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Jan Philipp Bange, David Schmitt, Wiebke Bennecke, Giuseppe Meneghini, AbdulAziz AlMutairi, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Daniel Steil, Sabine Steil, R. Thomas Weitz, G. S. Matthijs Jansen, Stephan Hofmann, Samuel Brem, Ermin Malic, Marcel Reutzel, Stefan Mathias

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[Probing electron-hole Coulomb correlations in the exciton landscape of a twisted semiconductor heterostructure](https://mdr.nims.go.jp/datasets/f2c078c4-90f8-47f1-8572-377b64af403b)

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Probing electron-hole Coulomb correlations in the exciton landscape of a twisted semiconductor heterostructureBange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e1 of 8O P T I C SProbing electron-hole Coulomb correlations  in the exciton landscape of a twisted semiconductor heterostructureJan Philipp Bange1, David Schmitt1, Wiebke Bennecke1, Giuseppe Meneghini2,  AbdulAziz AlMutairi3, Kenji Watanabe4, Takashi Taniguchi5, Daniel Steil1, Sabine Steil1,  R. Thomas Weitz1,6, G. S. Matthijs Jansen1, Stephan Hofmann3, Samuel Brem2, Ermin Malic2,7, Marcel Reutzel1*, Stefan Mathias1,6*In two-dimensional semiconductors, cooperative and correlated interactions determine the material’s excitonic prop-erties and can even lead to the creation of correlated states of matter. Here, we study the fundamental two-particle correlated exciton state formed by the Coulomb interaction between single-particle holes and electrons. We find that the ultrafast transfer of an exciton’s hole across a type II band-aligned semiconductor heterostructure leads to an un-expected sub-200-femtosecond upshift of the single-particle energy of the electron being photoemitted from the two-particle exciton state. While energy relaxation usually leads to an energetic downshift of the spectroscopic signa-ture, we show that this upshift is a clear fingerprint of the correlated interaction of the electron and hole parts of the exciton. In this way, time-resolved photoelectron spectroscopy is straightforwardly established as a powerful method to access electron-hole correlations and cooperative behavior in quantum materials. Our work highlights this capabil-ity and motivates the future study of optically inaccessible correlated excitonic and electronic states of matter.INTRODUCTIONAn exciton is a prime example of a quasiparticle that is built up by electrons and holes bound together via Coulomb interaction. As in the case of a hydrogen atom, the exciton’s properties are described by its quantum number, its binding energy, and its Bohr radius (1). For low-dimensional materials, these key parameters can be sub-stantially altered by cooperative interactions with surrounding qua-siparticles (2, 3). To study such cooperative and emergent behavior, artificial stacks of two-dimensional transition metal dichalcogen-ides (TMDs) have been shown to provide an exceptional playground for manipulating exciton properties. Examples include the ultrafast formation of interlayer excitons whose electron and hole compo-nents are charge-separated across the neighboring TMD layers (4–8), the confinement of excitons in a moiré potential well (9–12), the creation of correlated interlayer exciton insulators (13, 14) and ex-citon crystals (15, 16), and even the stabilization of Bose-Einstein condensates (17).It is therefore of fundamental importance to obtain insight into the energy landscape and the ultrafast dynamics of the two-particle correlated exciton state (18, 19). In TMD semiconductors, momentum-indirect and spin-forbidden excitons play a substantial role but are mostly inaccessible (7, 20) using all-optical experimental techniques (21, 22). Recently, time- and angle-resolved photoelectron spectroscopy (trARPES) experiments have been shown to be a pow-erful technique to fill this gap and to simultaneously probe the energy landscape and dynamics of optically bright and dark excitons in monolayer (23–25) and twisted bilayer (8, 12, 26, 27) TMDs. When using photoelectron spectroscopy, there is a fundamental aspect that needs to be considered (Fig. 1A): In the photoemission process, the Coulomb correlation between the electron and hole components of the exciton is broken. This is because a single-particle photoelectron is collected with the detector and a single-particle hole remains in the material (28–31). In consequence, photoelec-trons originating from excitons are detected at the exciton bind-ing energy below the conduction band minimum (8, 23–25, 32) and show a hole-like energy-momentum dispersion (32, 33). In this way, trARPES provides natural access to the electron contribution of the exciton and can be used to quantify the charge transfer of the exciton’s electron across a type II band-aligned heterostructure (Fig. 1B) (8, 27). However, to this day, only very limited energy- and momentum-resolved spectroscopic information on the exciton’s hole component is reported (12). Specifically, in contrast to all-optical spectroscopies (4–6, 18, 34–37), it has not been shown that trARPES can be applied to monitor the charge-transfer dynamics of the exciton’s hole across the TMD interface (Fig. 1C).Here, we demonstrate how the Coulomb interaction between the electron- and the hole components of the intra- and interlayer exci-tons facilitates the study of the ultrafast hole-transfer mechanism in a twisted WSe2/MoS2 heterostructure. We experimentally observe an increase in the exciton’s photoelectron energy upon the hole-transfer process across the interface. This is unexpected at first be-cause the electron remains rigid in the conduction band minimum during this hole-transfer process (Fig. 1C) and because any relax-ation mechanism is typically expected to cause an overall decrease in the measured electronic quasiparticle energies. However, when taking the correlated nature of the electron-hole pair into account, despite an overall decrease in the quasiparticle energies, we show that such an increase due to hole transfer must be expected for the corresponding exciton’s photoelectron. Our work provides micro-scopic insights into the ultrafast hole-transfer mechanism and, more 1I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany. 2Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany. 3Department of Engineering, University of Cambridge, Cambridge CB3 0FA, UK. 4Research Center for Functional Materials, National Insti-tute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 6International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany. 7De-partment of Physics, Chalmers University of Technology, Gothenburg, Sweden.*Corresponding author. Email: marcel.​reutzel@​phys.​uni-goettingen.​de (M.R.); smathias@​uni-goettingen.​de (S.M.)Copyright © 2024 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY). Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024mailto:marcel.​reutzel@​phys.​uni-goettingen.​demailto:smathias@​uni-goettingen.​demailto:smathias@​uni-goettingen.​dehttp://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adi1323&domain=pdf&date_stamp=2024-02-07Bange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e2 of 8generally, highlights the potential of time-resolved momentum mi-croscopy to probe optically inaccessible correlated excitonic and electronic states of matter.RESULTSEnergy landscape and photoemission fingerprints of bright and dark excitonsWe start the analysis of the hole-transfer dynamics by first calculat-ing the full energy landscape and formation dynamics of bright and dark excitons in the twisted WSe2/MoS2 heterostructure on a micro-scopic footing (details in Supplementary Text). The optically excited A1s excitons in the WSe2 and the MoS2 layer and their cascaded re-laxation via layer-hybridized excitons to the lowest energy interlayer excitons are illustrated in Fig. 2A. If the heterostructure is excited resonantly to the A1s-exciton of WSe2 with 1.7 eV pulses, then only intralayer KW-KW A1s excitons are optically excited and decay in a cascaded transition via layer hybridized KW-Σ excitons to interlayer KW-KMo excitons, as we have discussed in detail in our earlier work (8, 27) (i.e., KW-KW → KW-Σ → KW-KMo; Fig. 2A, left-hand side). In the single-particle picture, this cascaded transition can be associated with the transfer of the exciton’s electron across the TMD interface (Fig. 1B).Complementary, if the hole-transfer process across the WSe2/MoS2 interface is considered (Fig. 1C), then the dynamics must be initiated by an excitation of MoS2 A1s excitons with 1.9 eV light pulses (KMo-KMo excitons in Fig. 2A, right-hand side). Exploiting the density matrix formalism, we calculate the excitonic energy landscape (details below), and track the exciton dynamics, finding that the most efficient mechanism to form interlayer KW-KMo exci-tons occurs via layer hybridized Γ-KMo excitons, where the exciton’s electron resides in the KMo valley of MoS2 and the exciton’s hole can be found in the layer-hybridized valence bands at the Γ valley (38). Hence, the hole-transfer dominantly occurs via the KMo-KMo → Γ-KMo → KW-KMo exciton cascade.To differentiate the spectral contributions of different excitons in the experiment, we apply our setup for femtosecond momentum microscopy (39, 40) that provides direct access to the photoemission energy-momentum fingerprint of excitons (Fig. 2, B to E). In Fig. 2E, the momentum map of the intralayer KMo-KMo exciton is shown af-ter resonant optical excitation with 1.9-eV pump pulses. Photoelec-trons are detected at the in-plane momenta of the KMo and K′Mo valleys (0 ps). For better visibility, the Brillouin zone of MoS2 is over-laid in dark red. Because 1.9-eV pump photons also non-resonantly excite KW-KW excitons in WSe2, the momentum map in Fig. 2C shows photoemission yield at the KW and K′W valleys of WSe2 (or-ange hexagon, 0 ps). Note that the Brillouin zone of WSe2 is rotated by 9.8∘ ± 0.8∘ with respect to MoS2. Moreover, weak photoemission yield from hybrid KW-Σ excitons is detected at the Σ and Σ' valleys (grey hexagon). At a pump-probe delay of 10 ps (Fig. 2D), the major part of the intralayer excitons has decayed either via the electron- or the hole-transfer process, and spectral yield is dominated by the en-ergetically most stable excitation, i.e., the interlayer KW-KMo exci-tons (fig. S4). For these interlayer excitons, the electron and the hole contributions are now separated between both monolayers of the heterostructure, and the exciton photoemission momentum finger-print has to be described within the moiré mini-Brillouin zones built up by the κ valleys whose in-plane momentum can be constructed by the reciprocal lattice vectors of WSe2 and MoS2 (Fig. 2D, black hexagon) (8, 26).Hole- and electron-transfer dynamicsHaving identified the exciton fingerprints in the photoemission ex-periment, we can now proceed with the analysis of the hole-transfer dynamics. For this, fig. S4 provides an overview of the pump-probe delay-dependent evolution of photoemission intensity from intra-layer KMo-KMo and KW-KW excitons, the hybrid KW-Σ exciton, and the interlayer KW-KMo exciton after optical excitation with 1.9 eV (fluence: 140 μJ/cm2; optically excited exciton densities of 7 ×1011 Fig. 1. Probing Coulomb-correlated electron-hole pairs and their femtosec-ond dynamics using momentum microscopy. (A) Schematic illustration of the photoemission process from excitons. Visible femtosecond light pulses (red) are used to optically excite bright excitons that fully reside in the MoS2 monolayer. The transfer of the hole component into the WSe2 monolayer leads to the formation of charge-separated interlayer excitons (black arrow). A time-delayed extreme ultra-violet laser pulse (blue) breaks the exciton; single-particle electrons are detected in the photoelectron analyzer and single-particle holes remain in the WSe2 mono-layer. (B and C) Single-particle energy-level alignment of the valence and conduc-tion bands (v and c) of MoS2 and WSe2. KW-KMo excitons are formed due to interlayer charge transfer of the exciton’s hole or electron, respectively, from intra-layer KMo-KMo or KW-KW excitons. Note that in (C), the electron contribution to the exciton remains rigid in the conduction band minimum of MoS2 during the hole-transfer process. In the abbreviation of the excitons, the capital letters and the sub-scripts denote the valley (K, Σ, and Γ) and the layer (W and Mo) where the exciton’s hole (first letter) and electron (second letter) are localized. It is not differentiated between momentum-direct and momentum-indirect excitons (e.g., KW/Mo and K'W/Mo or Σ and Σ') because those cannot be differentiated in the photoemission experiment (see fig. S7).Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024Bange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e3 of 8and 3.5 ×1012 cm−2 in WSe2 and MoS2 (41), respectively). The for-mation and thermalization dynamics of all accessible excitons indi-cate that electron- and hole-transfer processes contribute to the formation of interlayer KW-KMo excitons, which, in consequence, we have to distinguish. To do so, we directly compare the interlayer KW-KMo exciton rise time for 1.7- and 1.9-eV pumping. In Fig. 3A, the black data points show the pump-probe delay-dependent buildup of interlayer KW-KMo exciton photoemission intensity that is formed by electron- and hole-transfer processes (1.9-eV pump photons). For comparison, the green data points show the pump-probe delay-dependent buildup of the interlayer KW-KMo exciton intensity that is formed only via the electron transfer process (1.7-eV pump pho-tons, fluence: 280 μJ/cm2, exciton density: 5.4 ×1012 cm−2). It is directly obvious that there is a strong hierarchy of timescales for the electron- and hole-transfer processes: When considering the electron-only transfer process (green symbols), the interlayer exci-ton signal increases rapidly with pump-probe delay and saturates on the sub-200-fs timescale. A quantitative evaluation with rate equation modeling yields a formation time of te − transfer = 40 ± 10 fs (see Supplementary Text). In contrast, the joint buildup of interlayer KW-KMo excitons via electron- and hole-transfer processes after 1.9-eV excitation saturates on the 1-ps timescale (black symbols). For fur-ther analyzing this dataset, we assume that the 1.9-eV pump pulses excite A1s excitons in WSe2 and MoS2 in a 1:5 ratio, as estimated from the optical absorption coefficient of both monolayers (41), and take the already deduced electron-transfer time te − transfer = 40 ± 10 fs into account. From this fit, we extract th − transfer = 2.2 ± 1 ps, which is more than an order of magnitude larger than the electron-transfer time te − transfer (see rate equation analysis based on fig. S3).Hence, our experimental data imply that the interlayer hole-transfer mechanism across the WSe2/MoS2 heterointerface is sub-stantially slower compared to the electron-transfer mechanism. To understand our findings on a microscopic footing, we exploit the density matrix formalism to derive excitonic equations of motion within the energy landscape of excitons shown in Fig. 2A and fig. S7 (see details in Supplementary Text) (38, 42). Here, we incorporate exciton-light and exciton-phonon interaction and assume again that the 1.9-eV pump pulses excite A1s excitons in WSe2 and MoS2 in a 1:5 ratio (41). We find an excellent qualitative agreement of the microscopic model calculations (Fig. 3B) with the experimentally Fig. 2. Energy landscape and energy-momentum fingerprints of excitons in WSe2/MoS2. (A) Calculated low-energy exciton landscape of intralayer, hybrid, and inter-layer excitons. The electron- and hole-transfer processes can be initiated via excitation with 1.7- and 1.9-eV light pulses, respectively, and proceed via the KW-KW → KW-Σ→ KW-KMo and KMo-KMo → Γ-KMo → KW-KMo cascades. The solid and dashed arrows, respectively, indicate exciton-phonon scattering events leading to inter- and intravalley thermalization of the exciton occupation. The effective mass of the exciton dispersion is extracted from many-body calculations. The inset schematically shows the align-ment of the WSe2 and MoS2 Brillouin zones and indicates the high-symmetry points in the first Brillouin zone. (B) Energy- and momentum-resolved photoemission spec-trum along the Γ-Σ-KW direction (inset) measured on the WSe2/MoS2 heterostructure after photoexcitation with 1.9-eV light pulses at a delay of 10 ps. The WSe2 and MoS2 valence band maxima are labeled with EWv and EMov , respectively. (C to E) Photoemission momentum fingerprints of the (C) intralayer KW-KW exciton (0 ps), the (D) inter-layer KW-KMo exciton (10 ps), and the (E) intralayer KMo-KMo exciton (0 ps) after photoexcitation with 1.9-eV light pulses. The photoelectron energies of the momentum maps are given in the figure with respect to the energy of the WSe2 valence band maximum and are indicated by colored arrowheads in (B). The energetic width of the arrowheads indicates the energy range used for generating the momentum maps (C, D, and E). The Brillouin zones of WSe2, MoS2, and the moiré superlattice are overlaid on the data by orange, dark red (dashed), and black hexagons, respectively.Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024Bange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e4 of 8quantified rise time (Fig. 3A) of interlayer KW-KMo excitons: The electron-only transfer process saturates for delays <200 fs (green), while the combined electron- and hole-transfer dynamics lead to an increasing interlayer KW-KMo exciton occupation for substantially longer delays (black). Hence, in experiment and theory, we find that the electron-transfer dynamics is roughly one order of magnitude faster than the hole-transfer dynamics.To understand this drastic difference in the rise time of interlayer KW-KMo exciton formation via the electron- versus the hole-transfer process, we evaluate the calculated exciton dynamics in more detail and make two major observations: First, it is important to realize that the exciton energy difference between the optically excited in-tralayer exciton and the interlayer exciton is roughly 200 meV larger in the case of 1.9-eV excitation, which initiates the hole-transfer process (see exciton energies in Fig. 2A and fig. S7). The dissipation of this extra amount of energy via exciton-phonon scattering events with typical phonon frequencies of 0.03 eV (43) leads to overall slower hole-transfer dynamics (arrows in Fig. 2A) (42, 44). In addi-tion, the first step of the exciton cascade leading to the formation of either KW-Σ or Γ-KMo excitons in the electron- and hole-transfer process, respectively, is markedly different. In the first Brillouin zone, the Σ and Σ' valleys are each threefold degenerate, while there is only one Γ valley (Fig. 2A, inset). Therefore, the density of final states for the KW-KW → KW-Σ versus the KMo-KMo → Γ-KMo transition is notably different (42, 43, 45–47). In consequence, hybrid KW-Σ excitons are more efficiently formed than hybrid Γ-KMo excitons, favoring faster interlayer exciton formation dynamics for the electron-transfer channel compared to the hole-transfer channel.Last, we want to point out two important deviations in the exci-ton dynamics between experiment and theory. First, on the few picosecond timescale, we find that the calculated occupation of in-terlayer KW-KMo excitons increases up to ≈4 ps and is composed of a 1:5 ratio of interlayer excitons that are formed from A1s excitons initially excited in the WSe2 and MoS2 layers (fig. S8). In contrast, in the experiment, the respective photoemission intensity saturates at roughly 1 ps and the 1:5 ratio cannot be identified (1.9-eV excitation; Fig. 3). This deviation between experiment and theory can be un-derstood by the fact that radiative and defect-assisted decay pro-cesses of intralayer, hybrid, and interlayer excitons with lifetimes ranging from 1 ps to tenths of picoseconds (8, 27, 34, 35) are not included in the model calculations. Hence, the model calculations overestimate the exciton occupation at large pump-probe delays.Second, we find that the experimental data for 1.7- and 1.9-eV excitation rises faster than estimated from the model calculations (sub-200-fs timescale in Fig. 3). This deviation could be related to the fact that the model calculations do not consider exciton-exciton scattering events, which might already contribute to the dynamics in the experiment (25, 48, 49). Although an in-depth pump fluence-dependent analysis of these dynamics appears to be highly interest-ing, it is beyond the scope of this manuscript, and, in the following, we focus on the identification of a spectroscopic fingerprint of the hole-transfer process.The spectroscopic signature of a correlated hole-transfer processOn the basis of this hierarchy of timescales between the electron- and the hole-transfer process, it is possible to separate the interlayer exciton formation dynamics: For delays >200 fs, the change in the exciton photoemission yield from the interlayer KW-KMo exciton is mainly caused by hole-transfer processes. Hence, the final ambition of our work is the unambiguous discrimination of the photoemis-sion spectral signature of intralayer KMo-KMo and interlayer KW-KMo excitons, where, in both cases, the electron contribution to the exci-ton is situated in the conduction band minimum of the MoS2 layer (compare Fig. 1C).In the most naive picture of photoemission, it might be expected that trARPES only yields information on the exciton’s electron. Hence, the experiment would not distinguish between photoelectrons being emitted from the conduction band minimum of MoS2, irre-spective of whether they result from the breakup of intralayer KMo-KMo or interlayer KW-KMo excitons (Fig. 1C). However, it is known that the spectral function in photoemission contains information about many-body interactions (50), and this is also the case for the correlated electron-hole pair. This leads to a very nonintuitive and Fig. 3. Femtosecond-to-picosecond evolution of the hole- and electron-transfer dynamics. (A) Direct comparison of the interlayer KW-KMo exciton formation dy-namics if the heterostructure is excited resonantly to the intralayer KW-KW exciton energy of WSe2 (1.7 eV, green circles) or the intralayer KMo-KMo exciton of MoS2 (1.9 eV, black circles). While the electron-only transfer process (1.7 eV) leads to a saturation of photoemission yield from interlayer KW-KMo excitons on the <200-fs timescale, the combined electron- and hole-transfer dynamics (1.9 eV) leads to an increasing photoemission yield up to 1 ps. The momentum-filtered regions of interest (black circles) used in the 1.7-eV (green contour) and 1.9-eV (black contour) measure-ments are shown in the bottom panel. The κ valley that overlaps with the original KMo valley is excluded in the analysis of the 1.9-eV measurement. (B) Microscopic model calculations of the interlayer KW-KMo exciton formation dynamics. The green curve describes the temporal evolution of the occupation of interlayer KW-KMo ex-citons after photoexcitation of intralayer KW-KW excitons. For the black curve, the interlayer KW-KMo exciton formation dynamics is induced by the initial excitation of intralayer KW-KW and KMo-KMo excitons. Note that the model calculations do not include additional decay processes.Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024Bange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e5 of 8intriguing experimental observation. Figure 4A shows the pump-probe delay evolution of energy distribution curves (EDCs) filtered for photoelectron yield at the κ valley, whose momentum coincides with the KMo valley, i.e., the momentum region where photoelectron yield from intralayer KMo-KMo and interlayer KW-KMo excitons is expected (Fig. 4A, inset). Astonishingly, we find that the energy of the photoelectrons shifts up as a function of pump-probe delay from E − EWv= 0.93 ± 0.03 eV at 15 fs to E − EWv= 1.10 ± 0.03 eV at 1 ps, i.e., a shift of ΔEh−transferPES= 0.17 ± 0.04 eV (Fig. 4B). At first glance, this is an unexpected observation: In temporal overlap of the pump and the probe laser pulses, the optical excitation deposits energy into the system, and the system subsequently relaxes from its excited state to energetically more favorable states via scattering processes. In consequence, energy-resolved pump-probe photoemission spec-troscopies of single-particle charge carriers typically show that the mean kinetic energy of the photoelectrons decreases with pump-probe delay (51). An increasing mean kinetic energy might indicate higher-order scattering processes such as Auger recombination (49, 52). For Auger recombination, however, we would expect to observe a decreasing mean kinetic energy on the few-picosecond timescale as the overall exciton density and thus the efficiency for Auger recom-bination decreases. However, the long-time evaluation of the mean photoelectron energy clearly excludes this scenario (Fig. 4A). In ad-dition, by evaluating the pump-probe delay evolution of the energy position of the MoS2 valence band maxima, we can exclude a photo-induced renormalization of the band energies (53, 54) (fig. S5). We thus search for the origin of the apparent increase of the mean kinetic energy beyond the single-particle picture, i.e., in the photoemission from excitons whose occupation is dynamically transferring from intralayer KMo-KMo to interlayer KW-KMo excitons.So far, we have referenced the energies of all emitted single-particle photoelectrons to the valence band maximum of WSe2 (left energy axis in Fig. 4B). However, especially for the intralayer KMo-KMo exciton that fully resides in the MoS2 layer, this is clearly not the intrinsically relevant energy axis. We overcome this shortcoming by using an energy scale that is more direct to photoemission from ex-citons by relating the total energy before (E = E0 + Eexc + ℏω) and after (E = E0 − Ehole + Eelec) the breakup of the correlated electron-hole pair (55). Here, Eexc is the energy necessary to resonantly excite an exciton with a two-particle binding energy Ebin (compare exciton energy landscape in Fig. 2A); Ehole and Eelec denote the energy of the single-particle hole and electron state after the breakup of the exciton, respectively; E0 is the ground state energy and ℏω is the photon en-ergy. As energy needs to be conserved when the exciton is broken, the energy of the detected single-particle electron can be expressed asTherefore, Eq. 1 fixes the energy of the single-particle hole Ehole remaining in the sample as the natural reference point of the photo-electron energy axis for each probed exciton (at a given probe photon energy ℏω). For the intralayer KMo-KMo excitons and the interlayer KW-KMo excitons, respectively, the valence band maxima of MoS2 ( EMov ) and WSe2 ( EWv ) set the energy scale [see Fig. 1 (B and C) and band energies labeled in Fig. 2B)]. Following Eq. 1, we can directly quantify the exciton energies of intralayer KMo-KMo and interlayer KW-KMo excitons from the photoemission data to EMoMoexc= 1.93 ± 0.08 eV and EWMoexc= 1.10 ± 0.03 eV , respectively, which are in excellent agreement with earlier results obtained with photoluminescence spectroscopy [(EMoMoexc,PL= 1.9 eV and EWMoexc,PL= 1.1 eV ; horizontal lines in Fig. 4B)] Eelec = Ehole + Eexc + ℏ𝜔 (1)Fig. 4. Coulomb correlation–induced excitonic energy fingerprints. (A) Pump-probe delay evolution of the energy distribution curves (EDCs) filtered at the momen-tum region of the KMo valley of MoS2 (region of interest indicated in the inset, 1.9-eV excitation). At this high-symmetry point, photoemission yield from intralayer KMo-KMo and interlayer KW-KMo excitons is expected (see Fig. 1C). As intralayer KMo-KMo excitons decay and form interlayer KW-KMo excitons, the peak maxima of the photoelectron energy shows an upshift by ΔEh−transferPES= 0.17 ± 0.04 eV (curved arrow). (B) Selected EDCs for pump-probe delays of 15 fs (dark red) and 1 ps (black) illustrating an ener-getic upshift of the exciton photoemission signal. The horizontal bars indicate expected photoelectron energies for the intralayer KMo-KMo (dark red) and interlayer KW-KMo (black) excitons calculated with Eq. 1 and data from photoluminescence measurements (56, 57). The left and right energy axes in black and dark red show the correspond-ing energy scales with respect to the valence band maximum of WSe2 and MoS2.Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024Bange et al., Sci. Adv. 10, eadi1323 (2024)     7 February 2024S c i e n c e  A d v a n c e s  |  R e s e ar  c h  A r t i c l e6 of 8(56, 57). In consequence, we can explain the experimentally observed upshift of the photoelectron energy by ΔEh−transferPES= 0.17 ± 0.04 eV with the energy difference between the single-particle electron final states Eelec of the interlayer KW-KMo and the intralayer KMo-KMo exci-tons, i.e., with (EWv+ EWMoexc+ ℏω) − (EMov+ EMoMoexc+ ℏω) ≈ 0.17 eV (with EWv− EMov= 1.00 ± 0.07 eV , see Fig. 2B). Hence, the energetic upshift is a direct consequence of the breakup of the correlated electron-hole pair during the photoemission process.Although the photoelectron energy increases during the hole-transfer process, we strongly emphasize that the overall energy of the system relaxes by ΔEh−transferexc= EWMoexc− EMoMoexc= − 0.83 ± 0.09 eV (see Fig. 2A). Consistently, if the same analysis is performed for the electron-only transfer process after photoexcitation with 1.7 eV pump pulses, then we find a reduction of the overall exciton energy by ΔEe−transferexc= EWMoexc− EWWexc= − 0.46 ± 0.07 eV (fig. S6). In this case, where the exciton’s hole remains in the WSe2 VBM (Fig. 1B), the reduction of the exciton energy directly translates to a reduction of the single-particle photoelectron energy ( ΔEe−transferPES= − 0.46 ± 0.07 eV ). Therefore, as expected, interlayer charge transfer always leads to a reduction of the exciton energy Eexc, which might, however, result in an up- or a downshift of the photoelectron energy in the photoemis-sion spectrum.DISCUSSIONWe have shown that femtosecond momentum microscopy is a pow-erful tool to study the correlated interaction between the exciton’s electron and hole in twisted semiconductor heterostructures. Exem-plarily, we show that the photoelectron of the correlated two-particle exciton contains direct information about the hole state. We use this correlation in combination with microscopic and material-specific theory to directly follow an ultrafast interlayer hole-transfer process that would otherwise be elusive. Our work opens up means for the future study of correlated states of matter in two-dimensional quan-tum materials.MATERIALS AND METHODSThe time- and angle-resolved photoemission data are measured with a time-of-flight momentum microscope (Surface Concept) (58, 59) that is connected to a table-top high harmonic generation beamline driven by a 300-W fiber laser system (AFS Jena) (40, 60). The overall experimental setup and its application to exfoliated two-dimensional materials are described in (39) and (8), respectively.In all experiments, the exciton dynamics are induced by resonant optical excitation of the A1s-excitons of WSe2 or MoS2. Therefore, 1.7- and 1.9-eV pump pulses with a duration of 50 fs are used (s-polarized), respectively. After a variable pump-probe delay, photo-emission is induced by 26.5-eV light pulses (20 fs, p-polarized).For the characterization of the temporal resolution and the de-termination of absolute time zero of the experiment, we have mea-sured the pump-probe delay-dependent photoemission yield of sidebands of the valence bands formed due to the laser-assisted pho-toelectric effect (40, 61). In fig. S1, a cross-correlation of the pump and probe laser pulse is shown, where both laser pulses are p-polarized (1.9-eV pump pulses). The gray line is a Gaussian fit to the data yielding a full width at half maximum of 60 ± 5 fs.The 9.8∘ ± 0.8∘ twisted WSe2/MoS2 heterostructure is stamped onto a 20- to 30-nm-thick hBN (62) spacer layer and a p +-doped native oxide silicon waver. Before the momentum microscopy ex-periments, the sample is annealed for 1 hour to 670 K. 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E.M. acknowledges support from the European Union’s Horizon 2020 research and innovation program under grant agreement no. 881603 (Graphene Flagship). K.W. and T.T. acknowledge support from JSPS KAKENHI (grant numbers 19H05790, 20H00354, and 21H05233). Author contributions: D.St., S.S., R.T.W., G.S.M.J., S.H., S.B., E.M., M.R., and S.M. conceived the research. D.Sc., J.P.B., and W.B. carried out the time-resolved momentum microscopy experiments. J.P.B. and D.Sc. analyzed the data. G.M. performed the microscopic model calculations. A.A. fabricated the heterostructure sample. All authors discussed the results. M.R. and S.M. were responsible for the overall project direction and wrote the manuscript with contributions from all coauthors. K.W. and T.T. synthesized the hBN crystals. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions of the paper are present in the paper and/or the Supplementary Materials.Submitted 5 April 2023 Accepted 10 January 2024 Published 7 February 2024 10.1126/sciadv.adi1323Downloaded from https://www.science.org at National Institute for Materials Science on February 09, 2024 Probing electron-hole Coulomb correlations in the exciton landscape of a twisted semiconductor heterostructure INTRODUCTION RESULTS Energy landscape and photoemission fingerprints of bright and dark excitons Hole- and electron-transfer dynamics The spectroscopic signature of a correlated hole-transfer process DISCUSSION MATERIALS AND METHODS Supplementary Materials This PDF file includes: REFERENCES AND NOTES Acknowledgments