1

ObservationofaTopologicalInsulatorDiracCone

ReshapedbyNon-magneticImpurityResonance

LinMiao,1,2† YishuaiXu,1†WenhanZhang,3†DanielOlder,1

S.AlexanderBreitweiser,1EricaKotta,1,HaoweiHe,1TakehitoSuzuki,4

JonathanD.Denlinger,2RudroR.Biswas,5

JosephCheckelsky,4WeidaWu,3L.AndrewWray,1,6*

1DepartmentofPhysics,NewYorkUniversity,NewYork,NewYork10003,USA

2AdvancedLightSource,LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA3RutgersDepartmentofPhysicsandAstronomy,RutgersUniversity,PiscatawayNewJersey

08854,USA4MassachusettsInstituteofTechnology,DepartmentofPhysics,Cambridge,MA,02139,USA5DepartmentofPhysicsandAstronomy,PurdueUniversity,WestLafayette,IN47907,USA

6NYU-ECNUInstituteofPhysicsatNYUShanghai,3663ZhongshanRoadNorth,Shanghai,200062,China

†Theseauthorscontributedequallytothiswork*Towhomcorrespondenceshouldbeaddressed;E-mail:lawray@nyu.edu.

2

Abstract

ThemasslessDiracelectronsfoundattopologicalinsulatorsurfacesare

thought to be influenced very little byweak, non-magnetic disorder.

However, a resonance effect of strongly perturbing non-magnetic

impurities has been theoretically predicted to change the dispersion

and physical nature of low-energy quasiparticles, resulting in unique

particle-likestatesthat lackmicroscopictranslationalsymmetry.Here

we report the direct observation of impurities reshaping the surface

Dirac cone of themodel 3D topological insulator Bi2Se3. For the first

time, a pronounced kink-like dispersion feature is observed in

disorder-enrichedsamples,andfoundtobecloselyassociatedwiththe

anomalycausedby impurityresonance inthesurfacestatedensityof

states, as observed by dichroic angle resolved photoemission

spectroscopy(ARPES).Theexperimentalobservationofthesefeatures,

which closely resemble theoretical predictions, has significant

implications for the properties of topological Dirac cones in applied

scenarios that commonly featurepoint defect disorder at surfacesor

interfaces.

3

Introduction

Three dimensional topological insulators are bulk semiconductorswith spin-helical

Dirac cone surface states that span the bulk band gap [1,2]. Since their discovery

around2007 [3-6], the topologicalDiracconehasappearedat theheartofawide

range of proposals for novel emergent quasiparticles and next-generation

electronics,suchasfortherealizationofexoticdyon-,axion-,orMajoranafermion-

based physics [1,2,7-10]. Moreover, the spin-helical Dirac surface states are very

robust against dilute non-magnetic impurities due to intrinsic immunities to

backscatteringandAndersonlocalization[11-16],andnumerousstudieshaveshown

the surface Dirac cone remains qualitatively intact in the presence of weak

non-magnetic disorder [17-19]. However, local probe studies have found that the

effectofdisorderon the real space electronic structurecanbe remarkably strong.

Scanning tunnelingmicroscopy (STM) experiments and complementary theoretical

workshave identified thateventhesimplest formof thenon-magnetic impurity,a

crystallographicpointdefect,willtendtogiverisetoresonancestatesverycloseto

the Dirac point in 2D Dirac fermion systems such as topological insulators and

graphene [20-27]. In systems likeBi2Se3, these surfacedefects are associatedwith

distinctivepatternsinSTMtopographyimages,andcanredistributelocaldensityof

states(DOS)bybuildingupanewpeaktensofmillielectronvoltsabovethesurface

Diracpoint.

Therelativesignificanceofimpurityresonancesforrealspaceelectronicstructureas

opposed to momentum space is easy to understand if the impurities are low in

density, because the associated resonance stateswill adhere locally to the sparse

defects.However, if there isa sufficientlyhighdensityofnon-magnetic impurities,

the dispersion of the topological surface Dirac cone is expected to change

significantly.Recentmodelshaveshownthatwhenthedensityofimpuritiesreaches

anexperimentally achievablehigh level, the impurity resonance stateswill behave

collectivelymuch like a flat band that hybridizes coherently with the upper Dirac

4

cone,breakingtheDiracbandintoupperandlowerbranches[28,29].

Measurements and theory suggest that electrons near the resonance adhere

spatiallytothedisorderedimpuritylattice,whichlackstranslationalsymmetry.This

scenario is at odds with the standard definition of a quasiparticle as a

near-eigenstate of momentum. The momentum operator (K) is the generator of

translations,and thespatial translationoperator isdefinedas ! x = exp (−ix!),implyingthat(near-)eigenstatesofoneoperatorshouldbe(near-)eigenstatesofthe

other. When an electron system is so disordered that translational symmetry in

single-particle wavefunctions is absent on the length scale of one de Broglie

wavelength, the result is termed a “bad metal”, and it is assumed that the

quasiparticle picture no longer applies. However, the resistance of topological

surfaceelectronstoAndersonlocalizationandbackscatteringisthoughttoresultina

uniquequasiparticle-likecharacter forelectronsatthe impurityresonance.Though

these electrons profoundly lack translational symmetry, simulations suggest that

their width cross-section in momentum space is narrower than one inverse

wavelength [28, 29], andmeets the nominal definition for a “good” quasiparticle.

This isquitesurprising,andmeansthat inducingdisorderata topological insulator

surfacemay enable the first experimental realization of an itinerant quasiparticle

that propagateswith awell-definedmomentum, but occupies a spatial basis that

lacks even near-neighbor translational symmetry. A quantitative correspondence

withSTMmeasurementsofthespatiallyresolvedDOSdistributionhasbeencitedas

experimental evidence for this novel quasiparticle character [28]. However, the

largerscalemorphologyofsuchhighlydisorderedsampleshasbeenproblematicfor

highresolutionangleresolvedphotoemission(ARPES),andatopologicalDiraccone

reshapedbynon-magneticdisorderhasnotbeenpreviouslyreported.

In this study, we present a high resolution linear-dichroic ARPES (LD-ARPES)

investigationofdefect-enrichedBi2Se3,andreportthefirstexperimentalobservation

of a topological surfaceDirac cone reshapedbynon-magnetic impurity resonance.

5

The LD-ARPES spectra reveal an anomalous kink-like feature in the Dirac cone

dispersion40meVabovetheDiracpoint,whichmatchesthepredictedsignatureof

coherent hybridization with an impurity resonance. Integrating over momentum

shows that the dispersion anomaly is associated with a DOS peak, and that both

featuresareprogressivelyattenuatedwhensuccessiveintervalsoflowtemperature

annealingareappliedtoreducedisorder.Alloftheseexperimentalresultsarehighly

consistentwiththeoreticalpredictionsandwithpreviousSTMfindings.

ModelingimpurityresonancesinatopologicalsurfaceDiraccone

Bismuthselenide(Bi2Se3)iswidelyseenasamodeltopologicalinsulatorsystem,with

asingleDiracconesurfacestateconnectingacrossabulkbandgapofroughly0.3eV.

An idealizedmodel of theARPES spectral functionof the linearly dispersiveBi2Se3

surface state is shown in Fig. 1a. When a surface is simulated with randomly

distributednon-magneticimpuritiesrepresentedbyscalardeltafunctionpotentials,

theDiracbandsarebroadenedandtheirdispersionischanged(Fig.1b).Thebands

developanapparentkinkatE~40meVabovetheDiracpoint,correspondingwitha

blurred region in the simulated spectrum (dashed lines in Fig. 1b).Weighting the

spectra with the participation ratio (PR) of each eigenstate, a method to reveal

spatiallyinhomogeneousstates[30],highlightstheimpurityresonantstatesasthey

aremoreconcentratedaroundtheimpuritysites(Fig.1c).Intheweightedspectrum,

the blurred feature then can be distinguished as being composed of two bands

(white dashed lines) that are broken by the impurity resonance. The two

disconnecteddispersionsareeasiertodistinguishathigherdefectdensities[28],and

thecorrespondingfeaturesbroadenastheyapproachtheresonanceenergyofE~40

meV. Integrating the simulation over the 2Dmomentum space extracts the DOS,

whichshowsahumpattheresonanceenergy(Fig.1d)wherealocalDOSpeakhas

beenobservedforpoint-defectsbySTM[20-22].

Results:

6

Crystallographic point defects occur in typical bulk-grown Bi2Se3 samples with

relatively low densities of ~<0.05% per 5-atom formula unit. In this study,

defect-enriched Bi2Se3 bulk samples are synthesized by abbreviating the final

annealing stage of sample growth (seeMethods), following the procedure in Ref.

[31].X-raydiffraction(XRD)data(Fig.2a)andSTMtopography(Fig.2b)indicatethat

theresultingBi2Se3samplesrealizealargedensityofpoint-defectswhilemaintaining

goodsingle-phasecrystallinity.Theresultingdefectspeciesare labeledontheSTM

topographymap,basedonpreviouslyidentifiedcorrespondences[32].Theprimary

typeofimpurityisinterstitialSeatomsresidingontheoutersurfaceorbetweenthe

first and second Bi2Se3 quintuple-layers, with a combined density ofρ~0.08% per

surfaceunitcell(i.e.per0.15nm2surfacearea).Asmallportionofanti-siteBiSeand

Se vacancy defects are also observed with densities of ρ~0.03% and ρ~0.01%,

respectively. This defect density has a good correspondence with the bulk Hall

carrier density, but the precise numbers seen by STM fluctuate considerably from

region to region (see Methods). The theoretical precondition for impurities

significantly reconstructing the electronic structure is that theremust be a defect

populationwithlocalresonancesatapproximatelythesameenergyERrelativetothe

Dirac point, and a density that exceeds a cutoff proportional to (ER)2 [28]. In the

sparse-defect limit, ER is proportional to the negative inverse of the effective

interactionstrengthbetweendefectsandthesurfacestate(Ueff,definedinMethods)

[27], suggesting that defects can be neglected if the ratio ρ/(Ueff)2 is significantly

smallerthanacriticalthreshold.Moreover,thesurfacestateskindepthinBi2Se3and

ARPES measurement depth are both limited to <~1 nm [33], meaning that the

density of states contribution from deeper-lying resonances will not be strongly

observed.Basedontheseconsiderations,the2Ddensityadoptedforsimulationsis

ρ=0.06%,representingtheassumptionthatroughlyhalfofthe impuritiesobserved

in the top nanometer of the crystal will effectively share a common resonance

energy,andcollectivelyexceedthecriticalthreshold.

7

High-resolution LD-ARPESwas used to perform a targeted study of defect-derived

changes in the surfaceelectronic structure.Measurementswereperformedat the

AdvancedLightSourceMERLINbeamline(BL4.0.3),whichalsoprovidesasmall50

μmbeamprofiletominimizefeaturebroadeningfrommacroscopicinhomogeneity.

Two linearly polarized photoemission experimental geometries were selected as

shownintheFig.2c-d.Theσ-polarizationconditionplacestheelectricfieldparallel

to the sample surface,and theπmeasurementconditionpolarization is inside the

scattering plane, with a primarily out-of-plane (crystalline c-axis) orientation.

Incidentphotonpolarizationwasswitchedbetweenπandσgeometriesviacontrol

of the synchrotron beamline elliptically polarized undulator (EPU), to keep exactly

the same beam spot on the sample. Previous ARPES measurements on the

topological Dirac conemainly used the π-pol experimental geometry, which gives

strongemissionfromtheprimaryPz-orbitalcomponentoftheDiraccone.Theσ-pol

conditionisrarelyusedduetoitslowefficiency.However,theweaknessofemission

fromtheelectronicstructureofapristineDiracconeisalsoapositivefeatureofthis

polarization condition, as the derivative term in the electron-photon interaction

couplesin-planepolarizationdirectlytonanoscalein-planeinhomogeneity,whichis

greatest within defect resonance states and defect-rich regions of the sample

surface. The asymmetric properties of these polarization matrix elements are

reviewed in the Online SupplementaryMaterial, and qualitatively associate the π

and σ geometries with selective sensitivity to defect-poor and defect-rich surface

regions,respectively.

HighresolutionARPESmeasurementsoftheDiracconeatafreshlycleavedsample

surfaceare shown for theπ-polandσ-polgeometries inFig.3a. ThesurfaceDirac

bandscrossattheDiracpointandtheARPESmatrixelementeffectgivesthebands

different intensity profiles under different polarizations. The lower Dirac cone is

moredifficulttotraceduetothecloseproximityofthebulkvalenceband,andboth

the lower Dirac cone and the valence band show much higher intensity in σ-pol

8

measurements.Momentumdistributioncurves(MDCs)oftheDiracbandsareshown

inFig.3e,andshowalargediscrepancybetweenσandπpolarizations.Atenergies

greater thanE~>30meV relative to theDiracpoint, theσ-polARPES imagedDirac

bands always appear to be centered at smaller momenta, indicating a dispersion

differentfromthestatesseenunderπ-pol.TheMDCsofthesimulatedimpurity-rich

surfaceshowaspectrumverysimilartotheDiraccone imagedunderσ-pol. Inthe

simulation (Fig. 3d), the Dirac bands have smallermomenta above the resonance

energy (E~>30meV) within the kinked Dirac cone. This polarization dependence

betweenthedispersionofARPES-imagedDiracbandsisnotpossibleforaperfectly

homogenous sample, but the σ-pol dispersion closely resembles the emergent

‘kink-like’ feature associated with higher impurity densities. To reveal the

quasiparticle dispersionsmore clearly, theMDCs of simulated and dichroic ARPES

imaged Dirac cones ((Fig. 3d-e) are fitted with Voigt functions to track their

dispersions (Fig.3h-i). For simplicity, the ‘kink-like’ feature in the Dirac conewith

resonance states was also treated as being composed of just two peaks for the

purposesof thefittingprocedure(SeeSupplementaryFig.1 for thecurve-by-curve

fittingofMDCs).Theσ-andπ-poldispersionshavearelativelyconstantmomentum

offset at energies high above the Dirac point. At lower energies approaching the

Diracpoint,theσ-polgroupvelocityappearstobecomeverylarge,asiscommonon

the low-energy side of dispersion kinks, and the two dispersions merge rapidly

beneath E~40-50meV. These anomalous features of the σ-pol dispersion can be

closelyreproducedbythesimulationofaDiracconewithdenseimpurities(Fig.3h).

Lowtemperature(LT)annealingprovidesarelativelysafewaytomobilizethe

interstitialSeatomsinthevandeWaalslayerwithoutcreatingnewimpuritiesofSe

vacancyorBiSeantisites.ThetemperatureT~120°C ischosentoremainwellbelow

the thermal activation energy for creating new point defects, and beneath the

T~>150°Clowenergycutoffforeliminatinglargermorphologicaldefects[34,35].To

reduce disorder, the same sample was treated with intervals of LT annealing

9

betweensynchrotronbeamtimes,andre-cleavedforeachnewARPESmeasurement.

In a second experiment following one hour of LT annealing, ARPES data (Fig. 3b)

showsignificantlysharperbands,whichisconsistentwithareduceddefectdensity.

FromthedichroicMDCcomparison(Fig.3f),thediscrepancyofdispersionbetween

the π-pol and σ-pol imaged Dirac cone still exists, but is visibly smaller. The

corresponding traced dispersion (Fig. 3j) shows the same kink-like feature around

E~40meVinσ-polimagedbandstructure,butwithasmalleramplitudeandanonset

slightly closer to the Dirac point. Themomentum offset betweenσ-pol and π-pol

dispersions is reduced to roughly 60% of the value before annealing, and is less

prominentoutsideofanarrowenergywindowfromE~50-70meVabovetheDirac

point.A finalexperiment followed2morehoursofLTannealing (3hours in total),

andfoundalmostnodifferencebetweentheπ-polandσ-polARPESspectra(Fig.3g).

Unlike the first 1hr LT anneal, very little change is noted in the sharpness of the

bands followingthis final2hrLTanneal.Thetracedbands (Fig.3h) showthesame

dispersion under both polarizations, and there is no such anomalous kink-like

feature.

Though changes inbanddispersionareof particular interest forphysics and

applications, a more basic property of impurity resonance known from STM and

theory is the build-up of a DOS peak at the resonance energy [20-29]. This DOS

feature cannot be identified from the ARPES band dispersions, as Luttinger’s

theoremdoesnotapplytodisorderedsystems[36-37].ToevaluateDOS,weinstead

sumtheARPESspectral functionoverthe2Dmomentumspace,makinguseofthe

continuous rotational symmetry near the Dirac point to define DOS E =2! !! ∗ !(!, !).Thissymmetrizationprocedureisappliedseparatelytotheσ-pol

andπ-poldichroicARPESdatatoobtaindifferentlyweightedapproximationsforthe

surface state DOS (Fig. 4a). In all cases, the π-pol imaged DOS curve has a linear

trend in the upper Dirac cone, matching expectations for a massless 2D Dirac

fermion. However, the σ-pol data reveal an extra hump around E~40meV in the

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non-annealedbasesampleandafter1hourofannealing.Toexcludethepossibility

that this feature is from an extraneous matrix element effect, a corresponding

simulationforapristineDiracconeisshowninFig.4bbasedontheenergy-resolved

ARPESmatrixelementsidentifiedinRef.[38].ThesymmetrizedDOScurvesforboth

measurement conditions show a good linear character, and neither has an

anomalous peak feature, suggesting that the extra hump in the symmetrizedDOS

curves represents a real anomalywithin theDirac surface state.A cleaner viewof

thedichroic feature isobtainedbysubtracting theπ-polcurve fromtheσ-polDOS

(Fig.4c),whichreveals theanomaloushumpasapeakatE~40meV in thedichroic

DOScurveofthenon-annealedsample.Thispeakcontinuously loses intensitywith

LT annealing, and is no longer identifiable after 3 hours of annealing. The

PR-weighted impurity resonance peak simulated in Fig. 1d is reproduced at the

bottomofFig.4c,andisenergeticallyconsistentwiththedichroicDOSfeature.This

correspondencecanonlybequalitativelymeaningfulas it isfilteredthroughARPES

matrixelements,however it indicates that thekinkedbanddispersionobserved in

σ-polARPESspectraisappropriatelyalignedwiththeimpurityresonanceinexactly

thewaythatwastheoreticallypredicted.

Discussion

TheseresultsshowthatBi2Se3sampleswithahighpointdefectdensitycanexhibit

significantchangesinsurfacestatedispersionandDOS,bothofwhicharereversible

viaanagingprocess that includes lowtemperatureannealing.Numericalmodeling

closelyreproducestheexperimentalfeatures,andsuggeststhatthedispersionkink

andhigherenergymomentumshift inσ-polARPESbandstructureoriginatefroma

smalldiscontinuityintheDiracbandsduetohybridizationwithimpurityresonance

states.Whilethismayseemlikeadisruptionofthetopologicalbandconnectivity,it

does not involve time reversal symmetry breaking, and should not necessarily be

viewedas a band gap. Band topology constraints are absent in the caseof strong

disorder,andtheDOSdistributionispeaked,ratherthangapped,attheresonance

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energy.

With respect toearlier studies, it isnoteworthy that theπ-poldatadonot showa

similar kink-like dispersion feature, suggesting that the measurement conditions

used for most ARPES experiments will give little weight to impurity-rich surface

regions (see Supplementary Note 1). Moreover, the in-plane σ-pol orientation

chosenforthisstudywasselectedtoachieveparticularlyfavorablematrixelements

forresolvingimpurityphysics(seeSupplementaryNote2).

Unliketheconventionalmanifestationofanon-dispersiveimpurityband,theimpact

of disorder is seen to play out over a wide energy scale of several hundred

millielectronvolts. Together with the theoretical protection against Anderson

localization[28],thissuggeststhattheDiracconeelectronshaveauniquecoherent

relationshipwiththedisordered impurity lattice,whichpreservesreasonablysharp

quasiparticle-like character in spite of allowing large changes to the overall

electronic structure. TheDOS peak found at the dispersion kink is consistentwith

real-space STM investigations of impurity resonance, and has been predicted to

greatlyenhance thesusceptibility tomagneticorder inmean-fieldmodeling foran

orderedimpurity lattice[27].Furthertheoreticalworkwillbeneededtomorefully

understand the many-body susceptibilities of a dispersive quasiparticle-like mode

thatisprofoundlyinhomogeneousona<100nmscale,andforwhichthenumberof

statesina`band'cannotbetreatedasconstantthroughoutmomentumspace(i.e.

forwhichLuttinger’stheoremdoesnothold).Theseresultsandpredictionssuggest

that the non-magnetic impurities found ubiquitously at the surfaces and buried

interfacesofreal-worldsamplesanddevicesmayprovideafar-reachingmechanism

forshapingthephysicalpropertiesofaTIsurface.

12

Methods:

1.HighresolutionlineardichroicARPESmeasurements

AllARPESmeasurementswereperformedattheBL4.0.3MERLINARPESendstation

at the Advanced Light Source, with a Scienta R8000 analyzer and base pressure

betterthan5×10-11Torr.ThesamplewasmaintainedatT~20K,thetimebetweens-

and p-polarization measurements is roughly 4 hours, and surface band structure

featureswereobservedtobestablewithin~10meVonthetimescaleoftheeach

LD-ARPES experiment (~<24 hours). The chemical potential for all samples was

E-ED~300meV above the Dirac point, whichmatches the expectation of E-ED=325

meVabove theDiracpoint for theHalleffect carrierdensityof2.6x1019 cm-3.This

surface potential is calculated using the band bending model in Ref. [39], which

treats the surface state and bulk charge carriers on equal footing in themodified

Thomas-FermiApproximation(MTFA).

Surface doping of Bi2Se3 by adatoms and photon exposure is a natural concern in

quantitative ARPES experiments, and multiple doping mechanisms can come into

play [33,39-48]. However, the observed stability of the measured surface in this

particularcaseisconsistentwithstrongbulkscreeningassociatedwiththehighbulk

carrier density, andwith the observation that aging effects from residual gas and

photonexposuretendtosaturateatlowersurfacepotentialsofE-ED~<290meV[40].

The overall energy resolution was between 15-20meV, and photon flux was well

below the regime on which photo-gating effects have been observed [41].

Measurements on the base sample were performed at h�=30 eV, and later

post-annealing measurements were performed at h�=34 eV to obtain a higher

photonflux,duetotherapidlossofphotonthroughputonthehighenergygrating

beneath50eV.

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2.GrowthandSTMcharacterizationofdefect-enrichedBi2Se3samples:

Highqualitydefect-enrichedsamplesweregrownfollowingtheproceduredescribed

inRef. [31].The resultingcrystals shownosignof impurityphases.TheHalleffect

carrier densitywas 2.6×1019 cm−3, corresponding to an expected defect density of

∼0.19%,whichcorrespondsreasonablywellwiththeroughly~0.12%defectcountinthetopnanometerofthecrystalseenbySTMtopographymapsdescribedinthe

main text. ARPES and STM measurements were performed close to the sample

center,wherethedefectdensityisexpectedtobelowerthanontheperiphery.The

Hallcarrierdensityandsurfacechemicalpotentialarenotgreatlychangedfollowing

the aging/annealing process A slight reduction in the surface chemical potential

suggeststhatthebulkcarrierdensity isreducedby10-20%in latermeasurements,

relativetodensitybeneaththebeamspotintheinitialmeasurement. Additionally,

itisexpectedthatthepost-annealeddefectdistributionmaybemorehomogeneous

acrossmicrocrystallinedomains.

STM data were obtained at low temperature (T<50K) with tips calibrated on an

Au(111)surface.ThetopographicmapinFig.2bwasmeasuredusingabiasof-0.7V

anda tunnelingcurrentof100pA.Rapid topographicalmapsofmultiple~100nm

regionswere sampled, andwere consistentwith previous analyses that suggest a

stochastically random placement of impurities within local regions (see the

supplemental material of Ref. [28]). However, the standard deviation in defect

densityfordifferentsurfaceregionsseparatedbyseveralmicronswasmuchhigher

than the variation expected from the Poisson distribution. This variation reveals

largefractionaldifferences(uptoafactorof~2)inthelocalimpuritydensitiesthat

areaveragedoverintheARPESspectralfunction.

14

3.ModelingtheTIsurface

Thesurfacestateismodeledasaspin-helical2DDiracconeonahexagonallattice,

perturbed by scalar delta-function-like impurities, as described in Ref. [28]. The

impurity potential is effectively reduced by the fact that the delta-function-like

potential isnotwell resolved in themodel,which imposesahighenergycutoffon

the kinetic basis for state diagonalization. An effective value for the potential is

calculated as the trace of the potential Hamiltonian for a single impurity

(Ueff=Tr(HU)=-1eV),whereastheuncorrectedpotentialwouldhaveavalueofU=-35

eV,asdefinedinRef.[28].Theimpuritiesarerandomlydistributedwithadensityof

ρ=0.06%.SpectralfeatureswereconvolutedbyaLorentzianfunctionwith30meV

peakwidthathalfmaximum,exceptwhereotherwisenoted.

IntensitiesinFig.1careweightedbytheparticipationratioPofeachsingle-particle

eigenstate. The participation ratio gives higher intensity for states that are less

evenlydistributed throughoutspace,and isused tohighlightemission fromdefect

resonancestates.Itisdefinedas:

!! = !!,!!!

wherethesumisoverallsites inthesystem,and !!,! isthelocalDOSonsite iof|α⟩,whichisaneigenstateofthefullHamiltonian.

15

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16

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Acknowledgements:

WearegratefulfordiscussionswithP.Chaikin,Y.-D.Chuang,D.Huse,andP.Moon.

ThisresearchusedresourcesoftheAdvancedLightSource,whichisaDOEOfficeof

ScienceUserFacilityundercontractno.DE-AC02-05CH11231.R.R.B.wassupported

byPurdueUniversitystartupfunds.SynthesisandanalysisinstrumentationatNYUis

supported by NSF under MRI-1531664, and from the Gordon and Betty Moore

Foundation’sEPiQSInitiativethroughGrantGBMF4838.WorkatNYUwassupported

by theMRSEC Program of the National Science Foundation under Award Number

DMR-1420073. The STM work at Rutgers is supported by NSF under grant

DMR-1506618.

18

AuthorsContribution:

L.M.andY.X.carriedouttheARPESexperimentswithsupportfromD.O.,S.A.B.,E.K.,

H.H., and J.D.; STMmeasurements were performed byW.Z., with guidance from

W.W.; high quality defect-enriched samples were developed by T.S. and J.C.;

simulationswereperformedbyY.X.withguidancefromR.R.B.;L.M.,Y.X.,W.Z.,and

L.A.Wparticipatedintheanalysis,figureplanninganddraftpreparation;L.A.W.was

responsible for the conception and the overall direction, planning and integration

amongdifferentresearchunits.

19

Figure1

Figure 1. Impurity resonance in momentum space. a, A simulated Bi2Se3 surface

Dirac cone without impurities. Red lines trace the linear band dispersion. b, A

simulatedDiracconereshapedbyscalarimpurities(Ueff=1eV,densityρ=0.06%per

2Dsurfaceunitcell).Akink-likedispersivefeatureoccursattheimpurityresonance

energy,andistracedwithdashedlines.c,ThesimulatedDiracconeisweightedby

participation ratio to highlight impurity-resonant states. The kink-like feature is

resolvedmoreclearlyascontainingthesplitdispersionspredictedinRef.[28](white

dashed lines).d,ThecorrespondingsimulatedDOScurvesof (blue)apristineDirac

cone, (red) a Dirac cone with impurities, and (yellow) a participation ratio (PR)

weightedsimulationwithimpurities.

20

Figure2

Figure 2.Defect-enriched Bi2Se3. a, XRD from the defect-enriched Bi2Se3 sample,

showingno impurity phase features.b, STM topographyof an 80×80nm2 cleaved

Bi2Se3surfacewithlatticedefects/impurities.Thedefectsarepredominantlyexcess

Se (red circles) on the top surface and (white circles) between first and second

quintuplelayers.(yellowandblackcircles)AntisiteBiSedefectsarealsocommon.An

expanded inset shows distinctive defect profiles used for characterization. c, The

π-polarization ARPES measurement geometry, with the electric field of incident

photonsmostlynormaltothesamplesurface(projecting82%ontothez-axis).d,The

σ- polarization ARPESmeasurement geometry gives an electric field that projects

100%ontothein-planey-axis(theARPESanalyzerslitaxis).

21

Figure3

Figure3.Measuringthedefect-deriveddispersionanomaly.Symmetrizedπ-poland

σ-pol ARPES images of Dirac cone band structure are shown for the same

defect-enrichedsample(a)beforeLTannealingandafter(b)1hourand(c)3hours

ofLTannealing.c,TheMDCsofasimulatedDiraccone(red)withand(blue)without

impuritiesareextractedfromFig.1a-b,andshownwitha10meVstep,startingfrom

theDiracpoint(setto0energy).Tofacilitatecomparison,allMDCsarenormalized

tothesameamplitude.e-f,ThecorrespondingMDCsofpanels(a-c)areshownwith

(red)σ-poland (blue)π-pol.h-k,Dispersionsareobtained fromfitting the redand

bluecodedMDCsinpanelsd-gwithtwoVoigtfunctions.Ahorizontalshadedregion

indicatestheexpecteddefectresonanceenergy[20,28].

22

Figure4

Figure 4.The impurity resonanceDOS peak.a,ARPESDOScurvesestimatedfrom

(red)σ-poland(blue)π-polareshownfordifferentlevelsofLTpost-annealing(PA).

Thecurvesareoffset in incrementsof2, andnormalizedatE=120meVabove the

Diracpoint(dashedline),anenergythatishigherthan(shadedregion)theexpected

impurityresonanceandlowenoughtoavoidthebulkconductionband.b,Simulated

ARPES DOS curves for a pristine Dirac cone, based on empirical photoemission

matrixelements fromaRef. [38].c,DichroicDOScurves the subtracting theπ-pol

ARPES DOS from σ-pol ARPES DOS. The dichroic DOS curves are compared with

(bottom) the PR-weighted impurity resonance simulation from Fig. 1d. The

anomalous peak-like feature that vanishes with annealing is indicated with filled

triangles.

SupplementaryMaterial:

ObservationofaTopologicalInsulatorDiracCone

ReshapedbyNon-magneticImpurityResonance

LinMiao,1,2† YishuaiXu,1†WenhanZhang,3†DanielOlder,1

S.AlexanderBreitweiser,1EricaKotta1,HaoweiHe,1TakehitoSuzuki,4

JonathanD.Denlinger,2RudroR.Biswas,5

JosephCheckelsky,4WeidaWu,3L.AndrewWray,1,6*

1DepartmentofPhysics,NewYorkUniversity,NewYork,NewYork10003,USA

2AdvancedLightSource,LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA3RutgersDepartmentofPhysicsandAstronomy,RutgersUniversity,PiscatawayNewJersey

08854,USA4MassachusettsInstituteofTechnology,DepartmentofPhysics,Cambridge,MA,02139,USA5DepartmentofPhysicsandAstronomy,PurdueUniversity,WestLafayette,IN47907,USA

6NYU-ECNUInstituteofPhysicsatNYUShanghai,3663ZhongshanRoadNorth,Shanghai,200062,China

†Theseauthorscontributedequallytothiswork*Towhomcorrespondenceshouldbeaddressed;E-mail:lawray@nyu.edu.

Supplementary Note 1: Photon polarization as a filter for impurity-resosnt or

non-resonantstates

Inthisinvestigation,σ-polarization(in-plane)isusedtoobtainahighersensitivityto

electrons that have a spatial distribution strongly influenced by defects, and π

polarization (mostly surface-normal) is used tomeasure electronic states that are

less defect-resonant and better resemble an ideal topological Dirac cone. This

associationisjustifiedfromtheoreticalandempiricalconsiderationsoutlinedbelow.

Adoptingthedipoleapproximationandsingle-stepphotoemissionpicture(standard

for the photon energies used in this study), the photoemission intensity is

determinedbythefollowingmatrixelement[1]:

! ! ~ ! ∇ ∙ ! ! ! (S1) where A is the vector potential of the incident beam, and |ψ⟩ is an occupiedsingle-electronstateinsidethematerial.Thefinalstate|f⟩ isassumedtohavethe

spatial formofa freeparticlestate,andtooverlapwiththetopmost∼1nmof the

material.Moreover,thisstateisassumedtobeorthogonalto|ψ⟩,sothatelements

ofthephotonperturbationthatcommutewiththeunperturbedHamiltonianofthe

systemcanbeneglected.

With σ-polarization, photoemission is sensitive to in-plane structure: For an

experimentperformedwithσ-polarizationona fullyhomogeneousmaterialwitha

2-dimensional surface, thephotonperturbationcommuteswith thekineticpartof

the Schrödinger equation, and thus has no cross section for photoemission.

Introducingin-planeinhomogeneityintheformofrandompointdefectswillcreatea

photoemission signal from spatially structured electronic states that have a

significantprobabilityofbeing found in the inhomogeneous region (suchasdefect

resonancestates).

The two implications of this idealized picture are that the signal from resonance

statesmaybeenhancedwithσ-polarization,andthatthesignalfromnon-resonance

states should be weak, giving improved signal to noise for observing defect

resonance. The second point is not generically true when one considers real

materials,butturnsouttobevalidforourmeasurements,asnotedinthemaintext.

In fact,dataacquisition times forσpolarizationwereapproximately5-10 timesas

long toachievecomparablestatistics toπ-polarization.Thesymmetries introduced

viadefect-mediatedhybridizationwithbulkbandstructureareexpectedtofurther

increasesensitivitytodefectsunderσ-polarization,astheclosestbandinenergyis

thevalenceband,whichhasverystrongintensityunderσ-polarization(visibleinthe

intensitytailfromlargebindingenergyinFig.4aofthemaintext).

Onan inhomogeneoussurface, filteringfordefect-resonantstateswill increasethe

fractional spectral weight from high-defect-density regions. In this context, it is

noteworthythatthedensityofimpuritiesseenbySTMvariedbyuptoafactorof2

indifferentregionsstudiedwithintheareaofanARPESbeamspot(seeMethods2),

and this inhomogeneitymay causemuchof the surface to be beneath the critical

impuritydensitythresholdforachievingthereconstructionofspectralfeatures.The

weightfromsurfaceregionswithimpuritydensitiesabovethethresholdisexpected

tobehigherunderσ-polarization.

Withπ-polarization,photoemissionneartheBrillouinzonecenterissuppressedby

in-planepointdefects:Forthecaseofπ-polarization,itisimportanttonotethatthe

ARPES matrix element includes a projection onto the basis of homogeneous free

particle states |f⟩. Non-defect-resonant states of the topological Dirac cone arecomposed of long-wavelength wavefunction components that are almost entirely

found in the momentum space region mapped by ARPES in this investigation.

However, resonance states have a significant admixture of short-wavelength

wavefunction components towhich our ARPES scans of the k<~0.1 Å-1 Dirac cone

momentumregionareblind(thiscanbeseenfromthesharplycontouredreal-space

structures seen around defects by STM). This means that impurity-resonant

electronscanbeexpectedtocountlesstowardsπ-polARPESmapsoftheDiraccone,

evenifadefect-resonantstatehasak-spaceintensitymaximumthatoverlapswith

theDiraccone.

Supplementary Note 2: Simulating the effect of ARPES polarization matrix

elementsontheDOSmeasurementforadefect-freeDiraccone:

The Fig. 4(b) in themain text presents simulated ARPES DOS curves of the Bi2Se3

Dirac cones, based onmatrix elements extracted from previous systematic ARPES

measurements[2].Forthissimulation,thegaplessdispersionneartheDiracpointis

set by a Dirac velocity of vD=2.6 eV-Å, and the ARPES intensity (Iavg(E)) under

σ-polarizationisobtaineddirectlyfromtheRef.[2]anisotropycurvesforenergiesof

-25,0,50,100,and200meV,andinterpolatedforintermediateenergyvalues.The

π-polarization intensity trend is takentobe flatasa functionofenergy,consistent

with the cleaner linear trend seen in Dirac cone DOS estimates based on this

measurementgeometry. GaussandLorentzbroadeningaresetto0.0162Å-1peak

widthathalfmaximum inmomentumspace,andon theenergyaxisare set to20

and40meV, respectively.Off-axis intensity inmomentumspacewasdescribedby

the cos-like trends identified in Ref. [2], and contributes to the simulated spectral

intensityduetotheisotropicmomentumbroadeningparameters.

With respect to the factors discussed in SupplementaryNote 1, theσ-polarization

measurement geometry corresponds to an azimuthal angle of 90o in Ref. [2], and

minimizes intensity fromtheupperDiracconeasdesired foroptimal sensitivity to

impurityresonance.Thispolarizationconditionalsoprovidesastrongphotoemission

matrix element for the energetically close valence band, which is expected to

contributetothepartialDOSofimpurityresonancestates.

SupplementaryNote3:ThesymmetrizationofLD-ARPESimagesandrelatedMDCs.

Bi2Se3(111)hasthree-foldsymmetry (C3)aboutthesurface-normalaxis.TheARPES

measurementcutsinourresearchwerealongthe2DM-Γ-Mdirection,whichmeans

there is strong left-right matrix element asymmetry on the momentum axis of

photoemission spectra (Supplementary Fig. 2). The interplay of these matrix

elementswiththecontinuumnatureoftheimpurityresonancestateswillleadtoa

slightleft-rightasymmetryintheapparentdispersionofthesurfacestateoneither

sideoftheDiracpoint,ascanbeseeninSupplementaryFig.2.

While this asymmetry provides support for the attribution of impurity physics, it

carriesthedownsideofaddingdegreesoffreedomwhenfittingbandstructure,and

givingaveryasymmetrical intensityprofile that increases thedynamic color range

needed for image plots. To achieve a clearer dichroic comparison, a left-right

symmetrizationhasbeenappliedtothe2DimagesandMDCsshowninthemaintext.

This does not impact the s- vs. p- polarization comparison, as the measurement

conditions (includingbeam spot) are identical. Theanalysis of Fig. 3-4 in themain

text is robust even when a deliberate centering error is introduced in the

symmetrizationprocess.

SupplementaryNote4:Sampleannealingandcleaving:

Foreachmeasurement,thesamplewastop-postedintheatmosphere,andcleaved

andmeasured insituat lowtemperature(~20K)underultra-highvacuum(<5*10-11

torr). Annealing was performed in atmosphere between synchrotron-based

experiments,whichwereseparatedby4monthintervals.

Following each annealing and cleaving process, the Fermi level was found to be

approximately 300meV above the Dirac point with a variation within 20meV.

EstimatedFermienergiesvaryfromaninitialvalueof305meVtoaminimumof285

meV (see Supplementary Fig. 2), suggesting a possible loss of up to 20% of bulk

carriers in post-annealedmeasurements. The fitting error in determination of the

Diracpointenergyisestimatedbylessthan10meV,fromonecleavagetothenext.

Thiserrordoesnotfactorintothelineardichroicdifferenceswithinagivencleavage.

References

[1]Damascelli,A.,Hussain,A.&Shen,Z.-X.,Angle-resolvedphotoemissionstudiesofthecupratesuperconductors,Rev.Mod.Phys.75,473(2003).

[2] Cao, Y. et al. Mapping the orbital wavefunction of the surface states inthree-dimensionaltopologicalinsulators,Nat.Phys.9,499-504(2013).

SupplementaryFigure1:

Figure S1. Curve-by-curve fitting of Fig. 3 dispersions. a,MDCs of the simulated

DiracconespectrafromFig.3ofthemaintext(blue)withoutand(red)withdefects

are fittedwith two Voigt profiles (black dashed) to track the effective Dirac band

dispersions. The same fitting procedure is applied to theMDCs of dichroic ARPES

spectrab,without LT annealing,c,with1hr LTpost-annealing andd,with3hr LT

post-annealing. In (b-d), the blue curves are from π-pol measurements and red

curvesarefromσ-polmeasurements.OnlytheMDCswithenergyE>=20meVabove

Diracpointprovidesufficientlyresolvedfeaturesforaccuratefitting.

SupplementaryFigure2:

Figure.S2.TherawdataofLD-ARPESmeasurements.RawLD-ARPESdatashowing

thefullupperDiraccone(a)beforeannealing,(b)after1hourofannealing,and(c)

after3hoursofannealing.