0.4 0.92 0.08
the latter option. If the pairing interaction originates in the same electronic subsystem that achieves the superconducting ground
state then the simultaneous self-consistent account of the essential features of superconductivity and the experimentally observed
highlysingularelectronicstructureisindispensable.
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Acknowledgements
ThisprojectwassupportedbytheGermanScienceFoundationunderGrantsNo.BO1912/2-2withinSPP1458.TheworkatPSIissupportedbytheSwissNational
ScienceFoundation(No. 200021-137783)andtheSino-SwissScienceandTechnologyCooperation(ProjectNo. IZLCZ2138954). WorkatETHwaspartially
supportedbytheSNSFandtheNCCRprogramMaNEP.A.C.acknowledgesfinancialsupportbytheAlexandervonHumboldtfoundation.
Authorcontributions
A.C.,D.V.E.,C.E.M.,N.X.,andS.V.B.carriedouttheexperiments.A.C.,D.V.E.,andS.V.B.analyzedthedata.A.C.wrotethemanuscript.N.D.Z.carriedoutthe
samplegrowthandcharacterization.S.V.B.,M.S.,B.Bg.,andB.B.supervisedtheproject.Allauthorsdiscussedtheresultsandreviewedthemanuscript.
Additionalinformation
SupplementaryInformationaccompaniesthispaperonwww.nature.com/scientificreports.
Competingfinancialinterests:Theauthorsdeclarenocompetingfinancialinterests.
CorrespondenceshouldbeaddressedtoA.C.([email protected])andS.V.B.([email protected])RequestsformaterialsshouldbeaddressedtoN.D.Z.
([email protected])andB.Bg.([email protected]).
5
Supplementary information
MATERIALSANDMETHODS
Angle-resolved photoemission measurements were performed at an angle-resolved photoemission spectroscope (“13–ARPES”
end-stationatBESSY)operatingbelow900mK[S1,S2],usingsynchrotronradiationwithintherangeofphotonenergies20-90eV
andvariouspolarizationsonin-situcleavedsurfacesofhighqualitysinglecrystals. Theoverallenergyandangularresolutionwere
∼4 meV and 0.3◦, respectively, for the low-temperature measurements (FS mapping). The FS maps represent the momentum
distributionoftheintensityintegratedwithina15meVwindowattheFermilevel. ToequalizetheintensityoverdifferentBrillouin
zonesthemapswerenormalisedateachkpointtothetotalrecordedEDCintensity.
High-quality single crystals of superconducting NdFeAsO F with masses of a few micrograms were synthesized by the
0.6 0.4
high-pressure high-temperature cubic anvil technique and were characterized by x-ray diffraction, transport and magnetization
measurements[S3]. Thelatterrevealedasuperconductingtransitiontemperatureofabout38K. Thewidthofthesuperconducting
transitionwasfoundtobelessthan1K,indicatingveryhighhomogeneityoftheinvestigatedsamples.
6
DETAILEDLOW-ENERGYELECTRONICSTRUCTUREOFNDFEASO F NEARTHEΓPOINT
0.6 0.4
We have carried out measurements at various energies of the incident X-ray photons to investigate the dependence of the low-
energyelectronicstructureofNdFeAsO F ontheout-of-planemomentumk . AsshowninFig.S1,neitherthesurface-related
0.6 0.4 z
bands,nor,moreimportantly,thebulkholebandedgesshowanyobservabledependenceonthephotonenergyandthusarestrongly
two-dimensional. Furthermore, the middle column of Fig. S1 clearly demonstrates the presence of two separate bulk bands at
bindingenergiesbelow56meV,asarguedinthemaintextandillustratedbydashedlinesbothinthepresentfigureandinFig.1of
themaintext.
Figure S2 shows a magnified version of the data in Fig.1i of the main text and their derivative to demonstrate the quality of
the Lorentz fit of the momentum-distribution curves (black circles in panel c) as well as the parabolic fit to the thereby extracted
quasiparticledispersionofthetopholebandattheΓpoint(whitesolidlineinpanelc).
Fig.S1. leftcolumn,Energy-momentumcutstakeninthesamedirectionasthoseinFig.1h,iusingphotonslinearlypolarizedperpendicular
totheplaneofincidenceandwithdecreasingenergyfrom60to45eVinstepsof5eV(toptobottom). Whitearrowsindicatethesurface-related
bandswhiletheblackdashedcurvesoutlinethethreebulkholebands,asdiscussedinthemaintext.Dashedrectangleinthebottompanelspecifies
themomentumwindowusedtoobtaintheintegratedenergy-distributioncurvesshownintherightpanel.middlecolumn,Secondderivativeofthe
datashowninthecorrespondingpanelsoftheleftcolumntakeninthedirectionofthemomentum. Whitearrowsanddashedlinesarethesame
asabove.rightpanel,Normalizedintegratedenergy-distributioncurvesobtainedbyintegrationinthemomentumwindowshowninthebottom
paneloftheleftcolumn.
7
a L P , h n = 3 0 e V , 5 0 K b L P , h n = 3 0 e V , 5 0 K c L P , h n = 3 0 e V , 5 0 K
2 0 2 0 2 0
(2 .3 (cid:1)0 .5 ) m e V
0 0 0
)
V
e
(m-2 0 -2 0 -2 0
y
rg
e
n
E
-4 0 -4 0 -4 0
-6 0 -6 0 -6 0
-0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4
-1 -1 -1
k ((cid:2) ) k ((cid:2) ) k ((cid:2) )
Fig.S2. a,SamedataasinFig.1iofthemaintext.b,c,Secondderivativeoftheexperimentaldatainpanela.Theparabolicfit(whitesolidline)
totheextractedquasiparticledispersionofthetopholebandattheΓpointoftheBrillouinzone(blackopencircles)isthesameasinFig.1iofthe
maintext.
TEMPERATUREDEPENDENCEOFTHEPHOTOEMISSIONINTENSITYNEARTHEΓPOINT
a b c d e
L P , h n = 3 0 e V , 1 K 1 0 K 2 0 K 3 0 K 3 5 K
2 0
)
V 0
e
(m -2 0
y
rg
e -4 0
n
E -6 0
-0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4
-1 -1 -1 -1 -1
k (A ) k (A ) k (A ) k (A ) k (A )
f g h i
4 0 K 4 5 K 5 0 K 1 3 m e V
2 0 1 .2
3 5 K
7 m e V
eV) 0 . u.)0 .9 44 05 KK
ergy (m --42 00 ity (arb0 .6 11 K0 K 5 0 K
n s 2 0 K
E -6 0 ten0 .3 3 0 K
In
0 .0
-0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -0 .4 0 .0 0 .4 -3 0 -2 0 -1 0 0 1 0
-1 -1 -1
k (A ) k (A ) k (A ) E n e rg y (m e V )
Fig.S3. a–h,Temperaturedependenceofthephotoemissionintensityintheenergy-momentumcutshowninFig.2c. Dashedrectangleinall
panelsspecifiesthemomentumwindowusedtoobtaintheintegratedenergy-distributioncurvesshowninpaneli.i, Energy-distributioncurves
integrated in the momentum window shown in panels a–h. Vertical dashed lines indicate the position of (left to right) the superconducting
coherencepeak,theleadingedgeofthesuperconductingcomponent,andtheFermienergy.
8
References
S1. Borisenko,S.V.“One-cubed”ARPESUserFacilityatBESSYII.SynchrotronRadiationNews25,6–11(2012).
S2. Borisenko,S.V.etal.Angle-resolvedPhotoemissionSpectroscopyAtUltra-lowTemperatures.J.Vis.Exp.68,e50129(2012).
S3. Zhigadlo,N.D.etal.High-pressurefluxgrowth,structural,andsuperconductingpropertiesofLnFeAsO(Ln=Pr,Nd,Sm)singlecrystals.Phys.Rev.B86,
214509(2012).
9