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Xing Zhu, David R. Bacon, Vivek Pareek, Julien Madéo, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Michael K. L. Man, Keshav M. Dani

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[A holistic view of the dynamics of long-lived valley polarized dark excitonic states in monolayer WS2](https://mdr.nims.go.jp/datasets/921bbdfe-2bb6-4a39-be02-0617271f30d3)

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A holistic view of the dynamics of long-lived valley polarized dark excitonic states in monolayer WS2Article https://doi.org/10.1038/s41467-025-61677-2A holistic view of the dynamics of long-livedvalley polarized dark excitonic states inmonolayer WS2Xing Zhu1,5, David R. Bacon1,4,5, Vivek Pareek1,5, Julien Madéo 1,5,Takashi Taniguchi 2, Kenji Watanabe 3, Michael K. L. Man 1 &Keshav M. Dani 1With their long lifetime and protection against decoherence, dark excitons inmonolayer semiconductors offer a promising route for quantum technologies.Optical techniques have previously observed dark excitons with a long-livedvalley polarization. However, several aspects remain unknown, such as thepopulations and time evolution of the different valley-polarized dark excitonsand the role of excitation conditions. Here, using time- and angle-resolvedphotoemission spectroscopy, we obtain a holistic view of the dynamics aftervalley-selective photoexcitation. By varying experimental conditions, wereconcile between the rapid valley depolarization previously reported in TR-ARPES, and the observation of long-lived valley polarized dark excitons inoptical studies. For the latter, we find that momentum-dark excitons largelydominate at early times sustaining a 40% degree of valley polarization, whilevalley-polarized spin-dark states dominate at longer times. Ourmeasurementsprovide the timescales and how the different dark excitons contribute to thepreviously observed long-lived valley polarization in optics.In two dimensional (2D) semiconductors, the Coulomb interactionbetween the electron and hole leads to tightly bound excitons thatexist even at room temperature. Moreover, in the case of transitionmetal dichalcogenides (TMDC)—prototypical 2D semiconductors,their honeycomb lattice structure creates two degenerate, butinequivalent valleys at the K andK’ points at the edge of the Brillouinzone (BZ)1. For monolayer (1 L) TMDC, the lack of inversion sym-metry enables valleytronics applications, with information encodedin the valley state of the bright excitons residing in the K- or K’-valley (Fig. 1a)2,3. Nonetheless, in these systems, the presence ofadditional nearly-degenerate spin- and momentum-dark excitons—those that do not interact with light due to the respective con-servation rules, complicates the picture. Phonon interactions createmomentum-dark excitons with the electron residing in the oppositeK’(K) valley or Q valley from the exciton-bound hole4,5, (Fig. 1a, b).Spin-dark excitons, that exist due to the presence of a relativelysmall spin-orbit split in the K (K’) conduction band (Fig. 1b), canform by intravalley scattering mechanisms6. In addition to theseinteractions that scatter the bright excitons into optically inacces-sible dark states, another primary impediment to valleytronics in 1 LTMDCs is the intervalley exchange interaction, which couples the Kand K’ valleys via a dipole-dipole interaction, flipping simulta-neously electron and hole spins7,8. This results in the transfer ofbright excitons from one valley into the other on a sub-100 fstimescale9,10, rapidly depleting valley information initially encodedinto the system11–13. Optically accessible interlayer excitons (ILX),found in heterobilayer systems, provide one possible way aroundthe problem as they do not undergo intervalley exchangeReceived: 29 October 2024Accepted: 26 June 2025Check for updates1Femtosecond Spectroscopy Unit, Okinawa Institute of Science and Technology, Okinawa, Japan. 2International center for Materials Nanoarchitectronics,National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan. 3Research Center for Electronics and Optical Materials, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba, Japan. 4Present address: Department of Chemistry, University College London, London, United Kingdom. 5These authorscontributed equally: Xing Zhu, David R. Bacon, Vivek Pareek, Julien Madéo. e-mail: KMDani@oist.jpNature Communications |         (2025) 16:6385 11234567890():,;1234567890():,;http://orcid.org/0000-0002-1711-5010http://orcid.org/0000-0002-1711-5010http://orcid.org/0000-0002-1711-5010http://orcid.org/0000-0002-1711-5010http://orcid.org/0000-0002-1711-5010http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0001-6043-3631http://orcid.org/0000-0001-6043-3631http://orcid.org/0000-0001-6043-3631http://orcid.org/0000-0001-6043-3631http://orcid.org/0000-0001-6043-3631http://orcid.org/0000-0003-3917-6305http://orcid.org/0000-0003-3917-6305http://orcid.org/0000-0003-3917-6305http://orcid.org/0000-0003-3917-6305http://orcid.org/0000-0003-3917-6305http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61677-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61677-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61677-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-61677-2&domain=pdfmailto:KMDani@oist.jpwww.nature.com/naturecommunicationsinteraction. However, the excitonic landscape in heterobilayersystems is even more complex, and includes the need for an intri-cate, non-resonant formation pathway for the ILX due to their weakoscillator strength14. Moreover, the need for precisely twistedadditional layers creates challenges for future scalable devicefabrication.Another potential route to overcome the above challenges withbright excitons is to encode the valley information into a dark exci-tonic state in 1 L TMDC. It has been theoretically proposed that thesewould exhibit a strong elongation of the valley-polarization lifetimesince they do not exhibit the intervalley exchange interaction betweenthe two K and K’ valleys8. Furthermore, due to their lack of interactionwith electromagnetic radiation, dark excitons are expected to livelonger15–17 and decohere less18,19, as compared to bright excitons. Pre-vious optical experiments have confirmed the presence of long-livedvalley-polarized dark excitons20 in monolayer WSe2, includingmomentum-dark excitons21, spin-dark excitons15 and dark trions22.Beyond this, several key aspects of valley-polarized dark excitonsremain unknown—both in terms of their fundamental properties andtheir potential applications in quantum technologies. For instance, welack information on the population of each of the different darkexcitonic states at a particular time-delay relative to all the excitonsthat are generated after photoexcitation. Understanding which specieof valley-polarized dark excitons dominate at a given delay is impor-tant to being able to manipulate information stored in the valleydegree of freedom of dark excitons. Furthermore, it is also unclearwhether experimental conditions can impact the relative contributionof a particular dark state to the overall photoexcited excitonic popu-lation and thereby affect the degree of valley polarization. Suchinformation likely lies beyond the reach of conventional optical spec-troscopy techniques.Time- and angle-resolved photoemission spectroscopy (TR-ARPES)—a powerful technique to access the momentum character ofexcitons, their dynamics and the absolute excitonic populations23–26has the potential to answer these questions. However, prior TR-ARPESmeasurements on atomically thinTMDCdid not observe the long-livedvalley polarization seen with optical spectroscopy. Instead, theyobserved a rapid valley depolarization due to the intervalley exchangeinteraction27, thus creating an apparent inconsistency between thesetwo powerful experimental platforms.In this letter, we perform time-resolved momentum microscopyon monolayer WS2 with sufficient energy resolution to resolve thevarious spin- and momentum-dark excitonic states that form over theentire BZ after the photoexcitation of the valley-polarized brightexcitons. Using a model based on rate equations, we extract theoccupation of the various excitonic states and the timescales ofintervalley exchange interaction, exciton-phonon scattering andintravalley spin relaxation. We find that under the experimental con-ditions of low temperature, low-intensity and resonant excitation, theintervalley exchange interaction of the initial K-valley-polarized brightexciton into the K’-valley is suppressed. Instead, one scatters almostexclusively into a specific, intermediate energy, valley-polarizedFig. 1 | Time-Resolved XUV ARPES of valley polarized excitons in monolayerWS2. a (left) Schematic depicting the hexagonal Brillouin zone (BZ) of monolayerWS2 showing the K and K’ valleys at the vertices of the BZ and intermediateQ valleyand (right) band diagram describing the bright excitons, the K’-K momentum-darkexcitons and the spin-dark excitons. The red dots represent the hole in the valenceband. The blue dots represent the location of the electron in spin-split states(dashed lines). The arrows represent the spin configuration in the K valley andarrows inbrackets in theK’ valley.b Simplified experimental setup using a circularlypolarized photoexcitation and a XUV photoemission probe on a WS2 monolayersample on hBN to photoemit exciton-boundelectrons that are collectedby the lensof amomentummicroscope. c (kx,ky) ARPESdata (energy integrated between 1.9 to2.2 eV above the valence band corresponding to the energy of the exciton-boundelectron signal), at 0 ps timedelay showing the valley contrast between theK andK’valley. A 120° rotating average centered at was performed to symmetrize thephotoemission signal of each K and K’ valleys (See SI §5).Article https://doi.org/10.1038/s41467-025-61677-2Nature Communications |         (2025) 16:6385 2www.nature.com/naturecommunicationsmomentum-dark exciton. This dark exciton maintains its valley selec-tivity for several picoseconds, nearly two orders of magnitude longerthan the bright exciton. In contrast, our measurements at room tem-perature or high excitation intensities show the more commonlyexpected behavior—the initial valley polarization vanishes within a few100 s of fs, also seen in previous measurements for non-resonantexcitation27.ResultsTr-ARPES experiment on 1 L WS2: Valley-selective excitationOur sample is an exfoliated WS2 monolayer, transferred on a thin hBNbuffer layer supported by a conducting Si substrate (seeMethods). TheTR-ARPES experiments (Fig. 1b) were conducted using a momentummicroscope28,29 as described in previous works23,25,30. Measurementswere performed at 90K, unless specified otherwise. With our currentinstrument capabilities and sample quality, we measure a FWHM line-width of 88meV of the top valence band in static ARPES (See SI §2). Toresolve the valley dynamics of excitons, the sample was photoexcitedwith a 2.1 eV circularly polarized pump in resonance with the A-excitonto selectively populate theK-valley as shown in Fig. 1c.Wephotoexciteda low density of 4:5 × 1011 cm-2 excitons (see SI §6), thus limiting pump-induced band broadening effects. Thereby, in our experiments, theFWHM linewidth of the top valence band after photoexcitation and thephotoexcited excitonic state did not exceed ~100meV (See SI). Asexplained in more detail later, this enabled the resolution of the spin-bright and spin-dark excitonic states (Fig. 2a–e). We also carefullyrotated our samplewith respect to the XUVprobe geometry to equalizethe photoemission matrix elements between two adjacent K and K’valleys of the 1st BZ (See SI §4). This allows direct quantitative com-parison of the photoexcited populations between the two valleys.Observation of valley-polarized momentum-dark excitonsFirst, let’s discuss the observation of long-lived valley polarizedmomentum-dark excitons. To do so, we resolve in momentum spacethe constituent electrons and holes of excitons in both K and K’ valleys(Fig. 2f). With the valley selective photoexcitation, at very early time-delays, we predominantly see (>90%) the bright K-valley excitons. Thisis evidenced by the large photoemission signal at the exciton energyfrom the exciton-electrons in the K valley and the correspondingpresence of holes (loss of photoemission signal) in the valence band ofthe same valley (Fig. 2f–Kvalley).We also clearly observed the negativedispersion from the exciton-electron photoemission signal (Fig. 2a)–ahallmark of the excitonic state30 (see SI §9). Additionally, at these earlytime-delays, we observe a weak signal in the K’ valley at the energy ofthe bright exciton (see Fig. 2c). This is expected from the rapid inter-valley exchange interaction of the photoexcited K-valley excitons intothe K’ valley (Fig. 2f–K’ valley).We rule out any significant contributionfrom a momentum-dark state with electrons in the upper K’ state as itrequires a spin-flip scattering process (enhanced at higher tempera-ture, see SI § 7). The weakly appearing (kx, ky) momentum distributionof holes in Fig. 2f in the K’ valley is due to too low experimental signal-to-noise for this low density ( ~ 7 × 1010 cm-2).Strikingly, at 1 ps, we find that the dominant excitonic species isnow a valley-polarizedmomentum-dark exciton (K’- K exciton), as seenby the large electron population in the K’ valley and a large holepopulation remaining in the K valley (Fig. 2g). As expected from themomentum-darkK’-K exciton, thephotoemission signal of the exciton-electrons is ~40meVbelow the signal corresponding to bright excitons(see Fig. 2d). This value is similar to the intravalley spin-split observedin Fig. 2e and is also in good agreement with previous reports of thespin-splitting energy Δ"#31,32. We note that the energy of themomentum-dark exciton is expected to be slightly higher than thespin-dark exciton, due to electron-hole exchange repulsion, whichreduces the binding energy of the spin-like momentum-dark excitonbut does not impact the spin-unlike spin-dark exciton33. However, thisis not currently accessible with our energy resolution. At 1 ps, wealso observe an exciton-electron signal in the K-valley, and the pre-sence of holes in the K’ valley (Fig. 2g). As discussed below, this is dueto the presence of a weaker population of the opposite valley-polarized K-K’ momentum-dark excitons, as well as the K-valley spin-dark excitons.Our observations show the presence of a large population ofvalley polarized K’-K momentum-dark excitons up to long time-delays.This is surprising as one expected the intervalley exchange interactionto rapidly deplete valley polarization12. In our experiments, the lowphotoexcitation intensity plays a critical role in minimizing valley-depolarization due to the intervalley exchange interaction since itresults in the creation of fewer excitons with non-zero center of massmomentum (QCM ≠0) (This is also seen in the very clear negative dis-persion of Fig. 2a that is exhibited by excitons with QCM =0). Excitonswith zero CMdo not undergo intervalley exchange interaction12,34, andhence, with the lower photoexcitation intensity, we get a smallerpopulation scattering to the bright K’ valley excitons. Besides thesuppression of valley-depolarization, it is also surprising that valleypolarization is preserved in a specific dark excitonic states, since onemight have expected that the numerous excitonic scattering pathwayswould result in the formation of a large variety of excitonic species.The preservation of the valley polarization in a specific state makes itmore feasible to control this polarization in future applications. Wenote that the long lifetime of the intermediate-energy K’-K excitonicstate is not unexpected due to the potential bottleneck of spin-flipscattering suppressing the decay to the lowest energy dark excitonicstate35.Dynamics of the long-lived valley-polarized momentum-darkexcitonTo effectively utilize the momentum-dark exciton in valleytronicapplications, one must study its dynamics, as well as the global exci-tation dynamics, after valley-selective photoexcitation of bright exci-tons. To do so, we resolve the valley and spin states (via our energyresolution—Fig. 2e) of the exciton-bound electrons and holes over theentire BZ. The electron and hole populations are obtained by energyand momentum integrating their respective signals (see SI §3 and §6).From thesemeasured electron and hole populations, we fit to amodelbased on rate equations, which enables us to extract the relevantexcitonic populations and scattering timescales (see Fig. 3a and SI §7).The rate equations describing the temporal evolution of the variousexcitonic states have the general form11:dXndt= gn tð Þ �Xm1τmnXn +Xm1τnmXm ð1ÞWhere Xn is the density of the considered excitonic states, gn tð Þ is ageneration term, τmn ðτnmÞ are the timescale corresponding to thedepopulationof theXn (Xm) populationby scattering to aXm ðXnÞ stateincluding intervalley exchange (τex), exciton-phonon (τph), andintravalley (τintra) scattering as well as recombination.Our data reveals a clear sequential formation of the differentexcitonic states following the resonant excitationof the valley-polarizedbright excitons (Fig. 3b) with an initial density of 4:5 × 1011 cm−2. First,only a small population of the bright K excitons (7 × 1010 cm−2) rapidlyscatters to the K’ bright excitons through intervalley exchange inter-action (τex =0.3 ps), due to the low photoexcitation intensity, as dis-cussed above. Following this, we see the predominant formation of theK’-K momentum-dark excitons (>60% at 1 ps) via intervalley phononscattering (τph =0.8 ps). Correspondingly, the initially photoexcitedpopulation of bright K excitons rapidly depletes (<0.5 ps). This K’–Kmomentum-dark exciton remains the dominant species across ourexperimental temporal range (10ps) and maintains a high degree ofvalleypolarization (>40%), definedasPðXK 0�K Þ= nXK0�K�nXK�K0nXK 0�K +nXK�K0, where nXiArticle https://doi.org/10.1038/s41467-025-61677-2Nature Communications |         (2025) 16:6385 3www.nature.com/naturecommunicationsis the density of exciton Xi, through this time (Fig. 3c). In comparison,the degree of valley polarization of the bright exciton is less than 10%within a few hundred fs (Fig. 3c). We expect that this long-lived polar-ization is due to the lack of intervalley exchange interaction for themomentum-dark excitons8, as well as the spin-flip or energy cost asso-ciated with the momentum-dark exciton scattering back into an intra-valley exciton.Our simple model also allows us to extract the dynamics of theother excitonic states that form after valley-polarized photoexcitationand their associated scattering times (see Fig. 3b). In particular, thespin-dark excitons formwith amuch slower scattering time of a fewps,consistent with previous report of spin relaxation in W-basedTMDCs22,35. Our data shows that the spin-dark excitons also carry asimilar degree of valley selectivity, albeit with an order of magnitudeFig. 2 | Valley polarized momentum-dark excitons. a–d Energy and momentumresolved linecut along the Γ-K-M axis showing. At 0 ps time delay, the resonantlyphotoexcited bright exciton signal in the K valley shows an exciton-bound electronwith negative dispersion, located 2.1 eV above the valence band (red). By 1 ps, in thesame valley, this electron signal has relaxed to a lower energy state (blue). In the K′valley, a weak electron population is observed at 0 ps at the photoexcitation energyof 2.1 eV (green). At 1 ps, it evolves into amuch larger population that shows up at alower energy (gray) (data around the exciton electron energy, 1.9–2.2 eV, werenormalized at each k-vector). The corresponding energy distribution curves in (e)shows the energy difference between the bright exciton state which dominates at0 ps and lower energy states that shows up at 1 ps. f Photoemission signals fromelectrons around the A exciton energy and from holes at the valence band duringphotoexcitation (0.1 ps). For the electrons, the ARPES signals were energy inte-grated between 1.9 and 2.2 eV and displayed in kx,ky momentum space. For theholes, we display the difference between negative time delay and after photo-excitation ARPES signals at the top of the valence band. The data were energyintegrated over 100meV (−0.05 to 0.05 eV) and a 120° rotating average around thecenterof the Γ valleywasperformed to clearlydisplay thephotoemission count losscorresponding to the presence of holes. g Photoemission signals from excitonbound electrons and holes around the A exciton energy at 1 ps using a similaranalysis as in (f).Article https://doi.org/10.1038/s41467-025-61677-2Nature Communications |         (2025) 16:6385 4www.nature.com/naturecommunicationslower density (see SI §8). We also note that although our energyresolution is insufficient to directly confirm that the spin-dark excitonis the lowest energy state, our observation that its population con-tinues to increase over our measured time window (see SI §8) is con-sistent with this prediction.We note that the above dynamics are under the specific photo-excitation conditions of low intensity (4 × 1011 cm−2), low temperature(100K) and resonant to the A-exciton. Increasing photoexcitationintensity (to a density of 2 × 1012 cm−2), sample temperature or photo-excitation energy leads to substantially different dynamics. In parti-cular, we observe that the initially photoexcited degree of valleypolarization is almost entirely depleted within a picosecond (Fig. 4), asalso seen in previous experiments27. At higher temperature (and lowintensity), by fitting our data with a model based on rate equation, wesee that scattering processes that involve a spin flip are enhanced,leading to a rapid depolarization as seen in Fig. 4e, f and that additionalscattering channel open that populate the Q-K momentum-dark exci-tons (see SI §7 for a detailed description of the dynamics and modelbased on rate equations). A higher intensity (Fig. 4c, d) provides excesscenter-of-mass momentum to the bright exciton that is expected toenhance of the intervalley exchange interaction33 and lead to a fasterdepolarization. This is confirmed by measurements showing thatincreasing pump intensity leads to a reduced valley polarization of thebright exciton, accompanied by a broadening of the exciton–electronmomentum distribution (See SI § 10).DiscussionOur results demonstrate that at low temperature, after a low inten-sity, resonant and valley-selective photoexcitation of bright excitons,the valley-polarized population of momentum-dark excitons dom-inate (85% of the population at 1 ps) and with a 40% degree of valleypolarization (for at least 10 ps). This provides important informationtowards achieving dark valleytronics, where the long-lived darkexcitons that are naturally protected from decoherence and valley-depolarization, are used as an information carrier. Our work showsthat, depending on experimental conditions, one can switch from arapid depolarization process to the formation of long-lived valley-polarized dark excitons. Future research in methods to briefly andcontrollably brighten the momentum-forbidden dark excitons, e.g.,with strain36 or phonon-assisted mechanisms4,5,21, as well as theinfluence of intervalley exchange interaction in these processes,would enable coherent initialization and read-out of the dark states –next steps in the development of dark excitons for quantum appli-cations. In addition to the momentum-dark excitons, our work alsoindicates that spin-dark excitons also host a valley-polarized popu-lation for even longer times, although they represent only a smallfraction of the initial population. Techniques utilizing magnetic fieldpulses15 or surface plasmons37 to briefly and controllably brighten thespin-dark excitons, and enhance their valley-polarized population,may offer an alternate viable path to using these excitonic species aswell for future valleytronics applications. Finally, we note theimportant role that 1 LWS2may play in enabling the transfer of valleypolarization from the bright to themomentum-dark excitons, due tothe specific spin- and energy-ordering of the excitons in this system.Relatedly, a different substrate as well as doping may also influencethe exciton dynamics and populations in each excitonic state. Futureresearch in the dark exciton dynamics in other atomically thinsemiconductors and their twisted heterostructures, with theirFig. 3 | Valley-polarizedbright exciton todark exciton scattering dynamics anddistribution at low temperature and low exciton density. aMeasured dynamicsof the electron density in the K and K’ valley for each spin-split state and holedensity in the valence band (dots). The dotted lines show the fit obtained from ourmodel based on rate equations. b Bright (XKb and XK’b), momentum-dark (XK’-K andXK-K’) and spin-dark (XKs andXK’s) dominant excitonpopulations extracted fromourmodel basedon the experimentalfit in (a). At 1 ps, wedisplay each excitonic speciescontribution to the total population. On the right, we present a diagram describingthe formation and scattering processes associated to each excitonic populations.Inset: Normalized early time dynamics showing the formation sequence of eachexcitonic state. c Temporal evolution of the degree of circular polarization andrelative population ratio for the XKb bright excitons (yellow) and for the XK’-K andXK-K’ momentum-dark excitons (blue).Article https://doi.org/10.1038/s41467-025-61677-2Nature Communications |         (2025) 16:6385 5www.nature.com/naturecommunicationsunique spin- and energy-ordering, could lead to unexpectedopportunities38,39.MethodsSample fabricationThe studied sample is composed of a mechanically exfoliated mono-layer WS2 transferred onto a hBN thin layer. hBN is used to preventexciton quenching from the n-doped Si substrate and to be consistentwith its routine use in optical experiments. The hBN is directly trans-ferred and cleaved on the Si substrate to obtain a pristine surface. Theexfoliated WS2 is transferred using the viscoelastic stamping methodbased on PDMS. After transfer, the sample is immediately rinsed inacetone and isopropanol followed by in-situ annealing at 350 °C for11 h in the ultra-high vacuum preparation chamber of the momentummicroscope.Time-resolved XUV-µ-ARPESThe experiment is driven by a high average power Yb:fiber amplifier(1030 nm, 250 fs, 100 µJ) operated at 1 MHz. 20 µJ are used to drive anoncollinear optical parametric amplifier tuned to the A excitonresonance (2.1 eV) of monolayer WS2. A quarter waveplate is thenused to create a circular polarization to photoexcite the sample. TheXUV probe is based on gas-phase High-Harmonic Generation. Aportion of the laser is frequency doubled using a BBO-crystal and10 µJ are focused into a Kr gas jet to an intensity of 2 × 1014W/cm².The resulting harmonic comb is then filtered by a set of Al and Snfoils to select the 21.7 eV harmonic with an estimated photon flux atsample of about 10 11 ph/s. No measurable space charge effects wereobserved with the probe. Both pump and probe are focused on thesample located in the ultra-high vacuum chamber of a momentummicroscope. A field aperture of 16 µm was positioned in the imageplane of the microscope to transmit only photoelectrons from themonolayer WS2 area. The microscope is then set to project a mag-nified image of the back focal plane of the objective lens on a microchannel plate and the electron energy is measured using a time-of-flight detector.Data availabilityThe data that supports the finding of this work are available uponrequest to the corresponding author.References1. Wang, G. et al. Colloquium: excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).2. Schaibley, J. R. et al. Valleytronics in 2Dmaterials.Nat. Rev.Mater. 1,16055 (2016).3. Vitale, S. A. et al. Valleytronics: opportunities, challenges, andpathsforward. Small 14, 1801483 (2018).4. Brem, S. et al. Phonon-assisted photoluminescence from indirectexcitons in monolayers of transition-metal dichalcogenides. NanoLett. 20, 2849–2856 (2020).5. Carvalho, B. R. et al. Intervalley scattering by acoustic phonons intwo-dimensional MoS2 revealed by double-resonance Ramanspectroscopy. Nat. Commun. 8, 14670 (2017).6. Malic, E. et al. Dark excitons in transition metal dichalcogenides.Phys. Rev. Mater. 2, 041002 (2018).7. Glazov, M. M. et al. Exciton fine structure and spin decoherence inmonolayers of transition metal dichalcogenides. Phys. Rev. B Con-dens. Matter Mater. Phys. 89, 201302 (2014).8. Selig, M. et al. Suppression of intervalley exchange coupling in thepresence of momentum-dark states in transition metal dichalco-genides. Phys. Rev. Res. 2, 023322 (2020).9. Hao, K. et al. Direct measurement of exciton valley coherence inmonolayer WSe2. Nat. 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K.W. and T.T. acknowledge support from the JSPS KAKENHI(Grant Numbers 21H05233 and 23H02052), theCREST (JPMJCR24A5), JSTand World Premier International Research Center Initiative (WPI), MEXT,Japan. We thank the OIST engineering support section for their support.We thank M. Naik and O. Karni for insightful discussions.Author contributionsJ.M., M.K.L.M. and K.M.D. designed the experimental setup. J.M.,M.K.L.M., X.Z., V.P. and D.B. built the experimental setup. D.B., X.Z. andV.P. performed the experiments. J.M., D.B., X.Z. and V.P. analyzed theexperimental data. D.B., M.K.L.M. and J.M. performed the rate equationanalysis. V.P. and X.Z. prepared the sample. T.T. and K.W. provided high-quality hBN for sample preparation. K.M.D. supervised the project. Allauthors contributed to the manuscript.Competing interestsJ.M.,M.K.L.M. andK.M.D. are inventorsonagrantedpatent related to thiswork filed by the Okinawa Institute of Science and Technology SchoolCorporation (US patent 11,372,199). The authors declare no other com-peting interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-61677-2.Correspondence and requests for materials should be addressed toKeshav M. Dani.Peer review information Nature Communications Riya Sebait and theother, anonymous, reviewer(s) for their contribution to thepeer reviewofthis work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-61677-2Nature Communications |         (2025) 16:6385 8http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications A holistic view of the dynamics of long-lived valley polarized dark excitonic states in monolayer WS2 Results Tr-ARPES experiment on 1 L WS2: Valley-selective excitation Observation of valley-polarized momentum-dark excitons Dynamics of the long-lived valley-polarized momentum-dark exciton Discussion Methods Sample fabrication Time-resolved XUV-µ-ARPES Data availability References Acknowledgements Author contributions Competing interests Additional information