Crystallographic orientation and induced potential effects in photoelectron emission from metal surfaces by ultrashort laser pulses
C. A. Rios Rubiano, R. Della Picca, D. M. Mitnik, V. M. Silkin, M. S. Gravielle
CCrystallographic orientation and induced potential effects in photoelectron emissionfrom metal surfaces by ultrashort laser pulses
C. A. R´ıos Rubiano and R. Della Picca
CONICET and Centro At´omico Bariloche (CNEA) Bariloche, Argentina.
D. M. Mitnik
Instituto de Astronom´ıa y F´ısica del Espacio (IAFE, CONICET-UBA),Casilla de correo 67, sucursal 28, C1428EGA Buenos Aires, Argentina. andFac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires.
V. M. Silkin
Donostia International Physics Center (DIPC), 20018 San Sebasti´an,Spain, and Depto. de F´ısica de Materiales, Facultad de Ciencias Qu´ımicas,Universidad del Pa´ıs Vasco, Apdo. 1072, 20080 San Sebasti´an, Spain andIKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
M. S. Gravielle
Instituto de Astronom´ıa y F´ısica del Espacio (IAFE, CONICET-UBA),Casilla de correo 67, sucursal 28, C1428EGA Buenos Aires, Argentina.
The influence of the crystallographic orientation of a typical metal surface, like aluminum, onelectron emission spectra produced by grazing incidence of ultrashort laser pulses is investigated byusing the band-structure-based-Volkov (BSB-V) approximation. The present version of the BSB-Vapproach includes not only a realistic description of the surface interaction, accounting for bandstructure effects, but also effects due to the induced potential that originates from the collectiveresponse of valence-band electrons to the external electromagnetic field. The model is applied toevaluate differential electron emission probabilities from the valence band of Al(100) and Al(111).For both crystallographic orientations, the contribution of partially occupied surface electronic statesand the influence of the induced potential are separately analyzed as a function of the laser carrierfrequency. We found that the induced potential strongly affects photoelectron emission distributions,opening a window to scrutinize band structure effects.
PACS numbers:
I. INTRODUCTION
In the last decade photoelectron emission (PE) frommetal surfaces has received renewed attention as a re-sult of the technological achievement of lasers with pulsedurations of the order of attoseconds, which make it pos-sible to study the behavior of electrons in condensedmatter at their natural temporal orders [1–8]. Such aremarkable experimental progress needs to be accompa-nied by intensive theoretical research since the underlyingquantum processes involve complex many-body mecha-nisms, whose complete understanding is still far from be-ing achieved [9–16]. This paper aims to contribute tothe study of PE from metal surfaces due to the inter-action of ultrashort laser pulses with valence-band elec-trons. In particular, the article focuses on the influenceof the crystallographic orientation of the surface on elec-tron emission spectra, investigating the contributions ofthe surface-band structure and the induced surface po-tential for different crystal faces.To describe the PE process we make use of atime-dependent distorted-wave method named band-structure-based-Volkov (BSB-V) approximation [17].The BSB-V approach includes an accurate description of the electron-surface interaction, given by the band-structure-based (BSB) model [18], while the action ofthe laser field on the emitted electron is represented bymeans of the Volkov phase [19]. The BSB model is basedon the one-dimensional pseudopotential by Chulkov et al .[18, 20], which takes into account the electronic struc-ture of the surface, replicating the width and position ofthe projected bulk energy gap and the surface and firstimage electronic states [21–25]. In this version of theBSB-V approximation we also incorporate the contribu-tion of the induced surface potential, which is generatedby the dynamic response of the metal surface to the laserfield [26]. The induced potential is derived in a consis-tent way from the unperturbed BSB electronic states byusing a linear response theory [27].The BSB-V approximation, including the dynamicinduced contribution, is applied to evaluate double-differential (energy- and angle- resolved) PE distributionsfor two different orientations of aluminum: Al(100) andAl(111). For both crystal faces, the influence of par-tially occupied surface electronic states (SESs) and theinduced potential are examined by considering differentparameters of the laser pulse. Our results indicate thatthe induced potential plays an important role in PE spec- a r X i v : . [ phy s i c s . a t m - c l u s ] S e p tra. It makes visible band structures signatures in PEspectra for the resonant case wherein the laser frequencycoincides with the surface plasmon frequency, as well asfor laser pulses with high carrier frequencies.The article is organized as follows. In Sec. II we intro-duce the extended version of the BSB-V approximation,which takes into account the effect of the induced sur-face potential through a Volkov-type phase. In Sec. IIIresults are shown and discussed, while our conclusionsare summarized in Sec. IV. Atomic units are used unlessotherwise stated. II. THEORETICAL METHOD
Let us consider a finite laser pulse, characterized by atime-dependent electric field F L ( t ), grazingly impingingon a metal surface S . As a consequence of the interac-tion, a valence-band electron, initially in the state Φ i , isejected above the vacuum level, reaching a final state Φ f .Within the framework of the time-dependent distortedwave formalism [28], the BSB-V transition amplitude forthe electronic transition Φ i → Φ f reads [17]: A if = − i (cid:90) + ∞−∞ d t (cid:68) χ ( BSBV ) f ( r , t ) |V ( r , t ) | Φ i ( r , t ) (cid:69) , (1)where V ( r , t ) = r · F L ( t ) + V I ( r , t ) (2)is the perturbative potential at the time t and χ ( BSBV ) f ( r , t ) is the final BSB-V distorted wave function,with r the position vector of the active electron. The firstterm of Eq. (2) represents the interaction potential withthe laser, expressed in the length gauge, while the sec-ond term, V I , denotes the induced surface potential thatis produced by electronic density fluctuations caused bythe external field. The frame of reference is placed at theposition of the crystal border, which is shifted outwardwith respect to the position of the topmost atomic layerby half of the interplanar distance, with the ˆz axis be-ing oriented normal to the surface, pointing towards thevacuum region.Within the BSB-V approach, the unperturbed statesΦ i and Φ f are solutions of the Schr¨odinger equation as-sociated with the one-dimensional electron-surface po-tential V S ( z ) given by Ref. [20], which depends on z , the component of r perpendicular to the surfaceplane. Hence, the states Φ i ≡ Φ k is ,n i ( r , t ) and Φ f ≡ Φ k fs ,n f ( r , t ) can be expressed asΦ k s ,n ( r , t ) = 12 π exp ( i k s · r s ) φ n ( z ) e − iEt , (3)where k s ( r s ) is the component of the electron momen-tum (position vector) parallel to the surface plane, φ n ( z )is the one-dimensional eigenfunction with eigenenergy ε n derived from the potential V S ( z ), and E = k s / ε n is the total electron energy. According to the grazing incidence condition and thetranslational invariance of the problem in the plane par-allel to the surface, the laser field is linearly polarizedperpendicularly to the surface, that is, F L ( t ) = F L ( t ) ˆz ,where the temporal profile of the pulse reads: F L ( t ) = F sin ( ωt + ϕ ) sin ( π t/τ ) , (4)for 0 < t < τ , and vanishes at all other times. In Eq. (4) F represents the maximum field strength, ω is the carrierfrequency, τ is the pulse duration, and ϕ is the carrierenvelope phase, which is defined as ϕ = ( π − ωτ ) / N of full cycles inside the envelope;then, the pulse duration is defined as τ = N T , with T = 2 π/ω the laser oscillation period.The induced potential V I is evaluated from a linearresponse theory based on the BSB wave functions of Eq.(3) [29]. Making use of a slab geometry to derive theone-dimensional wave functions φ n ( z ), the induced field F I = −∇ r V I ( r , t ) can be nearly expressed as F I ( z, t ) = (cid:26) F I ( t ) ˆz for − d < z < , d is the width of the slab, formed by a sufficientlylarge number of atomic layers of the metallic crystal. Thefunction F I ( t ) = − π (cid:90) ∞−∞ d ν (cid:101) F L ( ν ) f I ( ν ) e − iνt (6)is the induced field inside the metal at the time t , with (cid:101) F L ( ν ) denoting the Fourier transform of F L ( t ) and f I ( ν )being the dynamic response induced by a unitary andmonochromatic electric field of frequency ν .From Eqs. (2) and (5) it is possible to build χ ( BSBV ) f ( r , t ) by introducing the distortions of both theexternal and the induced fields in the momentum distri-bution of the final state Φ k fs ,n f , by means of a Volkov-type phase [17, 26, 30]. It reads: χ ( BSBV ) f ( r , t ) = Φ k fs ,n f ( r − ˆz α L ( t ) , t ) × exp [ iz A tot ( z, t ) − iβ L ( t )] , (7)where the function A tot ( z, t ) = (cid:26) A L ( t ) + A I ( t ) for − d < z < ,A L ( t ) outside,represents the position-dependent total vector potentialat the time t , with A µ ( t ) = − (cid:90) t + ∞ d t (cid:48) F µ ( t (cid:48) ) , µ = L, I, (8)being the vector potentials, with incoming asymptoticconditions, associated with the laser ( µ = L ) and induced( µ = I ) fields, respectively. In turn, the functions α L ( t ) = (cid:90) t + ∞ d t (cid:48) A L ( t (cid:48) ) , (9)and β L ( t ) = 12 (cid:90) t + ∞ d t (cid:48) [ A L ( t (cid:48) )] , (10)involved in Eq. (7), are respectively related to the quiveramplitude and the ponderomotive energy of the laser.Finally, by replacing Eqs. (2), (3), and (7) in Eq. (1),the BSB-V transition amplitude, including the inducedcontribution, reduces to A if = δ ( k fs − k is ) a if , wherethe Dirac delta function imposes the momentum conser-vation in the plane parallel to the surface and a if = − i (cid:90) + ∞ d t R if ( t ) e i [∆ εt + β L ( t )] (11)represents the one-dimensional transition amplitude,with ∆ ε = ε n f − ε n i being the energy gained by theelectron during the process. The function R if denotesthe form factor given by R if ( t ) = + ∞ (cid:90) −∞ d z φ ∗ n f (cid:0) z − α L ( t ) (cid:1) φ n i ( z ) g f ( z ) V ( z, t ) × exp [ − i z A tot ( z, t )] , (12)where g f ( z ) = e z Θ( − z ) /λ f accounts for the stopping ofthe ionized electron inside the material [17], with Θ beingthe unitary Heaviside function and λ f = λ ( E f ) being theelectron-mean-free path as a function of the final electronenergy E f = k fs / ε n f .Analogous to Ref. [17], the BSB-V differential prob-ability of PE from the surface valence band can be ex-pressed in terms of the one-dimensional transition ampli-tude of Eq. (11) as:d P d E f dΩ f = 2 k f ρ ( k fz ) (cid:88) n i | a if | Θ( (cid:101) k n i − k fs ) , (13)where Ω f is the solid angle determined by the final elec-tron momentum k f = k fs + k fz ˆz , with k fz = (cid:112) ε n f .The angle Ω f is defined as Ω f = ( θ f , ϕ f ), where θ f and ϕ f are respectively the polar and azimuthal angles, with θ f measured with respect to the surface plane. In Eq.(13), the sum indicates the addition over all the φ n i stateswith energies ε n i ≤ − E W ( E W the function work), ρ ( k fz )is the density of final states φ n f with perpendicular mo-mentum k fz , and the factor 2 takes into account the spinstates. The Heaviside function Θ( (cid:101) k n i − k fs ) comes fromthe momentum conservation in the direction parallel tothe surface plane, with (cid:101) k n i = (cid:112) − ε n i + E W ). III. RESULTS
We apply the BSB-V approximation to simulate PEdistributions from the valence band of Al(100) andAl(111). Since the ejection parallel to the polarization vector of the laser field is expected to provide the majorcontribution to the PE rate [17], in this work we only con-sider electron emission normal to the surface plane, i.e., θ f = 90 deg. The maximum field strength was chosenas F = 10 − a.u. (intensity I L = 3 . × − W/cm ),which belongs to the perturbative range, far from thedamage threshold of the material [31] .The BSB-V differential probability was evaluated fromEq. (13) by varying the carrier frequency and the dura-tion of the laser pulse. In the calculation, the BSB wavefunctions φ n ( z ) were numerically derived by expandingthem onto a basis of plane waves, defined as { exp [ i πj ( z + d/ /D ] , j = − n , .., n } , where 2 n + 1 is the number of basis functions and D isthe unit cell width, which acts as a normalization length.By using such an expansion in Eq. (12), the form fac-tor R if ( t ) was reduced to a closed form in terms of thelaser and induced fields, while the numerical integrationon time involved in Eq. (11) was done with a relativeerror lower than 1%. Moreover, taking into account thatthe functions φ n f do not allow to distinguish electronsemitted inside the solid from those ejected towards thevacuum region, to evaluate the emission probability weaveraged the contributions from the two different wavefunctions associated with the same positive energy ε n f by considering that ionized electrons emitted to the vac-uum region represent approximately a 50% of the totalionized electrons from the valence band [17, 32].The parameters associated with the different orienta-tions of aluminum are the followings. The Al(100) sur-face presents a work function E W = 0 .
161 a.u. and aninterplanar distance of 3 .
80 a.u., while the correspond-ing BSB wave functions φ n ( z ) were obtained by using abasis of plane waves with n = 220, a unit cell width D = 342 .
04 a.u., and a slab width d = 266 .
00 a.u.(i.e., 71 atomic layers). The Al(111) surface is charac-terized by a work function E W = 0 .
156 a.u. and aninterplanar distance of 4 .
39 a.u., and the φ n ( z ) wavefunctions were evaluated using a plane wave basis with n = 170, D = 394 .
92 a.u., and d = 307 .
16 a.u. (i.e.,71 atomic layers). Both faces of aluminum display thesame Fermi energy, E F = 0 .
41 a.u., and therefore, thesame surface plasmon frequency ω s = 0 .
40 a.u., whichcharacterizes the collective motion of valence-band elec-trons. The energy-dependent electron mean free-path λ ( E f ) was interpolated from data corresponding to thealuminum bulk, extracted from Ref. [33].First, in order to provide an overall scenery of the influ-ence of the aluminum crystal face, in Fig. 1 we comparePE distributions from Al(100) and Al(111) by consider-ing a different number of cycles (rows) - N = 2, 4, and6 - as well as different carrier frequencies (columns) - ω = 0 . .
4, 0 .
7, and 1 . ω = 0 .
057 a.u.), which corresponds to the experi-mental value for the Ti:sapphire laser system, PE spectra
FIG. 1: (Color online) Double differential PE probabilities in the normal direction (i.e., θ f = 90 deg), as a function of the finalelectron energy E f . Each column corresponds to a different carrier frequency of the laser pulse: ω = 0 . .
4, 0 . . N = 2(upper row), N = 4 (middle row), and N = 6 (bottom row) cycles inside the envelope, respectively. In all panels, BSB-Vresults for two aluminium faces are displayed: Al(100), with blue thick lines, and Al(111), with red thin lines. from the Al(100) surface are more than one order of mag-nitude higher than the ones corresponding to the Al(111)face. But when ω increases, emission probabilities fromboth aluminum faces become comparable in magnitude,departing appreciably each other only in the high en-ergy region for high carrier frequencies, as observed for ω = 1 . ω = 0 . N = 2 disappear almost completely as N increases.Concerning the influence of the pulse duration, it ismore appreciable for high and intermediate frequencies.On the one hand, for short pulses, with only two cy- cles inside the envelope, PE spectra (upper row of Fig.1) present a maximal emission at low electron energies,with smoothly decreasing intensity as the velocity ofejected electrons augments. Noteworthy, for carrier fre-quencies in the range ω (cid:38) ω s this low-energy maximumpresents a different structure depending on the crystalface. While for Al(111) it shows a single peak struc-ture, for the Al(100) face the maximum displays double-hump features, which are particularly visible for the fre-quency ω = 0 . γ = ω √ E W /F greater than the unity. For thehigher frequencies - ω = 0 .
4, 0 . . ω , which corresponds to the first of theabove-threshold-ionization (ATI) peaks. This ATI maxi-mum is roughly placed at E f (cid:39) (cid:104) E i (cid:105)− U p + ω , where (cid:104) E i (cid:105) is the initial energy averaged over all initial states, with (cid:104) E i (cid:105) (cid:39) − .
44 and − .
43 a.u. for Al(100) and Al(111)respectively, and U p = F / (4 ω ) is the ponderomotiveenergy, which results negligible in the present cases. Thewidth of these ATI peaks depends on the pulse dura-tion, decreasing as τ increases [26], as also observed inPE from atoms [34]. However, in contrast to the atomiccase, the electron emission from metal surfaces presentsa lower limit in the width of the ATI peaks, which is pro-duced by the energy spread of the metal valence band,characterized by the Fermi energy. This fact causes theabsence of ATI structures in the multiphotonic spectrafor ω = 0 .
057 a.u. (left lower panels of Fig. 1) becausethe energy difference between consecutive ATI peaks ismuch lower than the width of each peak.From Fig. 1 it is also observed that the multiphotonicspectra for ω = 1 . A. Photoelectron emission from SESs
One of the most remarkable effects of the crystal bandstructure is the presence of partially occupied SESs,which display a highly localized electron density at theedge of the crystal surface, favoring the release of elec-trons from the material. Even though for high carrierfrequencies, SESs were found to play a minor role in PEspectra from Al(111) [17], the relative importance of theSES contribution varies with the crystallographic orien-tation and the parameters of the laser pulse. In Fig. 2, weplot the surface potential V S ( z ) for Al(100) and Al(111),together with the square modulus of the correspondingSESs, | φ SES ( z ) | , with eigenenergies ε SES = − .
263 a.u.and ε SES = − .
32 a.u., respectively. The average depthof the potential well, defined as V S = E F + E W , is sim-ilar for both orientations. However, the corrugation of V S ( z ) for the (100) face is almost a factor 6 larger thanthe one corresponding to the (111) orientation, produc-ing a stronger localization of the SESs of Al(100) closeto the surface border, as observed in Fig. 2.The marked difference between the SES densities ofboth aluminum faces at the crystal border can be traced FIG. 2: (Color online) Potential V S ( z ) (lower graph), to-gether with the square modulus of the corresponding SESs, | φ SES ( z ) | (upper graph), for Al(100), with blue thick lines,and for Al(111), with red thin lines. from the superimposed structures of the PE spectra cor-responding to the resonant frequency ω (cid:39) ω s = 0 . ω = 0 . E f ≈ .
14 a.u. and E f ≈ .
24 a.u. respectively,whereas for Al(111) only one maximum at E f ≈ .
24 a.u.exists. This latter maximum, present for the two faces, isplaced at E f (cid:39) − E W + ω , corresponding to one-photonabsorption from initial states at the top of the valenceband, whose partial contribution is also displayed in thefigure. Instead, the peak at E f ∼ .
14 a.u., only visiblein the Al(100) spectrum, is produced by the absorption ofone-photon from partially occupied SESs, being placed at E f (cid:39) ε SES + ω . From the comparison of Figs. 3 (a) and(b) we conclude that the presence or absence of SES sig-natures in the PE distribution, depending on the crystalface, is associated with the mayor or minor localizationof the electronic density of SESs at the crystal border.For Al(100) such a localization is more than three timeshigher than the one corresponding to Al(111), makingits contribution clearly discernible in the PE spectrum.While for Al(111), the SES contribution results com-pleted concealed by emission from other initial states,which washes out SES footprints from the electron distri-bution. Therefore, PE spectra under resonant conditionsmight offer an attractive window to obtain informationabout the surface band structure. Besides, in the reso- FIG. 3: (Color online) PE distribution in the normal direc-tion, as a function of the final electron energy, for a 6-cyclelaser pulse with a carrier frequency ω = 0 . nant case the contribution of the plasmon decay mech-anism should be also included, producing an additionalstructure just at the electronic energy E f (cid:39) ω s .Previous band-structure effects disappear as the car-rier frequency departs from the resonant one. But note-worthy they become again visible for high frequencies,as shown in Fig. 4. In this figure we consider electronemission from Al(100) and Al(111) for a laser pulse with ω = 1 . B. Induced potential effects
With the aim of understanding how the collective re-sponse of valence-band electrons to the laser field affects
FIG. 4: (Color online) Analogous to Fig. 3 for ω = 1 . t/T , for a 6-cycle laserpulse impinging on Al(111). The carrier frequency of the laserpulse is: a) ω = 0 .
057 a.u., b) ω = 0 . ω = 0 . ω = 1 . F L ( t ) /F ; violet thick line, normalized induced field F I ( t ) /F . the distribution of emitted electrons, in this subsectionwe examine the contribution of the induced field to PEspectra.For laser pulses with several oscillations, the electronicrearrangement induced in the metal by the external per-turbation strongly depends on the carrier frequency. Toillustrate such a variation, in Fig. 5 we plot the laser andinduced fields for 6-cycle laser pulses, with different fre-quencies, impinging on the Al(111) surface. For frequen-cies much lower than ω s , like ω = 0 .
057 a.u., the induced
FIG. 6: (Color online) PE distribution from the valence band of both aluminum faces - Al(100) (upper row) and Al(111) (lowerrow) - as a function of the final electron energy. The impinging 6-cycle laser pulse has a carrier frequency ω = 0 . . . . ω = 1 . F L (induced field ˜ F I ) is displayed with black thin (violet thick) solid line.(b) The BSB-V PE distribution, as a function of the electron energy, is shown with blue thin line, and the SES contributionwith black dot-dashed line. The Fourier transform contribution, | ˜ F tot ( E f + ε SES ) | (in arb. units), is plotted with violet solidline. and external fields are similar in strength but in coun-terphase, tending to the static limit in which the totalelectric field vanishes inside the metal. But when the fre-quency augments to reach the resonant value ω (cid:39) ω s =0 . F I ( t ) is four timeslarger than F ; therefore, the total field inside the metalbecomes dominated by the induced response of the metalsurface. In turn, for ω > ω s surface electrons try to fol-low the external field, in such a way that the laser andinduced fields oscillate almost with the same phase, butthe intensity of the induced field decreases steeply as thecarrier frequency augments.The meaningful differences among the induced re-sponses for different frequencies of the external field, ob-served in Fig. 5, are directly reflected in their contribu-tions to the electron emission process. In Fig. 6 we com-pare BSB-V differential emission probabilities, derivedfrom Eq. (13), with BSB-V values obtained without in-cluding the induced surface interaction, that is, by fixing F I ( t ) = A I ( t ) = 0, considering the same laser parametersas in Fig. 5. Results for both crystallographic orienta-tions -Al(100) (upper panels) and Al(111) (lower panels)-are displayed in the figure. From Fig. 5 (a), for ω = 0 . ω = 0 . ω s , originating a large increase ofthe emission probability, greater than two order of mag-nitude. Notice that for this resonant frequency, the in-duced field is not only higher than the external field butalso it persists twice the original pulse duration (see Fig.5 (b)), contributing to augment the emission probabilityafter the external field turned off. For a carrier frequencyslightly higher than the surface plasmon frequency, like ω = 0 . ω = 1 . F I ( t ) is more than one order ofmagnitude lower than the one of the laser field, as dis-played in Fig. 5 (d). As it was expected, this small in-duced response does not affect appreciably the main elec-tron emission, which occurs around the first ATI peak.However, we remarkably found that the induced poten-tial introduces a pronounced growth of the probability atlow electron energies, just in the region where the double-hump low-energy structure associated with SES emission appears in the Al(100) case. To investigate in detail thisunforeseen contribution, in Fig. 7 (a) we plot the decom-position in frequencies of both the laser ( ˜ F L ( ν )) and theinduced field ( ˜ F I ( ν )) for this case. The utility of ana-lyzing the frequency domain of the fields lies on the factthat the PE spectrum can be roughly estimated as pro-portional to the square modulus of the Fourier transformof the total electric field, that is, | ˜ F tot ( ν ) | , evaluated at ν = E f + E i , with ˜ F tot ( ν ) = ˜ F L ( ν ) + ˜ F I ( ν ) and E i cov-ering the energy range of all initially occupied states. InFig. 7 (a), although the Fourier transform of the laserfield is several orders of magnitude higher than the oneof the induced field around the carrier frequency, ˜ F I ( ν )retains a peak associated with the resonance ν ∼ = ω s ,which largely overpasses the value of ˜ F L ( ω s ). This reso-nant peak is found to be the origin of the low-energy SEScontribution of the spectrum for Al(100), as shown in Fig.7 (b), where we observe that the curve corresponding to | ˜ F tot ( E f + ε SES ) | (multiplied by an arbitrary factor) al-most coincides with the SES contribution. IV. CONCLUSIONS
We have studied PE spectra produced by the inter-action of ultrashort laser pulses with the valence bandof two different faces of aluminium - Al(100) - Al(111)- by using of the BSB-V approximation. In the presentversion of the BSB-V approach we have incorporated thecontribution of the induced field, originated from the col-lective response of surface electrons to the external per-turbation. We found that the induced response of themetal surface strongly affects electron emission distribu-tions for a wide range of laser frequencies, including high ω - values. In the resonant case with the surface plasmonfrequency, the effect of the induced field contributes tomake visible signatures coming from partially occupiedSESs of the Al(100) surface, while for Al(111) these SESstructures are completely washed out by emission fromother initially occupied states. Similar features are alsoobserved in the low-energy region of the spectra for highcarrier frequencies of the laser pulse, for which the in-fluence of the induced potential was expected negligible.These findings open the way to investigate band struc-ture effects by varying the parameters of the laser pulse,the crystal orientation, and the observation region. Acknowledgments
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