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Wiebke Bennecke, Ignacio Gonzalez Oliva, Jan Philipp Bange, Paul Werner, David Schmitt, Marco Merboldt, Anna M. Seiler, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Daniel Steil, R. Thomas Weitz, Peter Puschnig, Claudia Draxl, G. S. Matthijs Jansen, Marcel Reutzel, Stefan Mathias

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[Hybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interface](https://mdr.nims.go.jp/datasets/06416289-8027-485e-9189-017ae986b3e0)

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Hybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interfaceNature Physics | Volume 21 | December 2025 | 1973–1980 1973nature physicshttps://doi.org/10.1038/s41567-025-03075-5ArticleHybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interface Wiebke Bennecke    1, Ignacio Gonzalez Oliva    2, Jan Philipp Bange    1, Paul Werner    1, David Schmitt1, Marco Merboldt    1, Anna M. Seiler    1, Kenji Watanabe    3, Takashi Taniguchi    4, Daniel Steil    1, R. Thomas Weitz    1,5, Peter Puschnig    6, Claudia Draxl    2,7, G. S. Matthijs Jansen    1  , Marcel Reutzel    1,8,9   & Stefan Mathias    1,5 Two-dimensional transition metal dichalcogenides and organic semiconductors have emerged as promising material platforms for optoelectronic devices. Combining the two is predicted to yield emergent properties while retaining the advantages of each. In organic semiconductors, the optoelectronic response is typically dominated by localized Frenkel-type excitons, whereas transition metal dichalcogenides host delocalized Wannier-type excitons. However, much less is known about the characteristics of excitons at hybrid interfaces between these materials, which determine the possible energy- and charge-transfer pathways. Here we identify a hybrid exciton at one such interface using ultrafast momentum microscopy and many-body perturbation theory. We show that this hybrid exciton, formed predominantly via resonant Förster energy transfer, has both Frenkel- and Wannier-type contributions: intralayer electron–hole transitions within the organic semiconductor layer and interlayer transitions across the interface give rise to an exciton wavefunction with mixed character. This work advances our understanding of charge and energy transfer processes across 2D–organic heterostructures.Hybrid Frenkel–Wannier excitons are Coulomb-bound electron–hole pairs that join the unique optical properties of Frenkel excitons with the wavefunction delocalization of Wannier excitons1–4. Such excitons have been observed to occur at the interface of organic–inorganic heterostructures1 and in organic–inorganic microcavities2. Moreover, hybrid Frenkel–Wannier excitons have been proposed to medi-ate charge and energy transport5–9 and to be a promising platform for studying many-body exciton physics10 as well as for nonlinear optical applications3. However, the experimental characterization of the fun-damental nature of such Frenkel–Wannier excitons has remained inac-cessible so far. Much is unknown about the electronic composition and the spatial characteristics of the interfacial excitonic wavefunctions.A highly promising platform for the realization of hybrid Frenkel– Wannier excitons is given by heterostructures of two-dimensional (2D) transition metal dichalcogenides (TMDs) combined with organic semiconductors (OSCs). Both these material classes are known for Received: 28 November 2024Accepted: 24 September 2025Published online: 29 October 2025 Check for updates1I. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany. 2Physics Department, CSMB, Humboldt-Universität zu Berlin, Berlin, Germany. 3Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 4Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 5International Center for Advanced Studies of Energy Conversion, University of Göttingen, Göttingen, Germany. 6Institute of Physics, NAWI Graz, University of Graz, Graz, Austria. 7European Theoretical Spectroscopic Facility, Berlin, Germany. 8Fachbereich Physik, Philipps-Universität Marburg, Marburg, Germany. 9mar.quest, Marburg Center for Quantum Materials and Sustainable Technologies, Marburg, Germany.  e-mail: gsmjansen@uni-goettingen.de; marcel.reutzel@uni-marburg.de; smathias@uni-goettingen.dehttp://www.nature.com/naturephysicshttps://doi.org/10.1038/s41567-025-03075-5http://orcid.org/0000-0001-9963-7527http://orcid.org/0000-0002-4229-708Xhttp://orcid.org/0000-0002-7355-8641http://orcid.org/0009-0007-7067-5854http://orcid.org/0000-0002-8958-7711http://orcid.org/0000-0002-9883-9220http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0001-7448-1167http://orcid.org/0000-0001-5404-7355http://orcid.org/0000-0002-8057-7795http://orcid.org/0000-0003-3523-6657http://orcid.org/0000-0003-4753-3173http://orcid.org/0000-0002-1085-2931http://orcid.org/0000-0002-1255-521Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41567-025-03075-5&domain=pdfmailto:gsmjansen@uni-goettingen.demailto:marcel.reutzel@uni-marburg.demailto:smathias@uni-goettingen.deNature Physics | Volume 21 | December 2025 | 1973–1980 1974Article https://doi.org/10.1038/s41567-025-03075-5that no signatures for hybridization of WSe2 valence states and PTCDA orbitals are observed. The energy level alignment of the WSe2 VBM  and the PTCDA HOMO found here (Fig. 1e) is consistent with earlier scanning tunnelling spectroscopy (STS) experiments27,28, and, in addi-tion, in qualitative agreement with our G0W0 calculations performed with the ‘exciting’ code29 (Fig. 1f; Methods). Combining all this infor-mation, we find that the single-particle energy-level alignment of the hybrid WSe2/PTCDA heterostructure is of type I, where the energies of both the lowest unoccupied and the highest occupied state are found in WSe2.Momentum-resolved characterization of excitons at the 2D–organic interfaceThe extension of the static ARPES experiment with a femtosecond pump–probe scheme is used to characterize the orbital contributions to optical excitations at the 2D–organic interface. The experimental conditions are chosen such that the driving photon energy of 1.7 eV (s-polarized, 40 fs) lies well below the lowest-energy optical excitation in PTCDA, which is ≿2 eV (ref. 25), that is, no PTCDA-only excitations can be created by the optical pump pulses. Instead, the laser pulses selectively excite the bright intralayer A1s-excitons in WSe2, which  we label as K-excitons here (peak fluence 280 ± 20 μJ cm−2, exciton density (5.4 ± 1.0) × 1012 cm−2). All other excitons that are detected in the photoemission experiment must result from subsequent charge and energy transfer processes, as will be further discussed below. Figure 2a,b shows time-delay-integrated photoemission momentum maps collected in selected energy windows above the WSe2 valence bands (see the Methods and Extended Data Fig. 3 for background subtraction). In the (kx,ky)-momentum-resolved data, we find a rich intensity structure that provides direct evidence for the presence  of excitons that are of pure WSe2 intralayer character, but also of  excitons with distinct orbital contributions from the PTCDA layer.First, we focus on the WSe2 intralayer excitons. Momentum- sharp photoemission features are detected at the K and Σ valleys  of the WSe2 Brillouin zone (BZ) after optical excitation (Fig. 2a, corners of the orange hexagon and grey circles, respectively; Σ is also  labelled as Q or Λ in literature). The K valley spectral weight can be attributed to photoemitted electrons originating from optically  bright K-excitons that we excite with the laser pulses (A1s-excitons) and momentum-indirect excitons where the electron and hole com-ponents reside at the K and K′ valley, respectively. As photoemission spectral weight from these excitons both appear at the K (K′) valley30 and cannot be differentiated within the energy resolution of our experiment23,31, we label those jointly as K-excitons (Fig. 2c). Likewise, the Σ valley spectral weight is indicative of the formation of momentum- indirect Σ-excitons whose electron and hole components reside in the Σ and K valley, respectively22,23,32. The energetic alignment of the K- and Σ-excitons can be analysed by evaluating momentum-filtered EDCs (Fig. 2e; see Extended Data Fig. 4 for chosen region of interests) and considering the conservation of energy as the EUV laser pulses  fragment the excitons into their single-particle electron and hole components in the photoemission process33 (EKexc = 1.61 ± 0.05eV, EΣexc = 1.61 ± 0.05eV; Extended Data Table 1).Next, we turn our attention to the two semi-circular photoemission  signatures at a radius of √k2x + k2y  ≈ 1.7 Å−1 found in momentum  maps with centre energies of E − EVBM = 1.57 ± 0.05 eV (Fig. 2a) and  E − EVBM = 0.38 ± 0.05 eV (Fig. 2b; see corresponding EDCs in Fig. 2e). Such circular structures of spectral weight are characteristic for photoelectrons emitted from molecular orbitals26,34,35 (see simulated  momentum map in Fig. 2d). Notably, the features are not found in the case of pristine monolayer WSe2, but only in the case of the WSe2/PTCDA heterostructure (Extended Data Fig. 2 and refs. 22,23). Because  the excitation energy of 1.7 eV is well below the direct HOMO →  lowest unoccupied molecular orbital (LUMO) excitation (≿2 eV;  reduced electronic screening that leads to the formation of strongly Coulomb-bound excitons. In OSCs, predominantly Frenkel-type  and charge-transfer excitons exist, which both derive their wavefunc-tion from molecular orbitals and which are commonly restricted to  only a single, or to just the neighbouring molecules11–13. Conversely, TMDs are known for hosting delocalized Wannier-type excitons whose wavefunctions are built up from Bloch states of the valence and conduction bands14. These individual properties make TMD/OSC heterostructures particularly promising for the realization of hybrid Frenkel–Wannier excitons, and it is predicted that both hybrid and charge transfer excitons can exist whose wavefunctions are composed of contributions of molecular orbitals of the OSC and valence/conduc-tion band Bloch states of the TMD15,16. However, the spatial structure of their wavefunction, that is, whether the Frenkel or Wannier con-tributions to the wavefunction are more dominant, or if an exciton  with both Frenkel and Wannier character can form and exist, remains largely unexplored. Moreover, experimental evidence for ultrafast charge- and energy-transfer processes is scarce.Here, using femtosecond momentum microscopy17 as well as G0W0 quasiparticle band structure18 and Bethe–Salpeter equation (BSE)19 calculations, we identify and characterize a hybrid Frenkel–Wannier exciton in the prototype system of monolayer 3,4,9,10- perylenetetracarboxylic dianhydride (PTCDA) adsorbed on monolayer tungsten diselenide (WSe2). We chose this system because, on the inorganic side, the electronic band structure20, the energy landscape  of excitons14 and the resulting ultrafast exciton dynamics21–23 are well characterized. Complementarily, on the organic side, PTCDA serves  as a key model system for fabricating flat molecular layers of OSCs adsorbed on pristine surfaces24 and for the study of optical excitations25,26. This is an ideal setting to study the orbital contributions to all relevant optically bright- and dark-exciton wavefunctions. This includes the momentum-direct and momentum-indirect intralayer excitons in WSe2 and, intriguingly, the formation of a hybrid WSe2/PTCDA exciton. Our joint experimental and theoretical results show that this hybrid exciton’s wavefunction is a coherent superposition  of intra- and interlayer contributions with Frenkel and Wannier charac-ter, respectively. Moreover, the orbital-resolved access to the exciton wavefunction combined with femtosecond time-resolution enables us to characterize the formation mechanism of the hybrid exciton. We show that, in response to the optical excitation of WSe2 A1s-excitons, exciton–phonon scattering and dominantly a Förster-type energy- transfer lead to the establishment of a steady state population between intralayer momentum-direct and momentum-indirect WSe2 excitons and the energetically most favourable hybrid exciton.TMD/OSC sample structure and single-particle energy level alignmentThe WSe2 monolayer was fabricated by mechanical exfoliation and transferred on bulk hexagonal boron nitride (hBN) on a Nb:STO  substrate (Fig. 1a; Methods). Subsequently, approximately a  monolayer of PTCDA was evaporated under ultrahigh vacuum con-ditions. By analysing the Umklapp scattering of the photoemitted electrons at the molecular superstructure (Extended Data Fig. 1e), we verified that PTCDA adsorbs in an ordered herringbone structure with a 20.2 × 13 Å2 supercell (Fig. 1b).To extract the energy-level alignment of this WSe2/PTCDA het-erostructure, we start with static angle-resolved photoelectron  spectroscopy (ARPES) experiments (26.5 eV extreme ultraviolet  (EUV) photons, 20 fs, p-polarized). The energy- and momentum- resolved photoemission data and the momentum-filtered energy distribution curves (EDCs) are shown in Fig. 1c,d. We find clear signatures of the K valley WSe2 valence band maximum (VBM) (E − EVBM = 0 eV)  and additional spectral weight at an energy of E − EVBM = −1.2 ± 0.1 eV that we identify with the highest occupied molecular orbital (HOMO) of PTCDA (see also momentum map in Extended Data Fig. 2f). We note http://www.nature.com/naturephysicsNature Physics | Volume 21 | December 2025 | 1973–1980 1975Article https://doi.org/10.1038/s41567-025-03075-5Supplementary Fig. 1 and ref. 25), these PTCDA orbital-like photoemis-sion signatures are expected to result from a charge- or energy-transfer process across the TMD/OSC interface and, in consequence, are of major interest to our study.A hybrid exciton bridging the 2D–organic interfaceThe question at hand is in how far these two fingerprints of molecular orbitals are an indication for multiple excitons with either interlayer or pure PTCDA character, or if they are a fingerprint of so far only  predicted hybrid Wannier–Frenkel excitons3 with multiple hole contributions36–39 from WSe2 and PTCDA. To address this question,  we start by solving the BSE on top of our G0W0 calculations of the  WSe2/PTCDA heterostructure. For computational feasibility, we neglect spin–orbit coupling (SOC) and adopt a simplified geometry consisting of a single PTCDA molecule in a 4 × 4 × 1 supercell, rather than the experimentally observed herringbone structure (Extended Data Fig. 5a; for a detailed discussion, see the Methods and Supplementary Information). These calculations yield the imaginary part of the in-plane frequency-dependent dielectric function lm(ϵ|| (q)) , containing  information on optical excitations at the 2D–organic interface, and allows us to identify the band/orbital contributions to the exciton wavefunctions in momentum and real space15. In the momentum- direct part of the spectrum (that is, with q = ke − kh = 0), the two lowest- energy excitons are of WSe2 (orange, EK,BSEexc = 1.74 eV) and hybrid  (blue, EhX,BSEexc = 1.72 eV) character, respectively (Fig. 3a, marked with arrows). In Fig. 3c,d, the electron and hole contributions to these excitons are analysed in reciprocal space. We find that the 1.74 eV K-exciton is of full WSe2 intralayer character and derives its wavefunction purely from WSe2 conduction and valence band Bloch  states (Fig. 3c). By contrast, for the 1.72 eV exciton, which we term  hybrid exciton (hX), the electron component derives its wavefunction from the LUMO of PTCDA, while the hole component has contributions from the WSe2 valence bands and also from the PTCDA HOMO (Fig. 3d). In contrast to typical charge-transfer excitons  that are exclusively of interlayer type, our G0W0 + BSE calculations show that the hX is composed of a coherent superposition of intralayer (HOMO → LUMO) and interlayer (VBM → LUMO) contributions.  We note that, at first glance, such a mixing might seem counter-intuitive because of the large energy difference of the intra- and interlayer single-particle band gaps (that is, ELUMO − EHOMO > ELUMO − EVBM; Fig. 3e). However, due to the stronger electron–hole interaction for the  case of intralayer HOMO → LUMO transitions as compared with  interlayer VBM → LUMO transitions, the individual exciton energies  of both electron–hole transitions can be sufficiently degenerate  to allow the mixing of both OSC and TMD components (Fig. 3f).  Notably, this implies that the hX originates from exciton-level hybridization between interlayer and intralayer excitons, which is  possible despite minimal single-particle band hybridization, as demonstrated here.Experimental characterization of the hXThe G0W0 + BSE prediction of the dual-component character of the hX is in excellent agreement with our experimental findings, as can be Γ K0 0.5 1.0 1.5 2.0kx (Å–1)−2.0−1.5−1.0−0.500.5E − E VBM (eV)00.3Intensity (a.u., arbitrary o�set)1.27 Å−1 1.40 Å−1 1.52 Å−1d10−21logintensity10 µmhBNWSe2Nb:STOPTCDAWSe2hBNacbHOMOVB1VB2KeLUMOHOMOSingle particle energy  ΣVBMCBM00.5Γ M K Γ−2.0−1.5−1.0−0.500.51.01.52.0Energy (eV)SpectralweightMKΓfHOMOLUMOCBMVBMG0W0, unfolded bandstructureFig. 1 | Sample layout and electronic structure of the hybrid WSe2/PTCDA heterostructure. a, A sketch of the layered sample structure and real-space photoemission image. The real-space region of interest addressed in the momentum-resolved photoemission measurement is marked by the dashed white circle, while the hBN flake and the WSe2 monolayer are indicated by coloured lines. b, Experimentally determined superstructure of PTCDA adsorbed on WSe2 monolayer (Extended Data Fig. 1). c, Energy–momentum cut of the static photoemission spectrum along the Γ–K direction of the WSe2/PTCDA heterostructure measured at 50 K. d, EDCs taken at the momenta indicated in c. The dispersive spin-split WSe2 bands (VB1 and VB2) and the non-dispersive HOMO level are marked by arrows. e, An overview of the type-I energy level alignment of the TMD/OSC heterostructure. The sketch is extracted from  static photoemission spectroscopy (c and d), the G0W0 calculation (f) and  STS experiments reported in refs. 27,28, which are in qualitative agreement.  f, Unfolded single-particle energy landscape of the WSe2/PTCDA heterostructure as retrieved from the scissor-shifted G0W0 calculation in a 4 × 4 × 1 supercell (Extended Data Fig. 5c; Methods).http://www.nature.com/naturephysicsNature Physics | Volume 21 | December 2025 | 1973–1980 1976Article https://doi.org/10.1038/s41567-025-03075-5verified by analysing three characteristic photoemission fingerprints in the (1) momentum domain, (2) energy domain and (3) time-delay domain. First, the measured momentum maps shown in Fig. 2 are  both in agreement with the LUMO orbital momentum map calculated within the framework of photoemission orbital tomography34 (Fig. 2d and Extended Data Fig. 2), clearly confirming experimentally that  the exciton’s electron component resides in the molecular layer37.  Second, it is known that photoelectrons that are emitted from  excitons are detected one exciton energy Eiexc above the energy of the single-particle bands where the hole component remains after photo excitation36–38. Here, we understand the exciton energy Eiexc  as the two-particle energy of the electron–hole pair. Thus, for the hX,  which has two hole contributions from the WSe2 VBM and the PTCDA HOMO (Fig. 3e), one can expect to observe not only one, but two  photoemission orbital signatures that are separated in energy by the energy difference between the WSe2 VBM and the PTCDA HOMO level: ΔEVBM,HOMO = EVBM − EHOMO = 1.2 ± 0.1 eV. Strikingly, the experimentally found peak-to-peak energy difference ΔEhX = 1.18 ± 0.08 eV (Fig. 2e)  of the two excitonic photoemission signatures is in quantitative  agreement with experimentally retrieved ΔEVBM,HOMO. Third, if both photoemission signatures result from the break-up of the same hybrid exciton, their population dynamics have to coincide. Indeed, as we will discuss later in detail, the delayed onset and decay dynamics of both photoemission signatures are in quantitative agreement (Extended  Data Fig. 6c and Extended Data Table 1). We therefore conclude  from experiment and theory that the WSe2/PTCDA heterostructure hosts a hybrid exciton whose wavefunction extends across the TMD/OSC interface.Real-space wavefunction distribution of hybrid Wannier–Frenkel excitonsHaving access to the excitonic wavefunction contributions of the  WSe2 Bloch states and the PTCDA orbitals from experiment and theory,  we are in the position to evaluate the real-space Frenkel and/or  Wannier character of the hX. Specifically, we aim to characterize the  exciton’s relative electron–hole distance parallel and perpendicular to the heterostructure in comparison with the size of the WSe2 and PTCDA unit cells. Therefore, we analyse the electron–hole correlation function, that is, the probability distribution of the electron–hole separation, Fi(r) = F(re − rh) with regard to the heterostructure’s out-of-plane (r⊥; Fig. 4a) and in-plane (r∥; Fig. 4b) coordinates40, which correspond to the exciton’s intra- or interlayer and Frenkel or Wannier character, respectively (see details in the Methods and the analysis for K-exciton in Extended Data Fig. 7).Intriguingly, for the out-of-plane component (Fig. 4a), there is not only a peak around r⊥ ≈ 0 Å that indicates intralayer character,  but also a peak centred at r⊥ ≈ −5 Å, which matches the distance between the tungsten plane and the PTCDA molecule and therefore indicates the additional interlayer character of the hX. Hence, the double-peak structure in Fig. 4a is a direct signature of the mixed intra- and interlayer contributions to the hX.Complementary, the in-plane electron–hole distribution function Fi(r∥) (Fig. 4b) contains information on the Frenkel and/or Wannier character of the hX. Here, we plot the intra- and interlayer contributions separately as purple and green lines in Fig. 4b. The relative probability of the intralayer contribution is almost entirely (to 99%) confined to values smaller than the lattice constant of the PTCDA supercell (aPTCDA), KΣca−202k y (Å–1)01b−2 0 2kx (Å–1)−202k y (Å–1)01d−2 0 2kx (Å–1)01eIntensity (a.u.)0.51.01.52.0E − E VBM (eV)K valleyΣ valleyMolecular featureFig. 2 | Energy- and momentum-resolved identification of the excitonic  photoemission signatures. a,b,e, Energy-filtered momentum maps at  E − EVBM = 1.6 eV (a) and E − EVBM = 0.4 eV (b) as well as the momentum-filtered EDCs (e) of excitonic photoemission signatures. The data were obtained by integrating over pump–probe delays from 100 to 500 fs, and applying a background subtraction using the non-negative matrix factorization formalism (Methods; Extended Data Fig. 3). In a, The WSe2 BZ is indicated by an orange hexagon. The  K valleys lie at the corners of the hexagon. The Σ valleys are marked by grey circles. The blue circle with a radius of √k2x + k2y  ≈ 1.7 Å−1 corresponds the expected  mean radius of the simulated momentum distribution of the LUMO of  PTCDA shown in d (see also Extended Data Fig. 2). c, Extended zone scheme with the BZ marked in orange, the Σ points marked with grey circles and the molecular photoemission feature indicated by the blue circle. d, Simulated momentum map from DFT calculation of the LUMO of PTCDA using the plane wave model of photoemission34. e, The EDCs are filtered in momentum for the K (orange),  Σ (grey) and molecular (blue) photoemission signatures (see Extended Data Fig. 4 for chosen region of interests) and fitted with a single or two Gaussian peaks (Methods). The resulting peak energies are marked with a horizontal bar in  the plot, and the corresponding exciton energies Eiexc are summarized in Extended Data Table 1.http://www.nature.com/naturephysicsNature Physics | Volume 21 | December 2025 | 1973–1980 1977Article https://doi.org/10.1038/s41567-025-03075-5indicating a Frenkel-like character. By contrast, only 82% of the inter-layer contribution is confined to values smaller than aPTCDA. Hence, similarly to the Wannier K-exciton, the interlayer component of the hX extends over multiple PTCDA unit cells (see Extended Data Table 2 and Extended Data Fig. 8 for a direct comparison), thereby exhibiting a more Wannier-like character. The different character is even more evident when considering the 2D representations of FhX(r∥) in the insets in Fig. 4b, which show that the interlayer component resem-bles the overall Gaussian intensity distribution known for a K-exciton (Extended Data Fig. 7 and refs. 31,41,42), while the Frenkel compo-nent shows a much stronger spatial structuring that stems from the molecular orbital.To further illustrate the spatial extent of the hX—both in terms of intra- and interlayer contributions, as well as its Wannier and  Frenkel character—Fig. 4c shows exemplary probability density iso-surfaces of the exciton’s electron and hole components (red-shaded  and cyan-shaded volumes) that are obtained by fixing the exciton’s hole (cyan dots) or electron components (red dot) at typical positions in the heterostructure. When the hole is placed in a delocalized state in the TMD layer (top left), we find a Wannier-like isosurface where  the electron is spread over multiple PTCDA molecules. By contrast, when the hole is placed on the PTCDA molecule (bottom left), the electron is completely localized on the same molecule, too. In other words, the isosurface now describes a Frenkel-type exciton. Most interestingly, when the electron is fixed on the PTCDA layer (right), the hole isosurface again shows the dual component characteristics with a localized part on the same PTCDA molecule, and also a (weaker) delocalized contribution on the TMD layer. Hence, the hole isosurface has both Wannier and Frenkel character. This hybrid intra- and inter-layer and Frenkel and Wannier nature of the hX is a unique feature  of the TMD/OSC interface that highlights the versatility of these combined platforms for controlling optoelectronic energy conversion pathways.Femtosecond time- and orbital-resolved  exciton dynamicsFinally, we want to elucidate the ultrafast formation and thermalization dynamics of all excitons involved. Figure 5 shows the femtosecond pump–probe delay dependence of photoemission spectral weight from K-excitons (K valley), Σ-excitons (Σ valley) and hXs (molecular features hX@1.6 eV and hX@0.4 eV). Subsequent to the optical excita-tion of K-excitons and the concomitant rise of spectral weight at  the K valley (orange), the photoemission intensities at the Σ valley  (grey) and for the molecular features (blue) rise with delayed onsets of 22 ± 4 fs and 61 ± 10 fs, respectively. The molecular features’  spectral weight peaks at about 150 fs, and their decay can be well described with a single-exponential function with a decay constant  of τhXdecay = 1.8 ± 0.7ps. Interestingly, following the increase of the hX spectral weight, the initially fast decay of the K and Σ valley spectral weight is slowed down and shows the same behaviour as the decay of the hX on longer timescales. This is confirmed by fitting bi-exponential functions to the decay of the K- and the Σ-exciton, which show slow decay constants of τKslow = 2.1 ± 0.4ps  and τΣslow = 2.2 ± 0.4ps, respectively (Extended Data Table 1). From this analysis, we conclude that γ m k γ−2−1012Energy (eV)c K-excitonWSe2 CBMWSe2 VBMγ m k γd hX-excitonHOMOWSe2 VBMLUMO1.0 1.2 1.4 1.6 1.8Energy (eV)0510Im ε||ahXKBSE@G0W0Pure WSe2HybridExciton pictureExciton energy EExcHybridexcitonsVBM–LUMO excitonHOMO–LUMO excitonfSingle particle energy LUMOHOMOeCBM–VBMhXSingle particle picturebKMmkγΣ K––++Fig. 3 | Reciprocal-space representation of the Bloch states and molecular orbitals contributing to the K-exciton and the hX wavefunction. a, Absorption spectrum of WSe2/PTCDA retrieved by G0W0 + BSE calculations. The oscillator strengths of the contributing excitons are indicated as solid lines where all values below one (dark-excitons) are set to one for visibility. Excitons with and without contributions from PTCDA orbitals are distinguished in blue and yellow, respectively. b, Backfolded BZ according to the theoretical superstructure (Extended Data Fig. 5a). c,d, The two lowest-lying excitons marked by arrows in a are analysed in detail in reciprocal space using the backfolded BZ in b. The electron and hole contributions are marked in red and cyan, respectively. While the K-exciton wavefunction is purely composed of TMD valence and conduction band states (WSe2 VBM and CBM) (c), the hX wavefunction has contributions from the TMD valence bands (WSe2 VBM) and from the PTCDA HOMO and LUMO orbitals (d). e, Visualization of the electron–hole transitions that contribute to the wavefunction of K-exciton, Σ-exciton and hybrid exciton (hX). The hX wavefunction is of partial intra- and interlayer composition and built up by HOMO → LUMO and VBM → LUMO transitions, respectively. f, An illustration of the hX in the exciton picture. The intralayer and interlayer electron–hole transitions are expected to be nearly degenerate in energy because of the stronger electron–hole interaction of the pure HOMO–LUMO exciton compared with the VBM–LUMO exciton. Mixing of the transitions leads to the formation  of a new bound hybrid excitonic state at lower exciton energies, that is, the hX.http://www.nature.com/naturephysicsNature Physics | Volume 21 | December 2025 | 1973–1980 1978Article https://doi.org/10.1038/s41567-025-03075-5subsequent to the optical excitation of K-excitons and on a sub-200-fs timescale, a Σ ⇌ K ⇌ hX steady-state population with common decay channels is established.However, while in pure TMD heterostructures charge and energy transfer across interfaces is mediated and explained by band structure hybridization effects31,43–45, the general preconception for TMD/OSC interfaces is that orbital hybridization is weak4,46 and that, as a conse-quence, related charge-transfer processes or Dexter-type energy- transfer processes that require wavefunction overlap47 are less likely. Indeed, neither experimental nor theoretical investigations reveal signatures of substantial orbital hybridization at the TMD/OSC  interface: the experimentally determined K- and Σ-exciton energies are in quantitative agreement with ARPES23 and photoluminescence48 data reported for monolayer WSe2 (Extended Data Table 1), that is, without a molecular overlayer. Specifically, compared with EKexc, no reduction of EΣexc  due to the PTCDA adsorption is observed, as is  the case of pure TMD few-layer systems with hybridized bands23.  Hence, the experimental results imply that the K- and Σ-exciton wave-functions are of mere WSe2 intralayer character, with negligible con-tribution from PTCDA orbitals. This is in agreement with our density functional theory (DFT) calculations that also do not show any hybridi-zation of the single particle PTCDA LUMO and WSe2 conduction band states (Extended Data Fig. 5c). In consequence, the formation of the hX cannot be mediated by hybridized states between the layers. Instead, we conclude that energy transfer must be dominantly medi-ated by dipole–dipole interactions, that is, in a Förster-type energy transfer process. Indeed, all requirements for such a process are fulfilled8,47: First, the K and hX energies are close in energy, satisfying the requirement of energy conservation (Fig. 2c and Extended  Data Table 1). Second, the dipole moment of the HOMO–LUMO con-tribution to the hX is polarized in-plane, facilitating the coupling to the in-plane dipole moment of the WSe2 K-exciton. Third, because of the mixed nature of the hX wavefunction and the contribution of HOMO–LUMO transitions, our G0W0 + BSE calculations predict that the oscillator strength is rather large (Fig. 3a), making the Förster-type process efficient. We note, however, that the hX formation is one to two orders of magnitude faster than typically found in other reports discussing the dynamics of Förster processes at TMD/OSC47 or TMD/graphene49,50 interfaces. We suspect that the fast rise time of the hX might be related to the fact that the dipole–dipole interactions do  not induce a complete energy transfer across the 2D–organic interface. Instead, the dipole–dipole interactions promote the conversion of WSe2 intralayer K-excitons to hXs, whose wavefunction is composed of PTCDA intralayer HOMO/LUMO and interlayer WSe2-VBM/LUMO −5 0 5Out-of-plane electron–hole distance r� (Å)00.20.40.60.81.01.2F(r �) (a.u.)dW,PTCDAa Relative probability distributionout-of-planeInterlayerIntralayer0 2.5 5.0 7.5 10.0 12.5 15.0 17.5In-plane electron–hole distance r|| (Å)00.20.40.60.81.01.2F(r ||) (a.u.)1 nmWannier-likeInterlayer1 nmFrenkel-likeIntralayerb Relative probability distribution in-planeaWSe2aPTCDAc    Probability density isosurfacesFixed hole Fixed electronFixed hole positionFixed electron positionProbability distribution of holeProbability distribution of electronFig. 4 | Real-space properties of the hX wavefunction. a, The out-of-plane component of the electron–hole correlation function Fi(r) = F(re − rh) shows two peaks separated by the distance between the tungsten plane and the PTCDA molecule (dW,PTCDA), which confirms a combination of both intralayer (r⊥ ≈ 0 Å) and interlayer (r⊥ ≈ −5 Å) character. b, By splitting the in-plane electron–hole correlation into intralayer (purple) and interlayer (green) contributions, it is possible to visualize the major difference in spatial extent. To compare these spatial distributions with the underlying atomic structure, the lattice constants of WSe2 and the PTCDA superstructure are indicated as dashed vertical lines. The insets show the r∥ = (rx,ry) resolved representation of the Wannier-type (green axis) and the Frenkel-type (purple axis) contributions. c, Orthographic side view of exemplary probability density isosurfaces for the hX for fixed hole (left) and fixed electron (right) position. Due to the dual Wannier–Frenkel character, the hX probability density isosurfaces depend strongly on the chosen hole location, where the isosurface extends over multiple molecules when the hole is placed in a TMD Bloch state (top), while the isosurface shows clear Frenkel nature when the hole is placed in the PTCDA HOMO (bottom). If the electron is fixed at the molecule (right), the isosurface of the hole has contributions in both the TMD and the PTCDA molecule.http://www.nature.com/naturephysicsNature Physics | Volume 21 | December 2025 | 1973–1980 1979Article https://doi.org/10.1038/s41567-025-03075-5orbital contributions. While future theoretical work is needed to verify the timescale of the Förster-type energy-transfer process at the WSe2/PTCDA interface, our work already highlights how excitonic wavefunc-tion engineering can directly contribute to efficient energy transfer processes in 2D–organic hybrid heterostructures.Online contentAny methods, additional references, Nature Portfolio reporting sum-maries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contri-butions and competing interests; and statements of data and code avail-ability are available at https://doi.org/10.1038/s41567-025-03075-5.References1.  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Commun. 14, 5057 (2023).Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025http://www.nature.com/naturephysicshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Nature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5MethodsSample preparationTo fabricate the WSe2/PTCDA heterostructure (Extended Data Fig. 1a), hBN was first exfoliated onto a 0.1% niobium-doped SrTiO3 substrate and an approximately 50-nm-thick flake was identified by optical microscopy. In a parallel procedure, WSe2 monolayers were directly exfoliated onto a silicone gel film (DGL Film, Gel-Pak) and identified through optical microscopy and Raman spectroscopy. Afterwards, a monolayer WSe2 flake was transferred from the silicone gel film onto the hBN flake on the SrTiO3 substrate (Extended Data Fig. 1b). After introduction into ultrahigh vacuum (<5 × 10−9 mbar), the sam-ple was annealed at 670 K for 2 h to ensure a clean sample surface. The bare monolayer WSe2 was analysed with the momentum micro-scope in real space (Extended Data Fig. 1c) and reciprocal space (Extended Data Fig. 2e), showing the expected characteristic features of monolayer WSe2, that is, the spin-split valence bands at the K valley and a single parabolic band at the Γ valley below the global VBM at the K valley (Fig. 1b and refs. 20,23). Moreover, the clear separation between the top and the bottom valence band (Fig. 1c) indicates the high-quality of the WSe2 with only contributions of inhomogeneous broadening.Subsequently, approximately a monolayer of PTCDA was ther-mally evaporated onto the sample, which was maintained at room temperature (base pressure <1 × 10−9 mbar). The deposition rate was monitored with a with a quartz crystal microbalance and calibrated using the known deposition of PTCDA onto a Ag(110) crystal surface. On the Ag(110) surface, the first monolayer of PTCDA is adsorbed in a brickwall structure whereas additional layers grow in a Herring-bone structure with a different superstructure that can be analysed by low energy electron diffraction (LEED)51. By step-wise evaporation of PTCDA onto Ag(110) and recording of the LEED pattern, the evapora-tion rate was determined and was then used to deposit a monolayer PTCDA onto monolayer WSe2. The successful deposition of a monolayer PTCDA onto monolayer WSe2 was confirmed by the observation  of additional spectral weight in the static ARPES data, which can be attributed to the HOMO of PTCDA (Fig. 1c,d) and backfolded WSe2 bands (Extended Data Fig. 1e), which are caused by the adsorbed molecular PTCDA superstructure (Fig. 1b). The superstructure matrixM = [1.58 6.784.39 1.32]was determined by LEED on a cleaved WSe2 bulk crystal (Extended  Data Fig. 1d) and is in good agreement with ref. 28 and the ARPES  data (Extended Data Fig. 1e).Femtosecond momentum microscopyAll photoemission data were acquired with the Göttingen in-house photoemission set-up17,52 that combines a time-of-flight momentum microscope53 (Surface Concept GmBH, ToF-MM) with a 500-kHz high-harmonic generation beamline (26.5 eV p-polarized, 20 fs). For the time-resolved measurements, the photon energy of the s-polarized pump was tuned to hν = 1.7 eV with 50 ± 5 fs pulse duration using an optical parametric amplifier. The experimental set-up is described in detail in ref. 17. The pump fluence was adjusted to 280 ± 20 μJ cm−2, which results approximately in an initial K-exciton density of (5.4 ± 1.0) × 1012 cm−2 (refs. 31,48). All experiments are performed with an energy, momentum and time resolution of 200 ± 30 meV, 0.04 ±  0.01 Å−1 and 54 ± 7 fs (refs. 17,31,54). The static measurements (Fig. 1c) were performed at T = 50 K, while all pump–probe delay-dependent measurements were performed at room temperature (300 K).Photoemission data processingThe time-of-flight momentum microscope enables the simultaneous measurement of the kinetic energy and both in-plane momenta of the photoemitted electrons53. However, the acquired three-dimensional photoemission data are affected by various lens aberrations and  other distortions, such as pump- and probe-induced space-charge effects and surface photovoltage55–57. Therefore, the photoemission data needs to be preprocessed before further evaluation by (1) cor-recting a time-dependent rigid energy shift and (2) correcting for distortions that are induced by the projection and focal lens system.First, the time-dependent energy shift was corrected by minimiz-ing the variance between the momentum-integrated spectra for E − EVBM < 1.8 eV. Second, an additional measurement was performed with a grid inserted in the Fourier plane58,59. We then determined the parameters for an affine transformation that maps the measured data onto an undistorted and energy-independent grid. This transformation is applied to all datasets. Small remaining distortions induced by the first lens system were corrected by fitting the positions of the K-excitons and mapping them onto an equilateral hexagon. The same positions were used to perform the momentum calibration using the lattice constant of WSe2 aWSe2 = 0.3297nm . In addition, for each delay step,  the data were momentum-wise normalized to the energy range between E − EVBM = −1.8 and −3.8 eV. This momentum-wise normalization accounts for potential changes in illumination due to possible instabilities during the long integration times of the time-resolved  measurements.Quantitative analysis of the exciton energies and dynamicsThe EUV laser pulses fragment the Coulomb-bound electron–hole pairs into their single-particle components. As this process conserves energy and momentum33,60,61, the exciton energies Eexc can be extracted by fitting the delay-integrated (100–500 fs), background-substracted (see the non-negative matrix formalism (NMF) method below) and momentum-filtered EDCs shown in Fig. 2c with either one (K- and Σ-excitons) or two (hX) Gaussian peaks Ip and an exponential back-ground Ibg, that is,Ip(E ) =Aσ√2πexp {(− (E − μ)22σ2 )} , (1)Ibg(E ) = Abg exp {(−Eτbg)} . (2)The extracted peak energies E − EVBM of the K and Σ excitons directly correspond to the exciton energies Eexc because the hole resides at the VBM of WSe2. For the hX, the peak energy of the higher lying peak at E − EVBM = 1.57 ± 0.05 eV directly corresponds to EhXexc, whereas the lower-energy peak at E − EVBM = 0.38 ± 0.05 eV has to be referenced to the HOMO at E − EVBM = −1.2 ± 0.1 eV, which results in the same exciton energy EhXexc = 1.58 ± 0.1 eV. In Extended Data Table 1, the quantified  exciton energies Eiexc are compared with the BSE@G0W0 calculations and ARPES and photoluminesence experiments on monolayer WSe2 (refs. 22,23,62). The total error of the experimental values is estimated to be approximately 0.05 eV, taking into account fitting errors and pos-sible errors induced by the energy calibration and space charge effects.To analyse the exciton dynamics of the K, Σ and hX photoemission signatures (Fig. 5), we filter the raw photoemission data, that is, without background subtraction, by their energy and momentum coordinate. The respective EDCs and the chosen region of interests are shown in Extended Data Fig. 4. To quantify the rise time, we fitted the energy- and momentum-filtered time-resolved photoemission spectral weight traces with an error functionI(t) = 12 (1 + erf ( t − μonset√2σrise)) (3)in the delay regions −200 fs to 0 fs, −200 fs to 20 fs and −200 fs to 150 fs, respectively (Extended Data Fig. 6). Here, μonset indicates the onset time, while σrise is directly related to the rise time.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Similarly, we fitted the decay of photoemission spectral weight with a bi-exponential decay (equation (4)) between 0 fs and 2,000 fs and between 20 fs and 2,000 fs for the K- and Σ-excitons, respectively. The hX was fitted with a single exponential decay function (equation (5)) between 200 fs and 2,000 fs:I(t) = A ( 11 + fexp {(− tτfast)} + f1 + f(− xτslow)) , (4)I(t) = A exp {(− tτslow)} . (5)The relevant time constants are given in Extended Data Table 1.Non-negative matrix factorizationDue to the small size of the WSe2 monolayer and the small real-space selection aperture (10 μm effective diameter), the measurement was susceptible to a time-independent background intensity. Therefore, the excited state momentum maps and momentum-filtered EDCs shown in Fig. 2 and in the insets of Extended Data Fig. 4 and 6 were background subtracted.For the background determination, we used NMF, as implemented in the scikit-learn package for Python63. NMF is a dimensionality- reduction method that so far remains unexplored in time-resolved ARPES, but it has recently found application in spatially resolved material science studies based on X-ray diffraction64 and also static ARPES experiments65. Similar to principal component analysis, NMF is based on the numerical factorization of a given matrix X  into two matrices W and H, with the additional condition that all  matrices have only non-negative elements. In our case, X is given by the time-dependent raw dataset where we consider only excited state data above E − EVBM = 0.15 eV. In addition, we fix W by a static background and the four extracted time traces of the K, Σ, hX@1.6 eV and hX@0.4 eV photoemission signal plotted in Fig. 5. The determined output then is the matrix H that consists of five components, each following one of the four given time dependencies and the time-independent background. Extended Data Fig. 3 shows extracted components integrated over the regions of interest in energy. Notably, the different components 1–4 can be assigned in reasonable agreement to the different excitonic photoemission signatures despite the strong overlap in time, energy and momentum (orange hexagons, grey circles and blue circle). Com-ponent 5 is time-independent and used for background substraction.Photoemission orbital tomographyUsing the plane-wave model of photoemission, the measured momentum-dependent photoemission intensity of electrons emit-ted from molecular orbital can be expressed as34I(k) = ||A ⋅ k||2|ℱ (ψ(r))|2δ (Eb + Ekin +Φ − hν) , (6)where ψ(r) is the real-space electronic wavefunction, ℱ  is the Fourier transform and ||A ⋅ k||2  is a polarization factor defined by the vector potential A of the incoming electromagnetic field. The Dirac δ function ensures energy conservation of the photoemission process, which includes the photon energy hν, the electron binding energy Eb, the work function Φ and the kinetic energy Ekin of the emitted photoelectron. This model has been successfully applied to analyse orbital wavefunc-tions of transient excited states in PTCDA26 and extended to the descrip-tion of the photoemission signature of excitons in C60 (ref. 36). According to refs. 36,37, the photoemission signature of the hX with multiple hole contributions, but only a single electron contribution, must feature a two-peak structure, where the momentum distribution of both peaks resembles the Fourier transform of the LUMO of PTCDA as described by equation (6). Based on this model, we calculate the expected momentum map of the HOMO and the hX considering all the different orientations of the PTCDA molecule28. The real-space molecu-lar orbitals calculated by DFT are extracted from ref. 66. The results are plotted in Extended Data Fig. 2c,g. We note that the theoretical momentum fingerprints were calculated for single-particle electrons (that is, using the Kohn–Sham orbitals). In the near future, progress  in the field of exciton photoemission orbital tomography36,37 may enable the calculation of predicted momentum fingerprints also for excitonic states; however, such calculations are currently not possible for the present WSe2/PTCDA structure.Calculation of the electronic structureA G0W0 treatment of the herringbone-type WSe2/PTCDA heterostruc-ture is beyond current computational possibilities. Instead, to meet the experimental conditions as closely as possible, we consider a con-figuration of a PTCDA molecule adsorbed on a 4 × 4 × 1 supercell of the pristine WSe2 structure with an in-plane lattice parameter of 3.317 Å (Extended Data Fig. 5; for a detailed discussion of the implemented supercell, refer to the Supplementary Information). We optimize the atomic structure, consisting of 86 atoms, using the all-electron code ‘FHI-aims’67 by minimizing the amplitude of the interatomic forces below a threshold value of 10−3 eV Å−1. For all species a tight basis is used. The resulting adsorption geometry is shown in Extended Data Fig. 5a. The PTCDA molecule is slightly tilted, with the shortest and longest distance to the substrate being 2.87 Å and 4.98 Å, respectively, meas-ured from the top of the substrate.The ground-state, G0W0 and BSE calculations are performed using the all electron full-potential code ‘exciting’29, which imple-ments the family of linearized augmented plane wave plus local orbit-als (LAPW+LO) methods. The muffin-tin spheres of the inorganic component are chosen to have equal radii of 2.2 bohr. For PTCDA, the radii are 0.9 bohr for hydrogen (H), 1.1 bohr for carbon (C) and 1.2 for oxygen (O). The electronic properties are calculated first using DFT with the generalized gradient approximation in the Perdew–Burke–Ernzerhof parametrization for the exchange–correlation (xc) func-tional. The sampling of the BZ is carried out with a homogeneous 3 × 3 × 1 Monkhorst–Pack k-point grid. To account for van der Waals forces and intermolecular interactions, we adopt the Tkatchenko–Scheffler method68. The quasi-particle (QP) energies are computed within the G0W0 approximation69, where we include 200 empty states to compute the frequency-dependent dielectric screening within the random-phase approximation. A 2D truncation of the Coulomb potential in the out-of-plane direction z is used70. The band struc-ture is computed by using interpolation with maximally localized  Wannier functions71 and Fourier interpolation (Extended Data Fig. 5b and Extended Data Fig. 5c, respectively). To keep the calculations feasible, SOC is not considered in this work. Although SOC leads to a splitting of the lowest-energy excitonic peak by approximately 450 meV (ref. 72), it would not alter the type-I level alignment of WSe2/PTCDA. Importantly, the molecular states involved in the formation of the hX, that is, the HOMO and LUMO, would not be affected by the inclusion of SOC.To allow a direct comparison with the experimental ARPES data (Fig. 1d), we unfold the theoretical band structure by symmetry map-ping of the Bloch-vector-dependent quantities defined in the supercell into the unit-cell calculations. Here, the wavefunctions are constructed in a uniform real-space grid of 120 × 120 × 120 and used to calculate the spectral function (Fig. 1f).The QP band gap of WSe2 in the heterostructure is in good agree-ment with that measured by STS28; however, the PTCDA gap is underes-timated, which is most evident in the level alignment of the HOMO. This discrepancy can be explained by the interplay of different effects such as SOC, the choice of the xc functional and its role as a starting point for the QP calculations, and the interlayer distance between PTCDA and WSe2. Uncertainties in the latter can be related to packing density, the xc functional and the treatment of van der Waals interactions,  http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5or temperature73. In earlier studies on ZnO/WSe2 it has been shown  that increasing the interlayer distance leads to a noticeable increase in the QP gaps on both sides of the interface74. Also in WSe2/PTCDA, increasing (decreasing) the interlayer distance will decrease (increase) the mutual screening, leading to an increase (decrease) in the  HOMO–LUMO gap. This, in turn, would lead to an increase (decrease) in the VBM–HOMO distance. Overall, there is an interplay of effects on the order of a few tenths of an electronvolt each, which can only  be resolved through extensive future QP calculations.To overcome this mismatch, we apply a scissors shift to the  molecular levels. Shifting the LUMO by −50 meV closer to the experi-mental value28 results in very good agreement of the excitonic spectrum with experiment (see below).Calculation of the exciton spectrumFor the calculation of the exciton spectrum, we solve the BSE on top of the QP band structure, where the screened Coulomb potential is computed using 100 empty bands. In the construction and diagonaliza-tion of the BSE Hamiltonian, 16 occupied and 14 unoccupied bands are included, and a 12 × 12 × 1 shifted k-point mesh is adopted. Calculations are performed using the BSE module75 of the ‘exciting’ code.Calculation of the correlation functionFollowing the definition in ref. 40, we calculate the electron–hole correlation functionFi(r) = ∫Ωd 3re|ψi(rh = re + r, re)|2, (7)where Fi describes the probability of finding electron and hole sepa-rated by the vector r = rh − re. We approximate this integral by a discrete sum over a finite number of fixed electron coordinates. For each elec-tron position, the hole probability ∣ψi(rh = re + r, re)∣2 is computed on an evenly spaced, dense grid of 100 × 100 × 100 sampling points, covering approximately 3 × 3 × 1 supercells. For the hX, we sampled 60 posi-tions on the PTCDA molecule (0.5 Å−1 below and above the carbon and oxygen atoms) because its electronic contribution is almost entirely composed of the LUMO of PTCDA. Similarly, we calculated the elec-tron–hole correlation function of the K-exciton (Extended Data Fig. 7), which is completely localized in the WSe2 layer. Here, we sampled 16 positions close to the W atoms where we expect a high probability of finding the electron.For further analysis, the three-dimensional correlation function  is split into its in-plane and out-of-plane components by integrating  over the other direction (Fig. 4 and Extended Data Fig. 7). Here, the intralayer (purple) and interlayer (green) in-plane distributions were  extracted by integrating exclusively over the respective peak of F(r⊥), that is, r⊥ = −3 to 4.5 Å and r⊥ = −10.5 to −3 Å for the intra- and interlayer components, respectively. Notably, the in-plane component  shows a distinct periodic pattern (see insets in Fig. 4b and Extended  Data Fig. 7b). Thus, to extract the in-plane radial profile and the root mean square (RMS) radius, we first filter the data in Fourier space, thereby smoothing it in the real space.Spatial analysis of the K-exciton and comparison with hXIn analogy to the analysis of the spatial structure of the hX in Fig. 4,  we analyse the K-exciton wavefunction (Extended Data Fig. 7).  From the BSE calculation, we find that FK(r⊥) is dominated by a single peaked feature centred around r⊥ ≈ 0 Å, implying that the exciton is of pure intralayer character (Extended Data Fig. 7a). Consequently, the probability density of finding K-excitons in the WSe2 layer is nearly 100%. Consistent with this, the two smaller side peaks located at a distance corresponding to the distance between the tungsten and selenium planes dW,Se, can be attributed to a residual probability of the electron and/or hole being at the selenium atoms.Due to its hydrogen-like structure, the in-plane electron–hole probability distribution of the K-exciton can be directly reconstructed from the experimental photoemission momentum fingerprint via Fourier analysis31,41,42,59. This allows a direct comparison of FK(r∥) between theory and experiment (Extended Data Fig. 7b). Both theory and experiment confirm the pure Wannier-like character of the K-exciton because the radial distribution is much larger than the WSe2 lattice constant. For a more quantitative analysis, we compare the extracted RMS radii to be (rBSEK  = 14 Å) (theory) and rexpK  = 10 ± 1 Å (experi-ment), which are in excellent agreement. Note that, due to the finite momentum resolution of the photoemission signal, the derived RMS radius represents a lower limit of the true value. The distinct intralayer and Wannier-like character of the K-exciton can be further visualized by plotting the isosurface of a representative fixed electron and hole position (Extended Data Fig. 7c), which stands in clear contrast to the isosurfaces of the hX (Fig. 4).After having identified the K-exciton as a Wannier exciton, we com-pare its in-plane correlation function directly to that of the inter- and intralayer contributions to the hX (Extended Data Fig. 8). Here, we find that the interlayer contribution resembles the spatial distribution of the K-exciton, while the intralayer contribution is more localized and exhibits a stronger spatial modulation stemming from the molecular orbitals. This direct comparison confirms the previously assigned Frenkel- or Wannier-type character of the intra- and interlayer contri-bution of the hX.For comparison, the calculated RMS radii of the K-exciton and both components of the hX are summarized in Extended Data Table 2.Data availabilityThe datasets that support the experimental findings of this study are available via GRO.data at https://doi.org/10.25625/BEKR3I (ref. 76). The theoretical data are available via NOMAD at https://doi.org/10.17172/NOMAD/2024.10.11-1 (ref. 77).References51.  Wießner, M. et al. Electronic and geometric structure of the  PTCDA/Ag(110) interface probed by angle-resolved photoemission. Phys. Rev. B 86, 045417 (2012).52.  Keunecke, M. et al. Electromagnetic dressing of the electron energy spectrum of Au(111) at high momenta. Phys. Rev. B 102, 161403 (2020).53.  Medjanik, K. et al. Direct 3D mapping of the Fermi surface and Fermi velocity. Nat. Mater. 16, 615–621 (2017).54.  Merboldt, M. et al. 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Replication data for: “Hybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interface”. GRO.data https://doi.org/10.25625/BEKR3I (2025).77.  NOMAD repository for: “Hybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interface. Dataset: PTCDA_WSe2”. NOMAD https://doi.org/10.17172/NOMAD/2024.10.11-1 (2024).AcknowledgementsWe thank C. Kern for valuable discussions. The Göttingen team is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—432680300/SFB 1456 (project B01), 217133147/SFB 1073 (projects B07 and B10), 535247173/SPP2244 and 510228793/SFB 1633 (project C01). C.D. and I.G.O. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via SFB 951 (project 182087777) and the European Union’s Horizon 2020 research and innovation programme under agreement no. 951786 (NOMAD CoE). I.G.O thanks the Deutscher Akademischer Austauschdienst (DAAD) for financial support and acknowledges fruitful discussions with S. Tillack and B. Maurer. Computing time on the supercomputers Lise and Emmy at NHR@ZIB and NHR@Göttingen is gratefully acknowledged. P.P. acknowledges support from the Austrian Science Fund (FWF) project I 4145 and from the European Research Council (ERC) Synergy Grant, Project ID 101071259. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan.Author contributionsD. Steil, R.T.W., P.P., C.D., G.S.M.J., M.R. and S.M. conceived the research. W.B., P.W. and A.M.S. fabricated the sample. W.B., J.P.B., P.W., D. Schmitt and M.M. carried out the time-resolved momentum microscopy experiments. W.B. analysed the experimental data. I.G.O. carried out the theoretical calculations guided by C.D. All authors discussed the results. G.S.M.J., M.R. and S.M. were responsible for  the overall project direction. W.B., I.G.O., G.S.M.J., M.R. and S.M. wrote the manuscript with contributions from all co-authors. K.W. and  T.T. synthesized the hBN crystals.FundingOpen access funding provided by Georg-August-Universität Göttingen.Competing interestsThe authors declare no competing interests.Additional informationExtended data is available for this paper at  https://doi.org/10.1038/s41567-025-03075-5.Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41567-025-03075-5.Correspondence and requests for materials should be addressed to G. S. Matthijs Jansen, Marcel Reutzel or Stefan Mathias.Peer review information Nature Physics thanks Kumaran Adarsh, Zhaogang Nie and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Reprints and permissions information is available at  www.nature.com/reprints.http://www.nature.com/naturephysicshttps://www.researchsquare.com/article/rs-4632588/v1https://homepage.uni-graz.at/de/peter.puschnig/research-1/https://homepage.uni-graz.at/de/peter.puschnig/research-1/https://doi.org/10.25625/BEKR3Ihttps://doi.org/10.17172/NOMAD/2024.10.11-1https://doi.org/10.17172/NOMAD/2024.10.11-1https://doi.org/10.1038/s41567-025-03075-5https://doi.org/10.1038/s41567-025-03075-5http://www.nature.com/reprintsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Fig. 1 | Analysis of the real-space structure of the WSe2/PTCDA  heterostructure. a Sketch of the layered sample structure. b, c Optical microscope and photoemission real-space image of the sample before PTCDA evaporation. The different flakes are marked with the same colors as used in a. Note that the marked WSe2 area corresponds to an intact monolayer (without cracks) whereas the complete monolayer as seen by the contrast in b and c was larger. d LEED pattern of monolayer PTCDA on multilayer WSe2 recorded with a beam energy of 24 eV. The red circles correspond the superstructure defined by the matrix M = ((1.58,6.78), (4.39,1.32)). e The presence of a well-ordered PTCDA monolayer on the WSe2 monolayer is confirmed by the appearance of umklapp-scattering replicas of the WSe2 band structure, here shown for the valence band maximum at the K point (red circles). The replicas can be directly compared to the LEED pattern in d.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Fig. 2 | Direct comparison of ARPES data collected on pristine monolayer WSe2 and the WSe2/PTCDA heterostructure. a,b,e,f Momentum-maps collected at energies of the valence bands (bottom row) and at energies of excitonic photoemission signatures (top row). Photoemission signatures of the HOMO and the hX are labeled by arrows in f and b, respectively. c,g Simulated momentum maps from DFT calculations of the LUMO and HOMO of PTCDA using the plane wave model of photoemission30 and accounting for the herringbone structure and the different mirror and rotational domains shown in d. The DFT data are extracted from ref. 66.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-51.35 - 1.75 eV0.32 - 0.62 eV01Comp 1 (K) Comp 2 (  ) Comp 3 (hX@1.6) + 4 (hX@0.4)Comp 5 (Background)Extended Data Fig. 3 | NMF component analysis of the ARPES data. Components 1, 2, 3, and 4 follow the temporal dynamics extracted for the K, Σ,  hX@1.6eV, and hX@0.4eV photoemission features, respectively. Comp 5 corresponds to the static component, that is, the time-independent background which is subtracted from the raw data for the momentum maps and EDCs shown in Fig. 2. The photoemission features of the K-excitons, Σ-excitons, and the hX are marked by an orange hexagon, gray circles and a blue circle, respectively, in the components where most prominent. The energy regions of interest are chosen to be the same as the one shown in Fig. 2. Each component is normalized to the maximal value of the upper and lower panel.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Fig. 4 | Momentum-filtered energy-distribution-curves of the K-exciton (a), the Σ -exciton (b), and the hX (c). The dashed vertical lines indicate the energy range used to extract the delay-dependent data shown in Fig. 5. c The vertical black arrow highlights the appearance of the lower energy photoemission maximum that is attributed to the hX photoemission signature.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5MLUMOHOMOab cWSe2/PTCDAPBE, backfolded bandstructure G0W0+shift, backfolded bandstructureExtended Data Fig. 5 | Calculated supercell and single-particle band structure. a Optimized structure of PTCDA adsorbed on WSe2 monolayer in a 4 × 4 × 1 WSe2 supercell. b,c Band structure of WSe2/PTCDA obtained by PBE and G0W0 calculation analyzed along the directions of the backfolded Brillouin zone indicated in the inset of c. The bands are colored according to their PTCDA (black) or WSe2 (orange) character. The G0W0 results in c already include the scissors shift applied to the LUMO according to existing STS data in literature27,28.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Fig. 6 | Exciton formation and relaxation dynamics of the bright K-exciton (a), the momentum dark Σ -exciton (b) and the hX (c). The respective regions of interest in momentum space are shown in the insets. The time-dependent data collected on WSe2/PTCDA (filled symbols) is directly plotted next to data collected on pristine monolayer WSe2 (open symbols; data taken from ref. 23 The hX double-peak photoemission structure is evaluated separately in energy ranges of 0.9-2.4 eV (circle) and 0.3-0.7 eV (triangles). The rise and decay dynamics are fitted with an error and a (bi-) exponential function, respectively (cf. methods). The fit parameters are summarized in Extended Data Table 1.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5ba Relative probability distributionin-planeRelative probability distributionout-of-planec     Probability density isosurfacesfixed hole positionfixed electron positionprobability distribution of holeprobability distribution of electronfixed holefixed electronrBSEKrexpKaWSe2dW,SeExtended Data Fig. 7 | Analysis of the real-space properties of the K-exciton. The relative out-of-plane (a) and in-plane components (b) of the electron-hole correlation function Fi(r) = F(re − rh) are analyzed. a The out-of-plane (r⊥) component directly confirms the intralayer nature (r⊥ ≈ 0 Å). Next to the dominant peak at r⊥ = 0 Å, two side peaks are present at a distance that matches the distance between the tungsten and selenium planes (dW,Se) of the WSe2 monolayer. b The in-plane component can be accessed by theory (black) and experiment (orange). Here, the experimental distribution corresponds to the weighted mean from the angular-averaged probability distribution of all  6 K-points. The shaded area corresponds the standard deviation of the weighted mean of all 6 K-points. The extracted RMS radius is marked by arrows. The inset corresponds to the two-dimensional representation of FK (r∥). c Orthographic side view of exemplary probability density isosurfaces of the K-exciton for fixed hole (top) and fixed electron (bottom) position confirming the pure intralayer and Wannier-like character of the K-exciton.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5aWSe aPTCDA2Extended Data Fig. 8 | Comparison of the in-plane correlation function of the K exciton, the intralayer and interlayer component of the hX. For better comparison, each component is normalized individually. The upper row (from left to right) shows the two-dimensional in-plane correlation function of the intra- and interlayer components of the hX and of the K-exciton. The line profiles correspond to the respective angular-averaged Fourier filtered in-plane correlation function.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Table 1 | Experimental and theoretical exciton energies (Eexc,EBSEexc ), as well as decay (τfast, τslow) and rise  (μonset, σrise) times of the excitons found in WSe2/PTCDAThe exciton energies are compared to those of pure monolayer WSe2 taken from literature as indicated in the table22,23,62. The decay- and rise-times are compared to those pure monolayer WSe2 determined by the same fitting routine based on data from ref. 23. Details of the applied fitting procedures can be found in the Method section.http://www.nature.com/naturephysicsNature PhysicsArticle https://doi.org/10.1038/s41567-025-03075-5Extended Data Table 2 | omparison of the spatial extent of the K-exciton and the hXTheoretical and experimental extracted RMS radii of the in-plane relative probability distribution of the K-exciton and the hX, as well as the probability that the in-plane relative electron-hole distance is smaller than the PTCDA lattice constant (P(r∥ < aPTCDA)).http://www.nature.com/naturephysics Hybrid Frenkel–Wannier excitons facilitate ultrafast energy transfer at a 2D–organic interface TMD/OSC sample structure and single-particle energy level alignment Momentum-resolved characterization of excitons at the 2D–organic interface A hybrid exciton bridging the 2D–organic interface Experimental characterization of the hX Real-space wavefunction distribution of hybrid Wannier–Frenkel excitons Femtosecond time- and orbital-resolved exciton dynamics Online content Fig. 1 Sample layout and electronic structure of the hybrid WSe2/PTCDA heterostructure. Fig. 2 Energy- and momentum-resolved identification of the excitonic photoemission signatures. Fig. 3 Reciprocal-space representation of the Bloch states and molecular orbitals contributing to the K-exciton and the hX wavefunction. Fig. 4 Real-space properties of the hX wavefunction. Fig. 5 Femtosecond formation of the hX at the hybrid WSe2/PTCDA interface. Extended Data Fig. 1 Analysis of the real-space structure of the WSe2/PTCDA heterostructure. Extended Data Fig. 2 Direct comparison of ARPES data collected on pristine monolayer WSe2 and the WSe2/PTCDA heterostructure. Extended Data Fig. 3 NMF component analysis of the ARPES data. Extended Data Fig. 4 Momentum-filtered energy-distribution-curves of the K-exciton (a), the Σ -exciton (b), and the hX (c). Extended Data Fig. 5 Calculated supercell and single-particle band structure. Extended Data Fig. 6 Exciton formation and relaxation dynamics of the bright K-exciton (a), the momentum dark Σ -exciton (b) and the hX (c). Extended Data Fig. 7 Analysis of the real-space properties of the K-exciton. Extended Data Fig. 8 Comparison of the in-plane correlation function of the K exciton, the intralayer and interlayer component of the hX. Extended Data Table 1 Experimental and theoretical exciton energies (), as well as decay (τfast, τslow) and rise (μonset, σrise) times of the excitons found in WSe2/PTCDA. Extended Data Table 2 omparison of the spatial extent of the K-exciton and the hX.