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[Ryuichi Arafune](https://orcid.org/0000-0003-4371-6116), [Hiroshi Ishida](https://orcid.org/0000-0003-2080-1561), [Chun-Liang Lin](https://orcid.org/0000-0001-8781-3650), [Noriaki Takagi](https://orcid.org/0000-0002-0799-9772)

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[Probing moiré Bloch bands of photoexcited electrons on graphene/Ir(111)](https://mdr.nims.go.jp/datasets/e41edaba-f1cb-43ae-8ce8-fc536d0ee567)

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Probing Moiré Bloch Bands of Photoexcited Electrons on1Graphene/Ir(111)2Ryuichi Arafune  ,1 Hiroshi Ishida  ,2 Chun-Liang Lin  ,3 and Noriaki Takagi  431Research center for materials nanoarchitectonics (MANA),4National Institute for Materials Science (NIMS), Tsukuba, Japan∗52College of Humanities and Sciences, Nihon University, Tokyo, Japan63Dept. of Electrophysics, National Yang Ming Chiao7Tung University (NYCU), Hsinchu City, Taiwan84Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan9(Dated: October 3, 2025)101https://orcid.org/0000-0003-4371-6116https://orcid.org/0000-0003-2080-1561https://orcid.org/0000-0001-8781-3650https://orcid.org/0000-0002-0799-9772Abstract11We have investigated the moiré Bloch bands of photoexcited electrons in image potential states12(IPS) on graphene covered Ir(111) surfaces using high-energy-resolution angle-resolved two-photon13photoemission spectroscopy. An energy gap of approximately 20 meV at the K̄ point of the moiré14Brillouin zone is resolved. The band structure is well reproduced by density functional theory15(DFT) combined with the embedded Green’s function technique. A simplified periodic potential16model, whose spatial distribution shows close agreement with the DFT results, also describes the17system well. These findings demonstrate that the electronic band structure of photoexcited states18can be engineered solely via moiré potential modulation. This opens a new avenue for excited-19state band engineering and the design of ultrafast optoelectronic functionalities in moiré-engineered20materials.21When a two-dimensional (2D) material is grown on a crystalline surface, or when multiple222D materials are stacked with a mismatch in their lattice periodicities or orientations, spa-23tial interference patterns known as moiré structures emerge[1]. Although moiré structures24were once appreciated mainly for their geometric aesthetics and usefulness in structural25analysis[2], their functional significance has come into focus more recently. In particular,26novel electronic transport phenomena arising from the moiré superlattice, such as the emer-27gence of superconductivity and Mott insulating states in twisted bilayer graphene at so-called28“magic angles” [3, 4] and fractal electronic spectra known as Hofstadter’s butterfly [5], are29regarded as one of the most impactful advances in condensed matter physics in the past30decades.31The relevance of moiré superlattice have been recognized also in optical processes. For ex-32ample, spatially localized excitons in moiré superlattices formed by stacked transition metal33dichalcogenides[6] has opened new possibilities for controlling photoexcitation and light–34matter interactions. However, in contrast to electronic transport, the implications of moiré35effects in optical phenomena remain poorly understood. To gain a deeper understanding36of such optical properties, it is important to focus on moiré Bloch bands[7], which played37a crucial role in explaining exotic electronic behavior. These miniband structures, formed38via hybridization of electronic states under the long-range periodic potential of the moiré39pattern, may also be key to understanding moiré-modified light–matter interactions.4041∗ ARAFUNE.Ryuichi@nims.go.jp2mailto:ARAFUNE.Ryuichi@nims.go.jpFIG. 1. (a) Scanning tunneling microscope (STM) image of graphene covered Ir(111) (Gr/Ir(111))surface, showing the formation of long-period moiré superlattice due to the lattice mismatch be-tween graphene and Ir(111) surface. The bias voltage and the tunneling current were set to -80 mVand 1.2 nA, respectively. (b) Brillouin Zones (BZs) of the Ir(111) surface and graphene lattices,drawn to scale. The moiré BZ, indicated by the red hexagon, shows a significantly reduced size,enabling the emergence of miniband. (c) LEED picture of Gr/Ir(111), showing sharp diffractionspots from Ir, carbon and the surrounding moiré satellites, indicating high structural quality anduniformity of the sample surface.In this Letter[8], we report the experimental observation of moiré Bloch bands of photoex-42cited electrons in image potential states (IPS) on the graphene-covered Ir(111) (Gr/Ir(111))43surfaces (Fig. 1), by using high-resolution angle-resolved two-photon photoemission (HR-44AR2PPE) spectroscopy [9, 10]. As shown in Fig. 1(a), Gr/Ir(111) provides a well-defined45moiré superlattices with a periodicity of approximately 25 Å, which is much larger than46the lattice constant of graphene (2.46 Å) and Ir(111) (2.72 Å) [11, 12]. It is widely ac-47cepted that the (10×10) supercell of graphene on the (9×9) cell of Ir(111) well describes48the Gr/Ir(111) superlattices, with the lattice vectors of graphene and Ir(111) being aligned49in orientation [11, 12]. Thus, the Brillouin zones (BZ) of these two surfaces and resulting50moiré BZ are drawn as shown in Fig. 1(b). IPS are quantized electronic states formed by the51Coulomb attraction between an electron and its induced image charge at a metallic surface.52Owing to their well-defined nature and surface sensitivity, IPS serve as an ideal platform53for investigating photoexcited carrier dynamics, including energy relaxation and quantum543interference phenomena on solid surfaces[13, 14]. We expected that their surface sensitivity55makes IPS particularly suitable for probing moiré potential effects, such as the formation of56moiré bands in photoexcited states. Previous works investigated IPS on graphene-covered57metal surfaces[15–20], revealing the energy positions, lifetimes, and the effective masses.58On certain metal surfaces such as the Ru(0001), graphene forms a relatively large rippled59structure, which leads to a band splitting of the IPS state[15]. However, the effect of the60moiré superlattice on the electronic structure of IPS has not been fully explored, and, to61our knowledge, the opening of a gap in the moiré Bloch bands of the unoccupied states has62not been reported. This motivates our present study on Gr/Ir(111) IPS, where we directly63probe the moiré-induced electronic reconstruction in the unoccupied states64The experimental setup consisted of a laser system and an ultra-high vacuum (UHV)65electron spectroscopy system. A Ti:sapphire laser oscillator generated infrared (IR) pulses66with 2.0 ps duration at 80 MHz. Part of the IR output was converted to ultraviolet (UV)67light using nonlinear crystals. P-polarized IR and UV pulses were aligned collinearly and68focused onto the sample. Two-photon photoemission (2PPE) measurements were conducted69in an ultra-high vacuum system with a base pressure below 7 × 10−11 mbar. The sample70temperature was held at 11 K during the measurements. Energy and momentum resolutions71were 9.5 meV and better than 0.01 Å−1, respectively. Graphene was grown by a two-step72thermal decomposition of ethene [11, 21] on the clean Ir(111), confirmed by a sharp moiré73induced spots in low energy electron diffraction (LEED) as shown in Fig. 1(c). First-74principles calculations were performed using density functional theory (DFT) combined75with the embedded Green’s function and full-potential linearized augmented plane-wave76methods[22–25] for modeling graphene on the semi-infinite Ir(111) substrate. The DFT77potential V̄eff(z) was smoothly matched to a classical image potential[26] to describe IPS.78Experimental and computational details are provided in the Supplemental Material[8], which79includes the following literatures [10, 11, 21–37].80Figure 2 shows the HR-AR2PPE spectra for the first IPS of Gr/Ir(111). The pump and81probe photon were 4.401 and 1.467 eV, respectively. At normal emission, the peak was82located at 5.308 eV with a width of 56 meV, indicating the binding energy of IPS with83respect to the vacuum level is -0.849 eV (The workfunction determined from the vacuum84level cutoff was 4.69 eV.). Unlike the 2PPE data of IPS on noble metal such as Cu(001) and85Ag(001), the maximum intensity does not occur at the bottom of the band. This strong864intensity originates from the surface resonances of the Ir(111) in the occupied region [37].87This surface resonance is known as a Rashba-type spin-split hole-like band. Although the88intensity is weak, photoelectrons coherently excited from the surface resonance state are89indeed observed[8]. These values and features are consistent with the previous report [17].90FIG. 2. Angle resolved two-photon photoemission spectra of graphene covered Ir(111). At lowangles, a single peak appears at around 5.3 eV final-state energy. The final state energy refers tothe excited state energy measured from the Fermi level. As the emission angle increases, a shoulderemerges and evolves into a pronounced double-peak structure, clearly visible at 23◦, indicating anenergy gap of ∼20 meV at the K̄ point of the moiré BZ. This angular-dependent splitting providesdirect experimental evidence of the formation of moiré Bloch bands in the unoccupied electronicstructure.Importantly, while a single peak is observed at low emission angles, the spectra exhibit a915pronounced double-peak structure at higher emission angles. As the emission angle increases,92a shoulder starts to develop around 17◦. At 23◦, the spectrum clearly exhibits a double-peak93structure, with an energy separation of 62 meV between the peaks. This splitting clearly94demonstrates the presence of an energy gap in the unoccupied electronic states, providing95direct experimental evidence of the moiré-induced band modification. By spectral fitting96using two Lorentzian curves, we have evaluated the energy gap at the K̄ point of the moiré97BZ to be 20 meV[8].98Figure 3 shows the log-intensity map of the electronic structure of moiré Bloch band99arising from IPS of Gr/Ir(111). This data is obtained form the HR-AR2PPE spectra taken100by using another photon energy pair: 1.600 + 4.800 eV. The measured IPS spectra along101the kx direction (along Γ̄-K̄, see Fig. 1(b)) show the energy splitting induced by the moiré102potential. We confirmed that the location of the energy gap in the momentum axis and its103magnitude are essentially independent of the excitation photon energy. Furthermore, one104can see the folded band appears well. These features also clearly imply a robust feature of105the moiré superlattice.106The emergence of the moiré band with an energy gap is supported by DFT calculations. In107supplemental materials[8], the calculated band dispersion was imposed on the experimental108results (see. Fig. S3). Since the band splitting due to spin-orbit coupling was less than a few109meV, we plotted the energy dispersion averaged over two spin components. The calculated110energy levels have been shifted upward by 80 meV to align the experimental results. Note111that the actual binding energy discrepancy between the experimental and theoretical energy112values is larger when considered relative to the vacuum level. The calculated work function113was 4.847 eV, resulting in a binding energy discrepancy of -89 meV. The calculated energy114gap at the K̄ point of the moiré BZ was 22 meV. Although the energy values does not precisely115reproduce the experimental results, the overall band structure shows good agreement with116the measurements.117118Since the electron in IPS essentially behaves as the free electron, the moiré Bloch band119arising from IPS is expected to be well described by a simplified nearly free-electron (NFE)120model under a periodic moiré potential. By fitting the DFT-calculated dispersion, we obtain121an effective mass equal to the free-electron mass, along with a complex Fourier coefficient122of the moiré potential V : V = α + iβ, where α = 7.5 meV and β = 1.1 meV. This confirms123that the essential features of the moiré band, including the energy gap at the K̄ point, can1246FIG. 3. A log-intensity map of electronic structure of moiré Bloch band arising from IPS ofGr/Ir(111). The kx direction is along the Γ̄-K̄ direction in BZ, as shown in Fig. 1(b). The pumpand probe photon energies were 4.800 eV and 1.600 eV, respectively. The vertical dotted linedenotes the BZ boundary in the Γ̄-K̄ direction for the moiré BZ. The folded features match wellwith the theoretical prediction, despite weak intensity. The clear splitting observed near the K̄point evidences the opening of a moiré-induced energy gap.be quantitatively described by NFE model. Details of the model and the resultant fitting125curves are provided in the Supplemental Material[8], which shows that the NFE model nearly126perfectly reproduces both the experimental and DFT results.127Now let us examine the effective potential landscape induced by the moiré superlattice128in the electronic system. Figure 4(a) presents a contour map of the potential distribution1297obtained from the NFE model, while Fig. 4(b) shows that derived from DFT calculations.130The height of the potential distribution in the plot (b) was determined by referencing the131charge density distribution along the surface normal. The first moment of the charge density132distribution was found to be 6 Å (Fig. 4(c)), and this value was used as the reference height.133While the potential distribution derived from the DFT calculations includes contributions134from atomic cores, the overall landscape of the potential is well reproduced by NFE model.135The situation α ≫ β implies that the system is essentially characterized by the sixfold136rotational symmetry, and the difference between the hcp and fcc sites in Gr/Ir(111) can be137neglected as shown in Fig. 4. This comparison further reinforces the interpretation that the138observed energy gap originates from the moiré potential.139140As shown in Fig. 3, the energy gap opens in the energy dispersion relation of the first141IPS alone, while no gap is observed in the higher order (n ≥ 2) IPS. This is consistent with142the theoretical prediction that the spatial variation of the moiré potential for the higher143order IPS is too weak to open the gap. It is well known that the first moment of the144wave function, and thus that of the charge distribution, moves farther from the surface as n145increases [13, 31]. This means that the electron in the higher order IPS feels a weaker moiré146potential, resulting in no gap opening. Indeed, the first moment of the charge distribution for147the second IPS is located at around z ∼ 14 Å in our DFT calculations as shown in Fig. 4(c).148Note that in Fig. 4(c), zb[8] denotes the position above the plane of the embedding surface149on the vacuum side. In our calculation, we assume that at this position the potential curve150is given by the classical image potential and is independent of x and y. This corresponds to151α = β = 0 in the NFE model, resulting in no energy gap. This result suggests that energy152gap can be controlled by tuning the modulation of the moiré potential.153We note that the IPS are free-electron-like states and therefore isotropic in k (i.e., the154constant energy surface should be circular). However, the moiré potential is not isotropic155and has a specific symmetry (see, e.g., the occupied spectrum in ref.[38]). In the present156work, we have measured the spectra only along the Γ̄–K̄ direction, but measurements along157other directions are planned for future studies to further explore the effects of the moiré158symmetry on the IPS. Our DFT calculations indicate that the band gap at the M̄ point is159about 15 meV, slightly smaller than that at the K̄ point. The NFE model also reproduces160this band gap at the M̄ point, although experimental confirmation is still required.161Before concluding, we would like to discuss the impact of the graphene structure on1628FIG. 4. (a) Contour map of the potential distribution calculated from the nearly free electron modeldescribed in the Supplemental Material. (b) Corresponding electrostatic potential distribution ata height of z = 6 Å above the Ir substrate, obtained from DFT calculations. The qualitativeagreement between (a) and (b) supports the validity of the simplified model. (c) Planar-averagedcharge density (ρ) distribution of IPS (n = 1, 2) at the K̄ point of the moiré BZ, which is used todetermine the effective height for evaluating the lateral potential distribution. The vertical dashdot line at z = 3.40 Å indicates the average height of the carbon atoms of graphene. The verticaldot lines at z = 4.13 Å and at z = 10.3 Å indicate the height of the image plane (zim), andthe plane of the embedding surface (zb), respectively. For z > zb, we model the potential as theclassical image potential. The triangles indicate the height corresponding to the first moment ofthe charge density distribution for IPS (blue: n = 1, orange: n = 2).9Ir(111) surface. It is well accepted that the graphene forms a rippled structure on the163Ir(111) surface [11, 12], and our calculations take this into account. The ripple amplitude164is smaller than that of graphene on the Ru(0001)[15]. As a result, we cannot identify the165energy splitting, even though the energy resolution of our experimental setup was better166than in previous works [16–20]. Nevertheless, the presence of this small ripple structure is167still significant. The periodicity of the rippled structure is identical to that of the moiré168superlattice. Which of the two, then, is fundamentally responsible for the origin of the gap169formation? In this context, we recently have demonstrated that the surface corrugation170caused by the surface reconstruction induces the energy gap of IPS[32]. To answer this171question, we have performed DFT calculations for flat graphene on the Ir(111) surface.172Despite the absence of the rippled structure, an energy gap is still observed in the calculated173band dispersion of IPS, and the magnitude of the gap was essentially identical to that174of the rippled graphene system. This result indicates that the gap formation originates175solely from the geometric moiré structure. Although macroscopic wrinkles may exist due to176thermal expansion mismatch between graphene and Ir[39], these features are non-periodic177and are unlikely to affect the moiré-induced gap observed in our measurements. This is178consistent with the sharp LEED spots across the sample. Beyond confirming the structural179origin of the gap, this result implies that moiré potentials can be used to deliberately tailor180the unoccupied electronic structure of excited states. This establishes a new conceptual181framework for excited-state band engineering using structural moiré design alone, without182relying on external fields or chemical modifications.183In conclusion, we have experimentally demonstrated the formation of moiré Bloch bands184with an energy gap in the unoccupied image-potential states of Gr/Ir(111), supported by185DFT calculations and a simple NFE model. The observed energy gap originates solely186from the geometric moiré potential. These findings provide direct evidence that excited-187state electronic bands can be modulated by structural moiré design, establishing a new188approach to excited-state band engineering. 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