Published in Physical Review B 57, issue 24, 15251-15260, 1998which should be used for any reference to this work

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Theoretical analysisof the electronic structure of the stable and metastablec„232… phasesof Na on Al „001…: Comparison with angle-resolvedultraviolet photoemissionspectra

C. StampflXeroxPalo Alto ResearchCenter,3333CoyoteHill Road,Palo Alto, California 94304

K. KambePrinzregentenstrasse56/57,D-10715Berlin, Germany

R. FaselandP. AebiInstitut de Physique,Universitede Fribourg, Prolles, 1700Fribourg, Switzerland

M. SchefflerFritz-Haber-Institutder Max-Planck-Gesellschaft,Faradayweg4-6, D-14195Berlin-Dahlem,Germany

UsingKohn-Shamwavefunctionsandtheir energylevelsobtainedby density-functional-theorytotal-energycalculations,the electronicstructureof the two c(232) phasesof Na on Al ~001! areanalyzed,namely,themetastablehollow-sitestructureformedwhenadsorptiontakesplaceat low temperature,and the stablesub-stitutionalstructureappearingwhen the substrateis heatedthereafterabove180 K or whenadsorptiontakesplaceat room temperaturefrom the beginning.The experimentallyobtainedtwo-dimensionalbandstructuresof the surfacestatesor resonancesare well reproducedby the calculations.With the help of charge-densitymaps,it is found that, in both phases,two pronouncedbandsappearasthe resultof a characteristiccouplingbetweenthevalence-statebandof a freec(232)-Na monolayerandthesurface-state/resonancebandof theAlsurfaces;that is, the clean~001! surfacefor the metastablephaseandthe unstable,reconstructed‘‘vacancy’’structurefor the stablephase.The higher-lying band,being Na derived,remainsmetallic for the metastablephase,whereasit lies completelyabovethe Fermi level for the stablephase,leadingto the formation of asurface-state/resonanceband structure resembling the bulk band structure of an ionic crystal.

I. INTRODUCTION

The adsorptionof alkali-metal atomson metal surfaceshasattractedmuchattentionin recentyearspartly dueto thediscovery of a variety of adsorbatephases,in particular,structuresthat involve a reconstructionof the metal surfaceinducedby the alkali-metalatoms~see,for example,Refs.1and 2, and referencestherein!. A commonfeatureof thesesystemsis that often thereis a metastablephaseat low tem-peratureinvolving no reconstructionof the metal surface,while, at higher temperatures,a stablereconstructedphaseoccurs.

In the presentpaperwe presenta combinedtheoreticalandexperimentalinvestigationof onesuchsystem,namely,that of c(232) phasesof Na on Al ~001!. Early dynamical-theory analysesof low-energyelectron-diffraction~LEED!intensities3,4 concludedthatNa occupiedthefourfold hollowsite. It was first demonstratedby high-resolutioncore-levelspectroscopy5 and surfaceextendedx-ray-absorptionfine-structure~Ref.6! studiesthatthehollow siteis takenonly forpreparationsat low temperature~LT!, anda different, stablestructureis formedby adsorptionat room temperature~RT!or by heatingof theLT phaseabovec. 160K. It wasshownlater by a density-functionaltheory ~DFT! study7 and by aLEED analysis8 that in the RT phasethe Na atomsoccupysubstitutionalsites,whereevery secondAl atom in the toplayer is removedand a Na atom adsorbedin its place.The

resultof an x-ray photoelectrondiffraction ~XPD! study9 ofthe RT phaseconcludingthat the surfacecontainstwo do-mains,could not be confirmed.8

In what follows, we performa theoreticalanalysisof theelectronicstructureof the two c(232) structures,andcom-pare the results with those of angle-resolvedultravioletspectroscopy.10 The measurementshavebeenperformedinwhatwe call ‘‘polar scan’’ modes,which deliverdisplaysofphotoemissionintensitiesasa function of energyandwave-vector componentparallel to the surface,lying in selected

symmetrydirections(G-M andG-X) in thetwo-dimensional~2D! Brillouin zone~seeFig. 1!. The displaysyield directly2D bandstructuresof surfacestates/resonances~i.e., surfacestatesor resonances,dependingon the positionof the statesin or out of the gapof the 2D projectedbulk bands!, whichmay be comparedwith calculatedresults.

Thebasisof our theoreticalanalysisareKohn-Shamwavefunctions, and their energy levels obtainedby DFT total-energy calculations.7 2D band structuresare derived andcomparedwith the experimentalresults.The obtained,satis-factory agreementbetweentheory and experimentmay beregardedassupportof theproposedatomicstructuremodelsmentionedabove,anda usefulbasisfor furtherstudiesof thepropertiesof thesesurfaces.

Also, single-statecharge-densitydistributionsof occupiedandunoccupiedstatesarederivedfrom theDFT calculation,

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and usedfor analyzingthe characterof the bands.We findthat adsorptionleads,in both LT andRT cases,to two mainbandsof surfacestate/resonancesasthe resultof a couplingbetweenthe valence-statebandof a free c(232)-Na mono-layer andthe surface-state/resonancebandof the Al surface.Acrossthe Fermi level the Al-derived bandis shifteddown,and the Na-derivedbandis shiftedup. As a consequence,achargetransfertakesplacefrom the adsorbatedirectly intothe pre-existentsurfacestate/resonanceof the substrate.

For theLT ~hollow! structure,it is foundthatthecouplingis relativelyweakandtheAl-derivedstatealmostretainstheperfect 131 periodicity of the clean surface.For the RT~substitutional! structure,theAl-derivedstateexhibitsa clearc(232) periodicityof thereconstructedAl surface.TheNa-derivedbandof the RT structureis completelyempty, andleads, except for the still existent backgroundbulk con-tinuum,to a surfaceelectronicstructurehavinga characterofan ionic monolayerlying on thesurface.We discusspossibleconsequencesof this finding.

The paperis organizedasfollows: In Sec.II, the experi-mentalmethodis outlined,and is followed in Sec.III by adescriptionof the calculationmethods.SectionIV containstheresultsfor thesurface-state/resonancebandstructuresandthe analysisof the characterof the bandsin termsof single-statecharge-densitydistributions.Also, the charge-transferprocessesareanalyzedby usingdensitydifferences.SectionV containsthe discussion,andSec.VI the conclusion.

II. EXPERIMENT

The photoemissionexperiments10 were performed in aVG ESCALAB Mark II spectrometermodifiedfor motorizedsequential angle-scanningdata acquisition,11 and with aworking pressurein the lower 10211-mbarregion.Ultravio-let photoelectronspectroscopymeasurementsweredoneus-ing unmonochromatizedHe I ~21.2eV! radiationfrom a dis-charge lamp. The 150-mm-radiushemisphericalanalyzerwas run with an energy resolution of 50 meV.Contamination-freesurfaceswerepreparedby a combinationof Ar1 sputteringand annealingat 500°C. Na was evapo-rated from a carefully outgassedSAES getter source.Par-ticular carewas takento ensureultracleanNa deposits:Allpartsof theevaporationsource,exceptthetiny exit slit, weresurroundedwith liquid-nitrogen-cooledwalls. In this way,the pressureduring evaporationcould be kept as low as

FIG. 1. SurfaceBrillouin zone of 131 ~full lines! and c(2

32) ~brokenlines! structures.The symmetrypoints G, M , and Xrefer to the (131) structure.

2.5310211 mbar.Na coveragesweredeterminedaccurately(60.03ML ! from core-levelphotoelectronintensities.12 Thesampletemperaturewas measuredwith a thermocoupleinmechanicalcontactwith the sampleholder.The temperaturegradientbetweenthe sampleandthe sampleholderwasde-terminedin a separatecalibrationexperimentwith an addi-tional thermocouplespot welded onto a dummy sample.Sampletemperaturesgiven hereare correctedfor this tem-peraturedifferenceand are estimatedto be correct within610 K.

In orderto obtaintwo-dimensionalbandstructuresof sur-face states/resonances,polar scansalong the G-M and G-Xdirectionsof the Al ~001! surfaceBrillouin zone were per-formed,recordingat eachangularsetting(DQ52°) the en-tire photoelectronspectrumbetween20.4- and4.3-eVbind-ing energy.The experimentaldatasetsI (Ei ,Q) acquiredinthis way weremappedontoa regular(Ei ,ki) grid, andvisu-alized as gray-scaleplots with low intensitiesin white andhigh intensitiesin black.

III. CALCULATION METHOD

Theab initio DFT total-energycalculations,andcompari-son with LEED resultsare describedin Refs.7 and 8. Thecalculationswereperformedusingthe local-densityapproxi-mation ~LDA ! for the exchange-correlationfunctional.Fur-therdetailsaboutthemethodcanbe found in Refs.7,13and14. The following two kinds of diagramshavebeenusedinthe presentanalysis.

~1! 2D band structures. For deriving 2D bandstructureswe use the following procedure.The projecteddensity ofstates~DOS! onto a chosenatomicorbital cAO(r ) is definedas

NAO~«!5(ki

NAO~ki ,«!, ~1!

wherethe ‘‘ ki-resolved’’ projectedDOS is given by

NAO~ki ,«!5(«8

U Er ,r c

d3r cAO* ~r !cki ,«8~r !U2

3g

p

1

~«82«!21g2. ~2!

For cAO(r ), we haveusedthe eigenfunctionsof the isolatedpseudoatomsfrom which the pseudopotentialswerederivedfor the total-energycalculation.7 The integralwas truncatedat a cutoff radiusr c . ~Herewe usedr c53.7 Å.! In the stan-dardsupercellmethodusinga slabgeometry,a Kohn-Shamstatecki ,«(r ) can be specified,exceptfor the presenceof

degeneracy,by indiceski and« ~both discrete!, the parallelwave vector, and the energy, respectively. The lifetimebroadeningparameterg is introducedfor conveniencein nu-merical work and for improving visibility of peaksin theresultingplots. ~Herewe takeg50.5 eV.!

A simple sum of NAO(ki ,«)’s are formed over atomicorbitalsof a specifiedatom.For example,for Na, we have

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NNa~ki ,«!5NNa3s~ki ,«!1NNa3px~ki ,«!1NNa3py

~ki ,«!

1NNa3pz~ki ,«!. ~3!

ThecorrespondingquantitiesNAl(ki ,«) areevaluatedfor theAl atoms in the uppermostlayer. The maximum peak ofthesequantitieswasalwaysfoundat thebottomof a surface-

state/resonancebandlying at G. Thosepeakshavinga frac-tional ratio to the maximumhigher than a properly chosenfixed value ~‘‘Min. Fraction’’ in Table I!, are selectedandtheir positionsin (ki ,«) spacedisplayed,using squaresfor

Na andcirclesfor Al ~seeTableI!. TheplotsalongX-G and

G-M ~seeFig. 1! arecombined,andarepresentedin Figs.2and3. We seethattheyproducesatisfactorily2D bandstruc-turesto be comparedto the experimentallyobtainedones.

Thebulk-bandcontinuumis separatedinto discretebandsdueto the useof finite ~nine layer! Al slabs.They appearinFigs. 2 and 3 as weak features.The discretenessof bulkbandsmay havecauseda small energyshift of the surfaceresonancebandslying inside the bulk continuum,becausetheseare replacedby one of the discretebulk bandslyingnearestto them.

We notethat in Figs.2 and3 thetheoreticalbandsfor theLT andRT structuresrepeatthemselvesinsidethe131 Bril-louin zone,exhibitingc(232) periodicity.That is, therange

G-M @M referingto (131)# is halved,andthe bandsin thesecondhalf becomea mirror imageof the first half. We callthis ‘‘backfolding’’ here~cf. Ref. 15!. It is a consequenceofour use of the density of statesprojectedto one specifiedatomin eachc(232) surfaceunit cell. We notethat this isobviouslya theoreticalconstruct,andnot quite adequateforfully representingthe characterof the wavefunctionsof thebands,particularly in the LT structure.In fact, there is noinformation includedabout the relation betweenthe valuesof wavefunctionsaroundthetwo Al atomsin a unit cell ~see

TABLE I. Legendsof the symbolsusedin calculated2D bandstructuresin Figs. 2 and3. The ‘‘minimum fraction’’ is definedinthe text ~the calculationmethodin Sec.III !.

Min. fractionStructure Symbol Projectedatom G-X G-M

clean big circles Al 0.8 0.8small circles Al 0.4 0.4

LT emptysquares Na 0.5 0.5big circles Al 0.7 0.8

small circles Al 0.35 0.4

RT big squares Na 0.4 0.5small squares Na 0.2 0.2small circles Al 0.5 0.55

vacancy big circles Al 0.5 0.5small circles Al 0.3 0.3

Fig. 4!. Thus, in reality the wave functionsmay happentohave approximately a 131 Bloch-type periodicity—thebackfoldingstill occurs.Thesamewould alsoresultevenforthe clean-surfaceband if the artificial c(232) unit cellwould be imposed.In our backfoldedbandstructure,a van-ishingdeviationfrom the131 Bloch-typeperiodicitywouldbecomevisible only in a vanishingbandgapat a Brillouin-zoneboundary,that is, in our caseon the line halving the

rangeG-M .On the otherhand,the photoemissionintensitywould be

determinedby a matrix element

M ~ki ,«!5E d3r c f* ~r !¹cki ,«8~r !. ~4!

Thesymmetryof thestructureleadsto the ‘‘selection rule,’’which selectsout initial-statebandsaccordingto thesymme-try relation betweenthe initial- and final-statewave func-tions. In the caseof the LT structure,the final statec f(r )samplestheinitial statecki ,«8(r ) at bothof thetwo Al atomsin a unit cell. Theselectionrule cantakeplacedifferently for

the first andsecondhalvesof the rangeG-M , destroyingthemirror symmetrybetweenthetwo halves.In particular,if thewavefunctionshavenearlythe131 Bloch-typeperiodicity,the selectionrule leadsto an ‘‘unfolding’’ of the backfoldedbandstructure.

~2! Charge-densitydistributions. The chargedensity isderivedfrom Kohn-Shamwavefunctionsas

r~r !5(ki

(« occ

ucki ,«~r !u2, ~5!

where« occ labelsthe occupiedlevels.We user(r ) for thestudyof chargetransferoccurringat adsorption.

The single-statechargedensityis definedhereas

rki ,«~r !5ucki ,«~r !u2, ~6!

and used for analyzing the character of surface states/resonances.We shouldkeepin mind that the charge-densitydistributionsarederivedfrom pseudo-wave-functionsresult-ing from the use of pseudopotentials,so that they give acorrect distribution only outside the critical radius of thepseudopotentials.

We usecrosssectionsof the chargedensitieson planesperpendicularandparallel to the surface.The perpendicularcrosssectionstakenarespecifiedin Fig. 4.

IV. RESULTS

In Secs.IV A, IV B, and IV C, we discusssuccessivelythe results for the clean Al ~001! and the twoc(232)-Na/Al~001! surfaces.It is to be notedthat the fig-uresare arranged,independentlyof the text, in the way tofacilitate a visual comparisonbetweenthe different struc-tures.

A. Clean Al „001…

Figure2~a! showsthe experimental~left panel! andtheo-retical ~right panel! band structuresfor the clean Al ~001!surface.It canbe seenthat both exhibit a surface-stateband

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FIG. 2. Comparisonof experimental~left panel! andcalculated~right panel! 2D bandstructures.The symbolsusedfor the calculatedbandsarespecifiedin TableI. ~a! Cleansurface.~b! LT phase~hollow site!. ~c! RT phase~substitutionalsite!.

n

t

t

t

n

justtheon-

of.

LTl

are-

which has a free-electron-like form. The paramaters obtaiby fitting by parabolas, as indicated by broken lines in F2~a!, are shown in Table II. The energy position of the ba

at G, E0, agrees well between theory and experiment, wvalues of 2.68 and 2.76 eV below the Fermi level, resptively. The theoretical value lies in the range of the resultsother calculations:16–23 2.6–2.9 eV. The experimental valuis in very good agreement with earlier experimenstudies.24–26

In Fig. 2 ~left panel!, it can be seen that the experimenresults display a number of additional features. Those whare common to all structures studied on this surface aresigned to bulk bands, as indicated by arrows. These bfeatures do not appear in the calculated band structures~rightpanel!, reflecting the fact that the density of states projeconto the uppermost Al atoms are dominated by the surfstates.

In Fig. 6~a! we display the single-state charge-density d

tributions at G for the main band. The two cross sectio

edig.nd

ithec-of

eal

alichas-ulk

edace

is-

s

~100! and ~110! are defined in Fig. 4~a!. An important char-acteristic of the surface state of the clean Al~001! surface isthat the charge density shows a pronounced maximumon top of the surface Al atoms. This can also be seen incross section parallel to the surface through the electrdensity maxima as shown in Fig. 7~a!. This particular featureof the surface state is apparently crucial in the formationthe electronic structure of the LT phase, as we see below

B. LT c„232… hollow structure

1. Al-derived band

In Fig. 2~b!, we show the experimental~left panel! andcalculated~right panel! surface states/resonances for thec(232) hollow structure. The lower-lying main band is Aderived, as indicated by the circles in the theoretical plot~cf.

Table I!. The position of the calculated band atG lies some-what lower in energy than the experimental value; comp3.61 to 3.12 eV~see Table II!. ~We note the calculated re

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sultsof the earlier theoreticalwork of Chulkov andSilkin18

is also'3.6 eV, althoughtheir non-self-consistentvalueofverticaldistance2.05Å, from Na to Al is differentfrom ours2.35 Å, which is nearerto the experimentalresult2.57 A.8!Comparedto the position of the surface-stateband of the

FIG. 3. 2D bandstructuresof ~a! theLT phase~hollow site!, ~b!the RT phase~substitutionalsite!, and ~c! the vacancystructure,including theenergyrangeaboveEF . Thesymbolsusedarespeci-fied in TableI.

cleanAl ~001! surface,the Al-derived bandlies lower in en-ergy, by 0.93 and 0.36 eV, as obtainedby the calculationsandasdeterminedfrom experiment,respectively.Thenatureof this downwardshift will be discussedbelow. The differ-encesbetweentheoryandexperimentmayhavebeencausedby the approximationsusedin the total-energycalculation~useof LDA, Rydbergcut, k-point sampling,etc.13,14!

Theexperimentalresultsshowclearly that theAl-derivedstatedoesnot have the c(232) periodicity, but rather the131 periodicity of the cleansurface.In fact, we find it asignificantexperimentalresult that the main bandin the LT

phasehas,throughoutthe whole rangeof G-M , almost thesameform as that of the clean surface,being only shifteddown.

In Fig. 6~b! we displaythesingle-statecharge-densitydis-

tribution at G for the Al-derived bandof the LT phase.Thetwo setsof crosssectionsdifferently chosenfor Al and Na@cf. Fig. 6~c!# aredefinedin Fig. 4~b!. It canbenotedin Fig.6~b! that themaximaof chargedensityremainson top of thesurfaceAl atoms,almostunchangedfrom thoseof the cleansurfaceshownin Fig. 6~a!. ~This hasalso beenpointedoutby Chulkov andSilkin.18! In the crosssectionparallelto thesurfaceshownin Fig. 7~b!, only a small deviationfrom the131 structureis seen,havinga c(232) period,with someindicationof a characterof a bondingstatebetweenthe Na

FIG. 4. Geometriesof the c(232)-Na/Al~001! surfacestruc-tures: ~a! clean surface~b! LT phase~hollow site!, ~c! vacancystructure,and ~d! RT phase~substitutionalsite!. The positionsofperpendicularcrosssectionsusedfor charge-densitydistributionsare indicated.The white circles representNa atoms,and the graycirclesAl atoms.

TABLE II. Parametersspecifying the main surface state/resonancebandsin Figs.2 and3. Theexperimentalvalues~Ref.10!areshownin brackets.

Structure E0 ~eV! kF @2p/a0# m* (me)

clean 2.68 ~2.76! 0.55 ~0.60! 1.05 ~1.18!LT 3.61 ~3.12! 0.64 ~0.66! 1.03 ~1.29!RT 2.14 ~2.31! 0.51 ~0.62! 1.12 ~1.55!vacancy 1.33 0.41 1.15

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and Al atoms.The smallnessof the deviationexplainsthesimilarity of the experimentalband structuresbetweenthecleansurfaceandthe LT phase.It is to be notedthat in thephotoemissionprocessesfrom this band,not only the initialstates,but also the final states,haveapparentlymaintainedapproximatelythe sameperiodicity as of the cleansurface.The theoreticalcurvesin Fig. 2~b! appeardifferent, but thisis only causedby the backfolding,asalreadymentioned.

2. Na-derivedband

In Fig. 2~b!, dark spotscanbe seenat G andM , neartheFermienergyEF , in theexperimentalresults.Althoughfromthefigurepresentedhereit is perhapsdifficult to distinguish,we find in the experimentaldatathat the dark featureat Mfor theLT phaseis markedlydifferent in characterfrom thatof the cleansurface,in that the intensityfor the LT phaseisstrongerandsometailing with dispersionis exhibited,as is

the casealsofor the featureat G. From the calculatedbandsof the LT phase@right panelof Fig. 2~b!#, we can seethatthere is a surface-state/resonanceband with an energy of

about0.7eV belowtheFermi level at G. As indicatedby theopensquares,it is a Na-derivedband.We assignthis bandas

giving rise to the experimentallymeasuredintensitiesat G

and M at ;0.4 eV below the Fermi level. The existenceofthis bandwasfirst theoreticallypredictedby Beneshet al.,27

and was also reproducedby Chulkov and Silkin.18 In Fig.3~a!, we showthe samecalculatedbandstructureas in Fig.2~b!, but where the energyregion extendshigher into thepositive range.Here we can see that the part of the Na-derived band aboveEF exhibits markedband-structureef-

fectsin themiddleof G-M , dueto thec(232) periodicityofthe adsorbedNa layer.

In Fig. 5~a!, we show the band structureof a free c(232)-Namonolayerfor comparison.It canbeobservedthatat

G thelowestbandlies '0.8eV lower in energyascomparedto theNa-derivedbandof theLT phase.Correspondinglytheoccupiedpartof thebandis notablylargerfor thefreemono-layer.

Figure 6~c! displays the distribution of the Na-derived

surfacestate/resonanceat G which clearly showsan anti-bonding character,the nodal line ~not shown! running be-tween the Na and Al layers.A comparisonwith Fig. 5~b!showsthat the stronglysmearedout characterof the densitybetweenthe Na atoms is maintained,appearing,however,only in the upper half of the Na layer. The lower half isapparentlycanceledby the Al surfacestatesdueto the anti-bonding coupling. A cross section parallel to the surfacepassingthroughthe electrondensitymaximaon top of theNa atomsis shownin Fig. 7~c!. Herewe seealsoa smearedout, free-electron-likedistribution.

3. Formation mechanismof the two surface-state/resonancebands

Combining the resultsabove,we can concludethat thetwo bandsareresultingfrom a couplingbetweenthe lowest-lying ~3s-derived! bandof a free c(232) monolayerof Naandthe surface-statebandof the cleanAl ~001! surface.Ap-

plying a simple two-termperturbationtheory,ascommonlydonein molecular-orbitaltheory,28,29 this maybeunderstoodas being due to the formation of bonding and antibondingstates,leadingto the downwardshift of the Al-derived bandby 0.9 eV ~calc.!, with an increasein populationand theupwardshift of theNa-derivedbandby 0.8 eV ~calc.! with adecreasein population.Alternatively, it may be understood,as in the caseof ionic crystals,that the shifts occur as theresultof Coulombfieldsbetweenthetwo oppositelychargedionic layers.The ionizationis to be expecteddueto the cat-ionic natureof Na, which donateselectronicchargeto thealuminum.

In Fig. 9, we showthe total chargedensityr tot. ; the den-sity differencebetweenthe adsorptionsystemandthe corre-spondingAl surface~for which thepositionsof theAl atomsare kept at those of the adsorptionsystem!, Drdiff.5r tot.2rAl , and the redistribution of charge,Dr redis.5r tot.2rAl2rc(232)-Na, which subtractsout the chargedensityof thefreeNa monolayer@Fig. 5~b!#, showingexactlywherechargehasbeenenhancedanddepleted.It canclearly be seenfromDrdiff. andDr redis. thatchargeenhancementoccursprimarilyat the maximaof the surfacestates,and indeedalmostpro-portionally. We can also note in Dr redis. some regions ofdepletion,showingthat the electronchargehasbeentrans-ferred from the upper half of the region betweenthe Na

FIG. 5. Free c(232)-Na layer: ~a! band structure,and ~b!charge-densitydistributionof valenceelctrons.The planesof crosssectionsaredefinedin Fig. 4~b!.

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atoms,wherethedensityfor thefreeNa layer @seeFig. 5~b!#is much larger than that of the Al surfacestates@seeFig.6~a!#. We maythusconcludethattheelectrontransferoccursfrom Na atomsdirectly into the pre-existingsurfacestatesof Al.

It is noted in passing that this characterof the LTphase shows a close analogy to the case ofc(232)-Cs/W~001!,30,31 both having the c(232) fourfoldhollow structure.Although the electronicstructureis muchmore complicatedfor Cs/W, the essentialfeature of thecharge transfer is the same. Thus the maxima of the4d-derivedsurfacestatesof the cleanW~001! surfacelie ontop of the surfaceW atoms ~seeFig. 7 of Ref. 30!. Themaxima maintain their form upon Cs adsorption.Chargetransfertakesplace from Cs to thesesurfacestates.Hencethis caseandoursmay be regardedasrepresentativesof thealkali-metal-onmetalsystems,for which thesurfacestatesofthe substrateplay an essentialrole.

TheupperNa-derivedbandcrossestheFermi level andispartly occupied,remaining ‘‘metallic.’’ In Figs. 6~c! and7~c!, its free-electron-likecharactercan be seen.We seeinFigs.6~b! and6~c! that the chargedensityof the Al-derivedband lies well below the smearedout density of the Na-derivedband,andalsobelow the positionof the Na atoms.Thus the traditional picture of a thin metallic film coveringan originally metallic substrateremainsqualitatively valid.We seebelow that this is not the casefor the RT phase.

It is to be notedthat the apparentlyweakinfluenceof theNa adsorptionon the Al surfacestatesis limited to the high

FIG. 6. Charge-densitydistribution of the surface state/resonanceof the main bandsat G for ~a! the cleansurface,~b! theAl-derived band of the LT phase~hollow site!, and ~c! the Na-derivedbandof the LT phase.The positionsof crosssectionsareindicatedin Figs. 4~a! and 4~b!. Large dots denoteNa atomsandsmall dots Al atoms.The contoursbegin at 1.0, and the contourspacingis 1.0. The units are31023e bohr23.

coverageof Q50.5 for the c(232) structure,for which thedensitymaximafor the Na valenceelectrons@Fig. 5~b!# liebetweentheNa atomsandaresituatedjust at thesamesiteasthe surface-statemaxima. In fact, it has been foundexperimentally10 that at low coveragesQ50–0.15 the sur-face statesare deterioratedby Na adsorption.Also, it hasbeen shown by DFT calculation32 for a fictive ordered-structure model p(232), with coverageQ5 1

4, that thesurface-statemaximaaremovedfrom the on-topsitesto thebonding-linepositionsbetweenthe Na andAl atoms.

C. RT c„232… substitutional structure

1. Al-derivedband

Figure 2~c! showsthe experimental~left panel! and cal-culated ~right panel! surface-state/resonancebandsfor theRT c(232) substitutionalstructure.It can be seenthat theexperimentalsurface-state/resonancebandclearly exhibitsac(232) periodicity,in contrastto theLT ~hollow! structure.As we will seebelow, this is dueto the significantly recon-structedAl ~001! surface.Thecalculations~right panel! showgoodagreementwith experiment,andindicatethat the bandis mainly Al derived~circles!, but hasa smallparticipationofNa ~squares!. Theenergypositionof themaintheoreticaland

experimentalbandsat G are2.14and2.31eV, respectively.The experimentalresultsdisplay someasymmetryin the

intensity nearki50.5 in G-M , i.e. a weakeningon the leftsideanda strengtheningandupwardshift on theright. A fewalternativeexplanationsmay be possiblefor this anomaly.Among others,it may be relatedto the closingof the bulk-bandgapin this region,causingthestateto go from beinga

FIG. 7. Charge-densitydistribution of the main surfacestates/resonancesin a plane parallel to the surfacepassingthrough theelectron-densitymaxima ~not the atom centers!: the cleansurface~a!; the Al- ~b! andNa-derived~c! bandsof the LT ~hollow! struc-ture, respectively;and the vacancystructure~d! and Al- ~e! andNa-derived~f! bandsof the RT ~substitutional! structure,respec-tively. The dots representthe positionsof the Na atoms.The con-tours begin at 1.0, and the contour spacingis 1.0. The units are31023e bohr23.

e

8

pure surfacestateto a surfaceresonance@seeFig. 10~c! ofRef. 10#. Also, additional coupling to bulk statesmay be-comepossibleby surfaceumklappprocesses.The peakpro-file may becomebroadandcomplicated,asindicatedby the

split structureof the band near ki50.5 in G-M . Differentprofiles for the left and right halvesmay result from thisbroadenedpeakin theformationof thematrix elementgivenby Eq. ~4!, the final statebeingdifferent.

An important finding in the presentanalysisis that themain bandin the RT structurecanbe regardedasbeingde-rived from the surface-state/resonancebandof a fictive, re-constructedcleanAl surface,that is, the ‘‘vacancy’’ struc-ture;seeFig. 4~c!. In this structuretheNa atomsarereplacedby ‘‘vacancies’’ of theAl atoms.Thesurface-state/resonancbandstructureof the vacancystructureis displayedin Fig.3~c!. By comparisonwith Fig. 3~b!, it is clearlyseenthat themain Al-derived bandof the RT phaseoriginatesfrom thatof thevacancystructure,andis only somewhatshifteddownin energy~by 0.81eV! dueto Na adsorption.

Figures8~a! and8~b! showthe single-statechargedistri-

bution at G for the main bandsof the ‘‘vacancy structure’’and the RT phase,respectively.Figures7~d! and7~e! showtheir crosssectionsparallelto thesurfacepassingthroughtheelectron-densitymaxima.Similarly to thecleanAl ~001! sur-face,themaximaof chargedensityfor thevacancystructurelie on top of the uppermostsurfaceAl atoms,having thistime thec(232) periodicity.For theAl-derivedbandof theRT phase,the maxima also lie approximatelyat the sameposition as that of the vacancy structure,with relativelysmall changesin their form. It canbe notedthat thesestatesare rather strongly localized. This explains the well-developedc(232) characterof the bandfound in Fig. 2~c!,

FIG. 8. Sameas Fig. 6, for the RT phase~substitutionalsite!.The positionsof the crosssectionsare specifiedin Figs. 4~c! and4~d!.

and its relatively small dispersion~larger value of m*, seeTableII !.

Similarly to the LT phase,in Fig. 2~c! we find a fewadditional theoreticalbulk bandswhich are not presentforthe clean surface.Theseare apparentlyintroducedby thec(232) periodicity as surfaceumklappprocesses.Thereisalso indication of a third, relatively weak bandlying at EF

andaroundG andM in boththeexperimentalandcalculatedband structures.From our analysis~not shown!, this bandcan be regardedas being derivedfrom a second,relativelyweak,surface-state/resonancebandof the vacancystructure.

2. Na-derivedband

In Fig. 3~b!, we see that the Na-derived band ~filledsquares! is foundonly in thecalculation,lying completelyinthepositive-energyrange,about2.7eV higherin energythanfor the free c(232)-Na layer. Notably, this shift is muchlarger thanthe downwardshift of the Al-derived band~ 0.8eV!. This will be discussedbelow.

Thesingle-statechargedistributionof theunoccupiedNa-

derivedstateat G is shownin Fig. 8~c!, indicatingagainanantibonding character. Figures 8~c! and 7~f! show itssmearedout, free-electron-likestructure,with the maximaresidingthis time abovethe Na atoms.

3. Formation mechanismof the two bands

We concludethatthetwo mainbandsareresulting,just asin the caseof the LT phase,from the couplingbetweenthestatesof a freec(232)-Na monolayerandthesurfacestate/resonanceof theAl surface,i.e., thevacancystructurein thiscase.Theelectrontransfercanalsoberegardedasoccurringfrom Na atomsinto the surfacestate/resonanceof the va-cancystructure.This can be seenclearly in comparingFig.10 with Fig. 8~a!. In thechargeredistributionDr redis. in Fig.10 we note someregionsof depletion:the electronchargehasbeentransferredin this casemainly from the regionontop of the Na atoms,wherethe densityof the free Na layerdominatesthe densityof the surfacestate/resonanceof thevacancystructure.Thechargedepletionfoundin Fig. 10 alsonear the centersof the Al atomsmay be interpretedas aresult of an upward shift of the maximum of the surfacestatesinducedby Na adsorption.

Thesefindings, combinedwith the unbalancedlarge up-ward shift of the Na-derivedbandand the existenceof thethird peak at EF , both mentionedabove,indicate that thecoupling betweenthe free Na monolayerstatesand the Alsurfacestates/resonancestakesplacein a little morecompli-catedway thanin theLT case.It canno longerbeinterpretedin a simple two-term-couplingperturbationscheme.Appar-ently the coupling is too strong,and involves other states,namely,the pz statesof Na lying originally at 11 eV @Fig.5~a!# and the secondsurfacestates/resonancesof Al lyingoriginally at 0 eV @Fig. 3~c!#.

We haveseenabovethat for the LT phasethe traditionalpicture of a thin metallic film coveringa metallic substrateremainsqualitatively valid. For the RT phase,on the otherhand, we see in Fig. 8~b! that the completely filled Al-derivedbandhasthemaximalying at thesameheightastheNa atoms.The maxima of the Na-derivedband lie indeed

s

9

higher, but they are empty. Thus, as far as the electronicstatesin the energyrangenear EF are concerned,the Al-derived band constitutespractically the ‘‘surface’’ of thisstructure.TheNa monolayer~or theNa/Al compositemono-layer! cannotbe regardedas a metallic film on a metallicsubstrate;rather,exceptfor thestill existentbackgroundbulkcontinuum,theelectronicstructureof themonolayermaybeviewed as being analogousto that of an ionic crystal, likeNaCl, wherethe completelyfilled Al-derived bandreplacesthevalencebandof Cl, andformswith theemptyNa-derivedbanda ‘‘band gap’’ of about3.5eV acrosstheFermienergy.

We notein passingthatwe find a similarity of thesurfaceelectronicstructureof the RT phaseto that of the system(232)-2Na/Al~111! which forms a compositedouble-layersurfacealloy with a similar, but more complexintermixingof Na and Al in the surfacelayers.33,34 For this systemwefind alsoa filled Al-derivedbandoriginatingfrom thecorre-sponding ‘‘vacancy structure,’’ and an empty Na-derivedband.~The latter may be assignedto that found by Heskettet al.35 usinginversephotoemissionspectroscopy.! Thesimi-larity indicatesthatalsothis layercannotberegardedsimplyasa thin metallic layer.

V. DISCUSSION

For all three systemsstudied@Al ~001! and the two c(232)-Na/Al~001! phases#, we find goodoverallagreementofthe surface-state/resonanceband structurebetweenexperi-ment and theory. In each case there is a prominent Al-

FIG. 9. Total charge-densitydistribution r tot. ~left panel!, den-sity difference Drdiff. ~middle panel!, and density redistributionDr redis. ~right panel!, of the LT phase~hollow site!. The crosssec-tion is in the ~001!Na plane @see Fig. 4~b!#. The units are1023e bohr23. In the left panelthe first contourbeginsat 4.0 witha spacingof 4.0; for themiddlepanelthefirst contourbeginsat 0.6with a spacingof 0.6; and in the right panel the contoursare thesameas the middle panel,with the addition of a negativecontourline ~unshaded! at 20.6.

FIG. 10. Sameas Fig. 9 for the RT phase~substitutionalsite!.For the middle panelthereis onecontourline at 21.2, and in theright panel there are three negativecontour lines ~unshaded! at21.8, 21.2, and20.6.

derivedsurface-state/resonanceband,showingsimilar free-

electron-likeparabolicdispersionat thebandbottomnearG,as indicatedby brokenlines in Fig. 2. We find that the ob-servedand calculatedvaluesof the Fermi wave vector, kFandtheeffectivemassm* of themainband~TableII ! agreeonly roughly, probably due to the approximationsused incalculation,asalreadymentioned.In any case,thesequanti-ties are to be regardedasglobal parametersspecifyingonlythe geometryof the bands,andarenot intendedto indicatethat the bandsare free-electron-like.In fact, the wavefunc-tionsof theAl-derivedbandsareratherstronglylocalized,aswe seefrom the charge-densitydistributions.The dispersionof the bandsmay be regardedas the result of the overlapbetweenthe localizedwavefunctions.

Thepictureof chargetransfertakingplacefrom Na to thesurfacestates/resonancesof Al is also supportedby the al-most equal valuesof the work-function change~decrease!DF'21.6 eV, obtainedboth experimentally36,37 and theo-retically in the presentwork for the LT andRT phases.Ob-viously the valueof DF resultsfrom r redis., shownin Figs.9 and 10, as the z componentof the dipole moment.Asalreadymentioned,the minima and maximaof r redis. corre-spondto the maximaof the Na- and Al-derived states,re-spectively.This canbeseenby comparisonof Figs.9 and10with Figs. 6~b! and6~c! and8~b! and8~c!. In thesefigures,the vertical distancesbetweenthe maxima of the Na- andAl-derivedstatesarefoundto havea ratio of about1.0 to 0.6betweenthe LT andRT phases.On the otherhand,a com-parisonbetweenFigs.5~a! and2~b! showsthat the decreaseof the occupancyof the Na-derivedstatesamountsto c. 0.6for the LT phase,in contrastto 1.0 for the RT phase~beingempty!. This leadsto the sameamountof DF betweenthetwo phases,asa productof chargeanddistance.It is essen-tial in this considerationto notethefact that,while theformsof the Al-derived statesremain always almost unchanged,the forms of the Na-derivedstateschangedrastically,fromthat of Figs. 5~b! to thoseof Figs. 6~c! and8~c!.

Our resultsverify the formationof the two surface-state/resonancebands.Variousexperimentalmethodsof studyingsurfaceelectronicpropertiesotherthanultravioletphotoelec-ton spectroscopy,asusedhere,maybeusefulfor finding outcharacteristicfeaturesinducedby thesetwo bands.Particu-larly, EELS ~electron-energy-lossspectroscopy! ~Refs. 38and39! andinversephotoemissionspectroscopy35,39 may beuseful for studyingthe effectsof the bandslying in the en-ergy rangeabovethe Fermi level.

For the RT phase,the fact that the surfacebandstructureis constitutedof a filled bandandanemptyband,with a gapof approximately3.5 eV, mayplay an importantrole in vari-ouspropertiesof thesurface.We maythink of, in additiontoEELS, an anomalousfeature in optical reflection spectra40

near3.5 eV and a correspondinganomalyin the dispersioncurveof surfaceplasmons.41

A significanteffect may be expectedin varioussurface-sensitivemethods,such as ion neutralization,42 metastabledeexcitation,42,43 etc.,which would reflect the dominanceofthesurfacestates/resonancesin theoutermostsurfaceregion,and henceexposethe difference in the characterof thesestatesbetweentheLT andRT phases.We mayalsothink ofthe relevanceof the occupancyof surfacestates/resonanceon surfacediffusion44 andcatalyticactivity.45

e

10

VI. CONCLUSION

We have analyzedthe electronicstructureof the meta-stable hollow and stable substitutional structuresof c(232)-Na on Al ~001!. The calculatedsurface-state/resonancbands agree well with those measuredby angle-resolvedphotoemissionexperiments.It is found that, in both phases,two pronouncedbandsappearastheresultof a characteristiccoupling between the valence-state bands of a freec(232)-Na layer and the surface-state/resonancebandsofthecorresponding~i.e., cleanandreconstructed! Al surfaces.While the experimentalbandstructureof the substitutional

structureshowsa clearc(232) characterdueto the signifi-cantreconstructionof thesurfaceAl layer, thehollow struc-ture doesnot: The main band, in fact, exhibits a quasi-(131) periodicity like that of the cleansurface.For the stablesubstitutional structure, the unoccupied surface-state/resonancebandlies completelyabovethe Fermi level, lead-ing to the formation of a surface-stateband structurethatresemblesthat of an ionic crystal. We await experimentalverification of the predicted unoccupied surface-state/resonanceband,andof thedifferencein thepropertiesof theLT andRT phasesin relationto the characterof the surfacestates/resonances.

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