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[Yu-Chan Tai](https://orcid.org/0009-0000-3010-9283), [Chih-Wei Luo](https://orcid.org/0000-0002-6453-7435), [Noriaki Takagi](https://orcid.org/0000-0002-0799-9772), [Hiroshi Ishida](https://orcid.org/0000-0003-2080-1561), [Chun-Liang Lin](https://orcid.org/0000-0001-8781-3650), [Ryuichi Arafune](https://orcid.org/0000-0003-4371-6116)

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[Coherent multiphoton photoemission spectroscopy of image-potential state on Ir(111) surface](https://mdr.nims.go.jp/datasets/a63a151f-2f96-4294-9416-314632b42dd9)

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Coherent multiphoton photoemission spectroscopy of image-potential state on Ir(111) surfaceCoherent multiphoton photoemission spectroscopy of image-potential state on Ir(111) surfaceYu-Chan Tai1,2 , Chih-Wei Luo2,3,4,5 , Noriaki Takagi6 , Hiroshi Ishida7 , Chun-Liang Lin2* , and Ryuichi Arafune1*1Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, Japan2Dept. of Electrophysics, National Yang Ming Chiao Tung University (NYCU), Hsinchu City, Taiwan3Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University (NYCU), Hsinchu, Taiwan4Institute of Physics, National Yang Ming Chiao Tung University (NYCU), Hsinchu, Taiwan5National Synchrotron Radiation Research Center, Hsinchu, Taiwan6Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan7College of Humanities and Sciences, Nihon University, Tokyo, Japan*E-mail: clin@nycu.edu.tw; ARAFUNE.Ryuichi@nims.go.jpReceived April 18, 2025; revised May 16, 2025; accepted May 19, 2025; published online June 6, 2025Multiphoton photoemission provides a means to investigate unoccupied electronic states via nonlinear light-matter interactions. In this work, weemploy five-photon photoemission spectroscopy to identify, for the first time, the image-potential state (IPS) on the Ir(111) surface. Distinct fromcommonly studied noble metals such as Cu and Ag, the Ir(111) electronic structure leads to a strong sensitivity to excitation energy: a reductionfrom 1.57 eV to 1.49 eV significantly diminishes the signal. The theoretical analysis attributes this effect to the d-band proximity to the Fermi level,which influences the initial-state population and transition probabilities governing the multiphoton excitation pathways.© 2025 The Author(s). Published on behalf of The Japan Society of Applied Physics by IOP Publishing LtdL aser-based photoemission spectroscopy has becomeessential in solid-state physics research, enabling thehigh-precision study of electronic states and dy-namics. Many phenomena that cannot be observed usingconventional light sources, such as discharge lamps orsynchrotron radiation, have been successfully studied usinglaser-based approaches.1–8) Among these, coherent nonlinearphotoemission spectroscopy with ultrafast laser pulses hasproven to be a powerful method for probing unoccupiedelectronic states, providing insights into excited-state dy-namics and band structures.Time-resolved two-photon photoemission (2PPE) spectro-scopy has significantly advanced our understanding ofelectron dynamics at solid surfaces, leading to numerousstudies in this field.1,2,9,10) However, multiphoton photoemis-sion (mPPE, m⩾3), termed higher-order nonlinear photo-emission, or above-threshold photoemission,6,11) which in-cludes both coherent and incoherent processes, remainunderexplored. The complex relationship between the elec-tronic band structures and multiphoton excitation pathwaysnecessitates further experimental investigations. mPPE spec-troscopy is a powerful tool for probing the relationshipbetween the electronic band structure and light–matterinteraction in the nonlinear regime.In this letter, we report the first experimental observationof the image-potential state (IPS) on Ir(111) using coherentfive-photon photoemission (5PPE) spectroscopy. The image-potential state is one of the important classes of unoccupiedstates. They are quantized electronic states arising from theCoulombic attraction between an electron and its inducedimage charge at a metallic surface. They are localized outsidethe surface and serve as model systems for electron-surfaceinteractions and quantum confinement. Their propertiesstrongly depend on surface screening, electronic structures,and dielectric responses, making them valuable probes ofsurface electronic properties. While IPSs have been wellstudied via 2PPE on noble metals like Ag12–15) andCu,14,16–18) these studies typically employ harmonic genera-tion to reach the required photon energy. In contrast, our useof 5PPE highlights the role of nonlinear excitation pathwaysand their sensitivity to band structure. Furthermore, to ourknowledge, no reports have been made on the clean Ir(111)surface. These results pave the way for further studies intolight–matter interaction in nonlinear regimes.The experiment was performed in a UHV chamber(2 × 10−10 Torr) with a Ti:sapphire oscillator (80 MHz)generating near-IR pulses at λ= 790 nm and 833 nm(ℏω= 1.57 eV and 1.49 eV) with laser powers of 1.1 Wand 1.2 W, respectively. The pulses (120 fs duration, 100 μmspot size) were focused onto the Ir sample. mPPE spectrawere measured in normal emission with the p-polarized lightincident at 45°. The Ir(111) surface was cleaned by sputteringand annealing, and its quality was confirmed by low-energyelectron diffraction and mPPE spectra. Photoelectrons weredetected with a hemispherical analyzer (Phoibos 100) and a2D detector, yielding Ef(k∥) spectra with 20 meV energyresolution.No signs of sample damage or signal distortion due tospace-charge effects19,20) were observed throughout theexperiment, and the corresponding stability was confirmedby the reproducibility of the multiphoton photoemissionspectra, even after prolonged irradiation of the same samplespot over several hours.We performed theoretical calculations using the computercode21) within the density functional theory (DFT) frame-work, combined with the embedded Green’s functiontechnique22) and the full-potential linearized augmentedplane-wave method23). This approach has been used tocalculate the electronic structure of semi-infinite Ir(001) andAu(001) surfaces24–26). We used the DFT-LDA exchange-correlation energy functional since DFT-GGA underesti-mates work functions of 5d metals typically by a few tenthsof eV. Furthermore, in order to be able to reproduce IPSs, theplanar average of the short-range DFT one-electron potential,Content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of thiswork must maintain attribution to the author(s) and the title of the work, journal citation and DOI.062001-1© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 18, 062001 (2025) LETTERhttps://doi.org/10.35848/1882-0786/addb1ehttps://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/addb1e&domain=pdf&date_stamp=2025-06-06https://orcid.org/0009-0000-3010-9283https://orcid.org/0009-0000-3010-9283https://orcid.org/0000-0002-6453-7435https://orcid.org/0000-0002-6453-7435https://orcid.org/0000-0002-0799-9772https://orcid.org/0000-0002-0799-9772https://orcid.org/0000-0003-2080-1561https://orcid.org/0000-0003-2080-1561https://orcid.org/0000-0001-8781-3650https://orcid.org/0000-0001-8781-3650https://orcid.org/0000-0003-4371-6116https://orcid.org/0000-0003-4371-6116mailto:clin@nycu.edu.twmailto:ARAFUNE.Ryuichi@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/addb1e¯ ( )V zeff with z being the surface normal coordinate, is admixedgradually with a model image-potential by using an inter-polation function proposed by Nekovee and Inglesfield 27) as⎡⎣⎢ ⎤⎦⎥( ) [ ( )] ¯ ( ) ( )( )( )V z z V z z Ez z114, 1eff vacimr r= - + --where Evac denotes the vacuum level, and ρ(z) variessmoothly from 0 at z zim= (the image plane) to 1 at z= zb(the embedding surface on the vacuum side). The effects ofthe asymptotic Coulomb potential beyond zb are incorporatedby the embedding potential acting on z= zb. The image plane( Åz 1.58im = ) position is determined by the center of massof the charge density induced by a weak static electric field,with the topmost Ir atom position defined as z = 0.27–30)Figure 1(a) shows the mPPE spectra of the clean Ir(111)surface at the Ḡ point. These spectra were measured using the1.57 and 1.49 eV laser photons, respectively. The workfunction was determined to be 5.83 eV from the lower cutoffenergy, consistent with previously reported values.31) Thesespectra result from 4PPE and 5PPE processes, as determinedby considering the photon energy and the measured workfunction. The solid curves in Fig. 1(a) are the fitting curves,which determine the peak positions and intensities of thespectra. The peak positions are 6.68 and 6.60 eV excited by1.57 and 1.49 eV photons, respectively. The photoemissionintensity excited by 1.57 eV photons is stronger than that of1.49 eV photons. At the Ḡ point, the intensity of the peakexcited by 1.57 eV photons, determined from the fitting, is0.28 cps, while that of 1.49 eV photons is 0.08 cps. Thisintensity difference arises from the difference in the densityof states (DOS) of the initial states corresponding to the twophoton energies, as will be discussed later.To understand the origin of the peaks observed in Fig. 1(a),we have examined their assignment based on spectral andmomentum-resolved characteristics. The band dispersion isevaluated from the momentum-resolved mPPE spectra shownin Fig. 1(b). The parabolic shape of the band yields an effectivemass of (1.1 ± 0.1)mo (where mo is the free-electron mass),showing a characteristic of IPS. However, it should benoted that the IPS of clean Ir(111) has not been determinedexperimentally. A careful analysis is required for thedefinitive assignment. In order to firmly assign the observedpeak to IPS, we consider the possible excitation pathways inthe mPPE process. The difference between the final-stateenergies (6.68 and 6.60 eV) matches the difference inphoton energies (1.57 and 1.49 eV), suggesting a commonintermediate state located at 5.11 eV above the Fermi level.This value indicates that four photons were absorbed forexcitation from the initial occupied state to the intermediatestate, followed by the additional photon causing an electronto emit into vacuum, as shown in Fig. 1(c). From the energyposition, the effective mass, and the band shape, weconclude that this peak originates from IPS.We further compare the energy position of experimentalobservation with theoretical predictions to validate the IPSassignment. The observed IPS (n = 1) is at 0.73 eV below thevacuum level at the Ḡ point. Figure 2 shows the intensity ofmomentum-resolved DOS calculated in the first layer of theIr(111) surface, consistent with prior findings32). The brightregion corresponds to a projected bulk band gap. In contrast,the dark-gray regions on the higher-energy sides are pro-jected bulk bands of Ir, except for the parabolic regionE− EV⩾ℏ2k2/2mo, which corresponds to the projection of theenergy continuum of the semi-infinite vacuum. The series ofIPSs (n= 1, 2,…) appeared inside the projected band gap atthe Ḡ point, exhibiting free-electron-like parabolic energydispersions with k. We obtained 5.88 and 0.63 eV as thework function and the binding energy referred to the vacuumlevel at the Ḡ point of the n = 1 IPS, respectively. Thesevalues agree well with our experimental values. Thesecalculation results further support our assignment.On most (111) surfaces of FCC metals, an energy gap existsaround the vacuum level and Ḡ point, which is a requisite forIPSs. While image-potential-included ab-initio calculated(a)(b)(c)Fig. 1. (a) The mPPE spectra of the clean Ir(111) surface excited with 1.57and 1.49 eV photons at the Ḡ point. Solid curves are peak-fitting (Lorentzian)results to evaluate the peak position and intensity. (b) The momentumresolved mPPE spectra excited with ℏω = 1.57 eV photons. A color barindicates photoemission intensity, while the dashed parabola highlights banddispersion. (c) Schematic illustration of the mPPE pathway leading to the firstIPS and subsequent photoemission at the Γ point of the Ir(111) surface. Thethree horizontal brown lines show the calculated IPSs (see Fig. 3 for wavefunctions and binding energies). Under four-photon absorption from aninitial state at the Γ point, electrons are excited to the first IPS before a fifthphoton emits them into vacuum.Fig. 2. (a) A log-intensity map of first-layer DOS, ρ(k, ò), for the Ir(111)surface electronic structure along the M-Γ-K direction. The blue and purplearrows highlight the four-photon photoexcitation pathways for the 1.57 eVand 1.49 eV conditions, respectively, illustrating how electrons transitionfrom initial states below the Fermi level to populate the IPS. The blue andpurple circles mark each excitation energy’s initial state. (b) The Γ pointDOS, averaged over the topmost five layers and incorporating an imaginaryenergy γ = 10 meV, highlights the initial states involved in the multiphotonexcitation processes at the two photon energies.062001-2© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 18, 062001 (2025) Y.-C. Tai et al.semi-infinite Ir(111) surface electronic structure providesdetailed insight, it is also informative to consider establishedanalytical models that describe IPS formation 1,15,33–36). Theanalytical model often makes it easier to understand how theresults depend on various parameters intuitively. Chulkovet al.35) developed a one-dimensional pseudo-potentialmodel to predict the binding energies of IPSs on such metalsurfaces. The model potential is represented by the fol-lowing formula:⎧⎨⎪⎩⎪( )( )( )( )( )( )( )/V zA A z a zA A z z zA e z z zz zcos 2 , 0cos , 0,2mz zez z10 120 2 13,1 im14 imz z1imimpb=- +- + <- <<a- ---l- -The potential V(z) and its derivative must be continuous atthe matching points z1 and zim, leaving four independentparameters (A1, A10, A2, β) to describe the potential profile:A1 and A10 govern the periodic potential below the surface,while A2 and β control the smooth transition to theasymptotic image-potential. Armbrust et al.36) estimated theparameters from the experimental results on the IPSs of thegraphene-covered Ir(111), as no such data were available forclean Ir(111). Here, we examine the validity of the para-meters they estimated by using our experimental results.Figure 3 shows the wave functions of the first three IPSs withthe model potential. The binding energies of them at the Ḡpoint are represented by the brown horizontal bars inFig. 1(c). The excited electron in the n = 1 IPS is mostlikely localized at 3.25 Å from the Ir(111) surface. Thebinding energy of the n = 1 IPS is 5.094 eV above the Fermilevel (−0.741 eV concerning the vacuum level), which isvery close to the experimental value.Having established the nature and energy of the IPS, wenow assess the efficiency of the multiphoton excitationpathways that lead to its population. As described above,the IPS peak intensity under 1.57 eV excitation (0.28 cps) isnotably higher than that under 1.49 eV excitation (0.08 cps),as determined from the peak fittings in Fig. 1(a). We havecarefully aligned the laser and sample positions to theanalyzer to ensure the two spectra are directly comparable.(The mPPE intensity is more susceptible to the laser fluenceand the sample position than in the 1PPE experiments; suchhigh sensitivity enables precise alignment.) To model theintensity, we adopt the general power-law dependenceI= c · Pm, where P is the excitation power and m = 5corresponds to the order of the nonlinear process. We furtherassume that the prefactor c reflects initial-state properties,mainly the local DOS at the excitation energy. This approachparallels the standard ARPES intensity expressionI∝ ∣M∣2ρ(ò), where ρ(ò) is the initial-state DOS and M thetransition matrix element. Assuming the matrix elements forthe excitation from the d-band to the IPS are comparable forboth photon energies, the intensity ratio can be primarilyattributed to differences in the initial-state DOS.To support this interpretation, in Fig. 2(b), we show our DFT-calculated DOS averaged over the topmost five layers. Toaccount for spectral broadening due to the lifetime effects andthe finite energy resolution, the DOS was calculated with animaginary energy γ= 10meV. Compared with the previousARPES measurement at the Ḡ point 37), the Ir d-band exhibits apronounced DOS peak near −1.15 eV. The 1.57 eV excitationaccesses an initial state of −1.18 eV, which is very close to thishigh-DOS region, enhancing the 5PPE transition probability. Incontrast, reducing the photon energy to 1.49 eV shifts the initialstate upward by approximately 320 meV, distancing it from thed-band peak and significantly reducing the local DOS availablefor excitation. The qualitative agreement with published ARPESdata and the observed intensity ratio confirms that the enhanced5PPE signal under 1.57 eV excitation can be attributed to itsfavorable alignment with a high-DOS region of the Ir d-band.These observations highlight how subtle changes in excitationenergy significantly alter the photoemission signal through theirinfluence on the initial-state DOS. While the present studyemploys two photon energies, which we find sufficient tosupport our main conclusions, systematic photon-energy-depen-dent measurements, in combination with ARPES, would enableus to more precisely analyze how the band structure influencesthe multiphoton excitation process.Identifying higher-order (n⩾2) IPSs and observing higher-order photoemission processes (m⩾6), even for n = 1 IPS,remains challenging. The above theoretical calculation showsthat 1.57 and 1.49 eV photons have sufficient energy toexcite the occupied electron to the higher-order IPSs via the5PPE process. However, the transition to the higher-orderIPSs is less likely compared to the n = 1 IPS because theirwave functions are spatially farther from the solid surface, asshown in Fig. 3. For example, the IPSs of Cu(001) measuredby using 2PPE, the intensity of 2PPE peak is approximatelyproportional to n−2 1). Although this n−2 scaling is derivedfrom 2PPE, it provides a reasonable first-order estimate forthe attenuation trend in higher-order processes. This attenua-tion of intensity poses challenges, especially in detectinghigher-order states. The 6PPE process provides a possibilityto overcome this challenge. In this scenario, four photons areused to excite the electron from the occupied states to theIPS, and two photons are used to excite it to emit intovacuum. Reutzel et al. have succeeded in detecting the 6PPEspectrum of the Cu(111), Ag(111), and Au(111) 6). In their(a)(b)Fig. 3. (a) A one-dimensional pseudo-potential model was used todetermine the binding energies of IPSs at the Γ point of the Ir(111) surface.The corresponding eigenfunctions for the first three IPSs are shown,illustrating that the first IPS wavefunction (z > 0) localizes the image-potential charge about 3.25 Å from the Ir(111) surface. (b) The calculatedbinding energies of these three IPSs, approximated using the Rydbergformula En = − 0.85/(n + a)2 with a 7.03 × 10−2 quantum defect.062001-3© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 18, 062001 (2025) Y.-C. Tai et al.experiments, the initial occupied state is a surface state withhigh DOS. They observed m= 4 to 6 photon photoemissionspectra of the surface state and showed that the 6PPEintensity is at least ten times weaker than the 5PPE intensity.We suppose that the ratio of the 6PPE intensity to the 5PPEintensity of the IPS is also attenuated in the same order. Suchweak 6PPE signals fall below our detection threshold,making them difficult to observe. Note that the 6PPE spectraof the IPSs have not been observed in the literature. It wouldbe interesting to detect this 6PPE, 3PPE by using second-harmonic generated photons or other combinations of thephoton energies38,39) from the perspective of the physics ofmultiphoton excitation on solid surfaces.In summary, we have measured 5PPE spectra of the cleanIr(111) surface and determined the energy position of the firstIPS. Furthermore, our mPPE results disclose how the surfaceelectronic structure and DOS govern multiphoton excitationpathways, eventually dictating the observed spectra. Theseresults exemplify the applicability of mPPE spectroscopy forprobing initial, intermediate, and final states in complexexcitation processes and enrich our understanding of howIPSs in high-work-function transition metals are populatedvia multiphoton excitation. Future investigations may focuson time-resolved studies to measure IPS’s lifetime or extendthis approach to other metallic surfaces with varyingscreening properties, expanding our understanding of non-linear photoemission dynamics at metal-vacuum interfaces.Acknowledgments This work was financially supported by JSPSKAKENHI (Grant No. 22H0196) and the World Premier International ResearchCenter Initiative (WPI) on Materials Nanoarchitectonics, MEXT, Japan. TheNational Science and Technology Council (NSTC) of Taiwan supported thisstudy, in part, under the contracts of NSTC 113-2119-M-A49-001-MBK,113-2112-M-A49-020-MY3, 114-2923-M-A49-001-MY2, 113-2628-M-A49-006-MY3, 112-2923-M-A49-001-MY2, and NSTC T-Star Center Project, FutureSemiconductor Technology Research Center, under NSTC 114-2634-F-A49-001-.ORCID iDs Yu-Chan Tai https://orcid.org/0009-0000-3010-9283Chih-Wei Luo https://orcid.org/0000-0002-6453-7435Noriaki Takagi https://orcid.org/0000-0002-0799-9772Hiroshi Ishida https://orcid.org/0000-0003-2080-1561Chun-Liang Lin https://orcid.org/0000-0001-8781-3650Ryuichi Arafune https://orcid.org/0000-0003-4371-61161) U. Höfer, I. L. Shumay, C. Reuß, U. Thomann, W. Wallauer, and T. Fauster,Science 277, 1480 (1997).2) H. Petek, M. J. Weida, H. Nagano, and S. Ogawa, Science 288, 1402 (2000).3) T. Kiss et al., Phys. Rev. Lett. 94, 057001 (2005).4) R. Arafune, K. Hayashi, S. Ueda, Y. Uehara, and S. Ushioda, Phys. Rev.Lett. 95, 207601 (2005).5) J. 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