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

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[Ultrafast dynamics of bright and dark excitons in monolayer WSe<sub>2</sub> and heterobilayer WSe<sub>2</sub>/MoS<sub>2</sub>](https://mdr.nims.go.jp/datasets/3e68b94d-70ea-491a-a3fe-26ecd4af6548)

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Ultrafast dynamics of bright and dark excitons in monolayer WSe2 and heterobilayer WSe2/MoS22D MaterialsPAPER • OPEN ACCESSUltrafast dynamics of bright and dark excitons inmonolayer WSe2 and heterobilayer WSe2/MoS2To cite this article: Jan Philipp Bange et al 2023 2D Mater. 10 035039 View the article online for updates and enhancements.You may also likeParameters optimization of tuned massdamper using fast multi swarmoptimizationR Frans and Y Arfiadi-Influence of Carrier Concentration atFront- and Back-Channel on TransferCharacteristics of Bottom-Gate n-Ga-Zn-OThin-Film TransistorsDaichi Koretomo, Tokiyoshi Matsuda,Mutsumi Kimura et al.-Parameter identification for active massdamper controlled systemsC C Chang, J F Wang and C C Lin-This content was downloaded from IP address 220.150.154.100 on 08/07/2023 at 03:22https://doi.org/10.1088/2053-1583/ace067/article/10.1088/1755-1315/419/1/012127/article/10.1088/1755-1315/419/1/012127/article/10.1088/1755-1315/419/1/012127/article/10.1149/MA2016-02/33/2139/article/10.1149/MA2016-02/33/2139/article/10.1149/MA2016-02/33/2139/article/10.1149/MA2016-02/33/2139/article/10.1088/1742-6596/744/1/012166/article/10.1088/1742-6596/744/1/0121662D Mater. 10 (2023) 035039 https://doi.org/10.1088/2053-1583/ace067OPEN ACCESSRECEIVED3 May 2023REVISED12 June 2023ACCEPTED FOR PUBLICATION21 June 2023PUBLISHED3 July 2023Original Content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERUltrafast dynamics of bright and dark excitons in monolayer WSe2and heterobilayer WSe2/MoS2Jan Philipp Bange1, Paul Werner1, David Schmitt1, Wiebke Bennecke1, Giuseppe Meneghini2,AbdulAziz AlMutairi3, Marco Merboldt1, Kenji Watanabe4, Takashi Taniguchi5, Sabine Steil1,Daniel Steil1, R Thomas Weitz1,6, Stephan Hofmann3, G S Matthijs Jansen1, Samuel Brem2,Ermin Malic2, Marcel Reutzel1,∗ and Stefan Mathias1,6,∗1 I. Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany2 Fachbereich Physik, Philipps-Universität, 35032 Marburg, Germany3 Department of Engineering, University of Cambridge, Cambridge CB3 0FA, United Kingdom4 Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan5 Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan6 International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany∗ Authors to whom any correspondence should be addressed.E-mail: marcel.reutzel@phys.uni-goettingen.de and smathias@uni-goettingen.deKeywords:moiré materials, time- and angle-resolved photoelectron spectroscopy, interlayer exciton, hybrid exciton, dark exciton,transition metal dichalcogenide, exciton dynamicsAbstractThe energy landscape of optical excitations in mono- and few-layer transition metaldichalcogenides (TMDs) is dominated by optically bright and dark excitons. These excitons can befully localized within a single TMD layer, or the electron- and the hole-component of the excitoncan be charge-separated over multiple TMD layers. Such intra- or interlayer excitons have beencharacterized in detail using all-optical spectroscopies, and, more recently, photoemissionspectroscopy. In addition, there are so-called hybrid excitons whose electron- and/orhole-component are delocalized over two or more TMD layers, and therefore provide a promisingpathway to mediate charge-transfer processes across the TMD interface. Hence, an in-situcharacterization of their energy landscape and dynamics is of vital interest. In this work, usingfemtosecond momentum microscopy combined with many-particle modeling, we quantitativelycompare the dynamics of momentum-indirect intralayer excitons in monolayer WSe2 with thedynamics of momentum-indirect hybrid excitons in heterobilayer WSe2/MoS2, and draw three keyconclusions: First, we find that the energy of hybrid excitons is reduced when compared to excitonswith pure intralayer character. Second, we show that the momentum-indirect intralayer and hybridexcitons are formed via exciton-phonon scattering from optically excited bright excitons. Andthird, we demonstrate that the efficiency for phonon absorption and emission processes in themono- and the heterobilayer is strongly dependent on the energy alignment of the intralayer andhybrid excitons with respect to the optically excited bright exciton. Overall, our work providesmicroscopic insights into exciton dynamics in TMDmono- and bilayers.1. IntroductionExfoliated and artificially stacked monolayers oftransition metal dichalcogenides (TMDs) have beenshown to be a highly tuneable material platform forexploring optical excitations and correlated interac-tions on the atomic scale [1–7]. After first experi-ments identified the transition from an indirect to adirect semiconductor when exfoliating bulk TMDs tothe monolayer limit [8, 9], subsequent studies char-acterized the strong exciton response to an opticalexcitation [10–13]. Importantly, these pioneering all-optical experiments are for the most part only sens-itive to radiative recombination processes within thelight-cone [14, 15]. However, in addition to thesebright excitons, it is meanwhile well-known that© 2023 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/ace067https://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/ace067&domain=pdf&date_stamp=2023-7-3https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-7355-8641https://orcid.org/0000-0001-9963-7527https://orcid.org/0000-0002-1889-2380https://orcid.org/0000-0002-8958-7711https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-7448-1167https://orcid.org/0000-0001-5404-7355https://orcid.org/0000-0001-6375-1459https://orcid.org/0000-0003-4753-3173https://orcid.org/0000-0001-8823-1302https://orcid.org/0000-0002-1085-2931https://orcid.org/0000-0002-1255-521Xmailto:marcel.reutzel@phys.uni-goettingen.demailto:smathias@uni-goettingen.de2D Mater. 10 (2023) 035039 J P Bange et alFigure 1. Real-space sample structure and energy landscape of monolayer WSe2 and heterobilayer WSe2/MoS2. (a) Real-spaceresolved photoemission image of the monolayers WSe2 (orange polygon) and MoS2 (dark red dashed polygon). Femtosecondmomentum microscopy experiments of the monolayer WSe2 and the heterobilayer WSe2/MoS2 are performed in theregions-of-interest indicated by the orange and dark red circles, respectively. (b) Schematic sketch of the TMD heterostructureafter excitation with a 1.7 eV light pulse. Intralayer excitons are formed in the WSe2 monolayer and the WSe2/MoS2 heterobilayer.In the WSe2/MoS2 heterostructure, the energetically most stable state is the interlayer exciton where the electron and the holecomponent are localized in the WSe2 and the MoS2 layer, respectively. In addition, hybrid excitons are formed for which theexciton’s hole is fully localized in the WSe2 layer and the exciton’s electron has probability density in the WSe2 and the MoS2 layer.(c), (d) Single-particle energy landscape of monolayer WSe2 and heterobilayer WSe2/MoS2. The filled bars indicate thesingle-particle valence and conduction band extrema at the Brillouin zone’s high-symmetry points. The ovals indicate theCoulomb correlation between the single-particle electrons and holes, and the letters label the electron–hole pairs, as introduced inthe main text. (e), (f) Energy landscape of excitons in the WSe2 monolayer and the WSe2/MoS2 heterobilayer. The energies Eexcare obtained in experiment, and the blue arrows indicate the dominant scattering pathways.also tightly bound dark excitons contribute to theenergy landscape of excitons [16–21]. For example,formomentum-indirect dark excitons in amonolayerTMD, the exciton’s electron and hole component canreside in different valleys of the TMD Brillouin zone(figures 1(c) and (e)). In the case that TMD homo-and heterostructures are assembled by more than onelayer, the situation can become even more complex:The twist-angle between two neighbouring TMD lay-ers can be varied from 0◦ to 60◦, and, in this way,the high-symmetry points of the Brillouin zones areoffset in momentum space. Hence, so-called inter-layer excitons for which the electron- and the hole-component are charge-separated across the interfaceare typically momentum-indirect and thus opticallydark (figures 1(d) and (f)) [22].First direct access to these dark excitons hasbeen provided in optical-pump-midinfrared-probeexperiments [23, 24]. With the development ofhigh-repetition rate extreme ultraviolet light sources[25–28], time- and angle-resolved photoelectronspectroscopy (trARPES) [29, 30] has become applic-able to probe the energetics and dynamics of brightand dark excitons. First experiments focused ontothe ultrafast exciton and charge carrier dynamicsin semiconducting bulk [31–35] and wafer-scale[36–40] TMDs. More recently, empowered by thedevelopment of time-of-flight momentum micro-scopes (ToF-MMs) [41, 42], trARPES has been suc-cessfully applied to probe the formation dynamics ofmomentum-indirect intralayer excitons [43, 44] andthe valley depolarization dynamics [45] in exfoliatedmonolayer TMDs. In addition, the cascaded excitontransition from bright intralayer to dark interlayerexcitons has been quantified in an artificially stackedTMD heterobilayer [46, 47].These seminal trARPES experiments of exfoliatedTMDs all focus on excitons that are either of full intra-or interlayer character: The exciton’s electron andhole either reside both in a single TMD layer, or arecharge-separated between both layers. Until today, notrARPES experiment has focused on the case wherehybridization between the neighbouring TMD layersleads to the formation of a new type of exciton whereeither the electron-, the hole-, or the electron- and thehole-component are delocalized between both lay-ers (figure 1(b)). Importantly, these so-called hybridexcitons are of great interest due to their potentialto mediate charge transfer across a TMD interface[34, 46, 48–52]. Moreover, they have a high oscillator22D Mater. 10 (2023) 035039 J P Bange et alstrength and a sensitivity to external electrical fieldsdue to their partial intra- and interlayer character[20, 53–59].In this article, we study the effect of interlayerhybridization on the energy landscape of excitonsand the resulting femto- to picosecond dynam-ics. We follow-up on our recent work [46], wherewe have studied the ultrafast exciton dynamics inheterobilayer WSe2/MoS2 and found that interlayerexcitons are formed in a step-wise process via inter-mediate hybrid excitons. Here, we directly com-pare the impact of layer-localized Σ excitons in amonolayer WSe2 with hybrid hΣ excitons in a het-erobilayer WSe2/MoS2 on the exciton dynamics. Forboth excitons, the hole-component to the excitonis fully layer-localized and found in the KW valleyvalence band maximum (VBM) ofWSe2. In contrast,the exciton’s electron, which resides in the Σ valleyof the conduction band, is either fully layer local-ized (WSe2) or has a significant degree of interlayerhybridization (WSe2/MoS2). First, we experimentallyquantify the bright and dark exciton energies Eiexc ofthe correlated two-particle energy landscape. Second,we identify exciton-phonon scattering as the dom-inating mechanism for the formation of intralayerΣ and hybrid hΣ excitons. And third, we show thatthe sub-ps exciton thermalization dynamics are sig-nificantly affected by the energy alignment of the Σand hΣ exciton with respect to the optically excitedexciton.2. Bright and dark excitons inWSe2 andWSe2/MoS2Themajor goal of thismanuscript is the identificationof hybrid excitons in the trARPES experiment andthe evaluation of their impact on the exciton relaxa-tion dynamics. Therefore, we describe the low energylandscape of excitons as calculated by solving theWannier equation [6, 20, 21, 49, 60, 61]. All relevantexcitation energies are summarized in the energy dia-grams in figures 1(c)–(f) and table 1. The calculationsare performed on the same basis as in our previousworks for monolayers [61] and heterobilayers [46].If the monolayer WSe2 is pumped with 1.7 eVphotons, bright A1s excitons of WSe2 are resonantlyexcited (black arrow in figure 1(c)). We label thisexciton asK as its electron and hole component residein the KW valley conduction band minimum andVBM, respectively. Note that throughout the manu-script, we do not differentiate betweenK excitons thatare bound at KW or K ′W valleys, because we cannotdistinguish them in experiment. In addition to thebright A1s exciton, two distinct momentum-indirectdark excitons can be formed in a subsequent scatter-ing process: On the one hand, there are momentum-indirect dark excitons for which the electron- andthe hole-component are found in the ΣW and theKW valleys, respectively; these excitons are labelledas Σ throughout our work (figures 1(c) and (e)).On the other hand, momentum-indirect excitonsfor which the electron- and the hole-component aremomentum-offset and found in the KW or K ′W val-leys can be formed. Importantly, while it is expec-ted that these momentum-indirect excitons are ener-getically favourable over the optically excited brightexcitons [21, 57, 58], where the electron- and thehole-component are bound in the same KW or K ′Wvalley, within the energy resolution of the photoe-mission experiment, it is not possible to separatethese excitons. Hence, we label both of them with Kthroughout the manuscript.In the WSe2/MoS2 heterostructure, 1.7 eVphotons can be used to resonantly excite the A1sexciton in WSe2 (black arrow in figure 1(d)). A sim-ilar resonance frequency for the optical excitation ofWSe2 A1s excitons in themono- and the heterobilayerregion can be rationalized based on the fact that wave-function hybridization at the KW valleys is negligible[48, 51, 60, 62, 63]. In addition, because the opticalexcitation of A1s excitons of monolayer MoS2 wouldrequire at least 1.9 eV light-pulses [47, 50, 63, 64], theMoS2 monolayer is not directly excited. The optic-ally excited WSe2 A1s excitons can decay to formmomentum-indirect excitons, where the electron-and the hole-component are momentum-offsetbetween the KW and K ′W valleys. Because we can-not differentiate between these momentum-indirectexcitons and the bright A1s excitons in the photoe-mission experiment, as in the case of theWSe2 mono-layer, we label both these bright and momentum-indirect excitons with K. More interestingly for ourstudy, momentum-indirect hybrid hΣ excitons areformed for which the exciton’s hole and electron canbe found in the KW and the Σ( ′) valley, respectively:Here, the Σ( ′) valley conduction bands of the WSe2and MoS2 are hybridized, and, in consequence, thehΣ exciton can be described in the hybrid excitonbasis with approximately 30% intra- and 70% inter-layer character [46]. Note that the hybrid character ofthis exciton’s electron component is indicated by theletter ‘h’ in the abbreviation. With this hybrid char-acter of the hΣ excitons, interlayer charge transfer isstrongly favoured and interlayer excitons (ILX) canbe formed [46, 49]. For ILX, because of the negligiblehybridization of the wavefunctions at the WSe2 K( ′)WandMoS2 K( ′)Mo valleys, the exciton’s electron and holecomponent are again fully localized in the monolay-ers (figure 1(d)).3. Momentummicroscopy: energylandscape of excitonsIn this section, we experimentally quantify the excitonenergies of the bright and dark excitons in the WSe2monolayer and the WSe2/MoS2 heterolayer. All ener-gies are summarized in table 1.32D Mater. 10 (2023) 035039 J P Bange et alTable 1. Overview of the exciton energies Eiexc in monolayer WSe2 and heterobilayer WSe2/MoS2. The table compares experimentallydetermined values of this work with many-particle calculations (heterobilayer values reproduced from [46]). In addition, excitonenergies obtained in photoluminescence (PL) [62] and other trARPES [43, 65] experiments are reproduced. The theory values arecalculated based on the model for the mono- and the heterobilayer, as detailed in [46, 61]. Note that the exciton energy of the opticallyexcited bright exciton in the model is adapted to experiment. If two calculated exciton energies are noted, the first is attributed to theexciton where the electron- and the hole-component are found at a high-symmetry point of the Brillouin zone with the same valleydegree of freedom (e.g. KK excitons). The second value then gives the energy of the exciton where the electron- and the hole-componenthave different valley degrees of freedom (e.g. KK′ excitons).Monolayer WSe2 Heterobilayer WSe2/MoS2 PL trARPES trARPESExperiment Theory Experiment Theory [46] Reference [62] Reference [43] Reference [65]EKexc (eV) 1.67± 0.05 1.67 and 1.61 1.66± 0.05 1.66 and 1.61 1.66 1.73 —EΣexc (eV) 1.60± 0.05 1.62 and 1.83 — — — 1.73 —EhΣexc (eV) — — 1.46± 0.05 1.37 and 1.48 — — —EILXexc (eV) — — 1.20± 0.05 1.24 and 1.25 1.05 — ≈1.13.1. Femtosecondmomentummicroscopy ofexfoliated TMDsIn order to establish the most direct experimentalcomparison of the exciton energy landscape of theWSe2 monolayer and the twisted WSe2/MoS2 het-erobilayer, we fabricate a single sample that con-tains distinct areas in which the monolayer WSe2flake and the WSe2/MoS2 heterostructure are found(figure 1(a)). We have chosen a doped siliconwafer with a native oxide layer as the substrate forthe heterostructure, because it ensures high qualitytrARPES data that is not affected by sample charging(figure 1(b)). Moreover, the TMD flakes are stackedon 20–30 nm hexagonal boron nitride [66] for bestinterface quality [67]. Before the trARPES experi-ments, the sample is annealed for 1 h to 670 K. In thereal-space-resolved photoemission electron micro-scopy image in figure 1(a), the boundaries of theWSe2 and MoS2 monolayers are traced by orangeand dark red (dashed) polygons, respectively. Thetwist-angle of the heterostructure is quantified to9.8± 0.8◦ [46].Time-resolved photoemission spectroscopy ofexfoliated mono- and heterobilayers becomes pos-sible by using our setup for femtosecond momentummicroscopy (see [25, 68, 69]). We resonantly excitethe bright A1s exciton of WSe2 with 1.7 eV 40 fs lightpulses (s-polarized). Photoemission from the occu-pied band structure and the excitons is induced withtime-delayed 26.5 eV 20 fs light pulses (p-polarized)that are created in a table-top 500 kHz repetition ratehigh-harmonic generation beamline [25, 70, 71]. Foreach delay between the pump and the probe laserpulse, the ToF-MM(Surface Concept GmbH) collectsthree-dimensional data cubes that contain inform-ation on the two in-plane momenta kx and ky andthe energy E of the detected photoelectrons [25, 42].Notably, by inserting an aperture into the real-spaceplane of the microscope, the experiment is sensitiveto the exciton dynamics in a sample region with a dia-meter of 10 µm (orange and red circles in figure 1(a))[43–46].The momentum microscopy experiment can beused to directly characterize and compare the occu-pied band structure of monolayer WSe2 and het-erobilayer WSe2/MoS2 (figure 2). In both sampleareas, the spin-split valence bands at the WSe2KW valley can be identified (labelled (1) and (2)in the magenta energy-distribution-curves (EDCs)).For the characterization of the inhomogeneity of theheterostructure, we analyse the linewidth of the topWSe2 valence band at the KW valley, and find a fullwidth at half maximum of ≈280 meV (figure 2(b)).The linewidth is composed of the spectral width of theprobe laser pulse (≈200 meV) and inhomogeneousbroadening of about≈200 meV due to imperfectionsand inhomogeneities within the probed sample area(≈100µm2) [46, 72]. In the heterobilayer, in addition,the MoS2 valence band is observed at E− EVBM =0.94± 0.05 eV (labelled (3) in figure 2(b)). While thedispersion of the WSe2 valence bands are similar atthe KW valleys of the mono- and the heterobilayer,it is strikingly different at the Γ valley: In the mono-layer, only a single band at the Γ valley is observed(horizontal arrow, figure 2(a)). In contrast, in the het-erobilayer, we find two energetically separated bandsthat are a clear indication for interlayer hybridization(two horizontal arrows in figure 2(b)) [73–75].3.2. Spectroscopy of excitons in monolayerWSe2and heterobilayerWSe2/MoS2Having identified these distinct spectroscopic sig-natures of the electronic band structure that allowthe direct discrimination of the mono- and the het-erobilayer region in the trARPES experiment, in thenext step, we probe the energetics of the optical excit-ations of the WSe2 monolayer. Therefore, opticalpump pulses with a centre energy of 1.7 eV are used inorder to be resonant to theWSe2 A1s exciton (fluence:280 µJ cm2, exciton density: 5.4×1012 excitons cm2).We find spectral weight above the valence bands thatwe attribute to photoelectrons being emitted fromexcitons (figure 2(a)). Specifically, at a pump-probedelay of 1 ps, photoemission yield is detected at the42D Mater. 10 (2023) 035039 J P Bange et alFigure 2. Energy- and momentum-resolved photoemission spectra of monolayer WSe2 and heterobilayer WSe2/MoS2 along theΓ-KW direction (inset). (a) The occupied valence band structure of monolayer WSe2 is dominated by a single-band at the Γ valley(black horizontal arrow) and the spin-split valence bands at the KW valley (labelled (1) and (2) in the EDC). At a pump-probedelay of 1 ps and a photoemission energy of≈1.7 eV, exciton photoemission yield from intralayer K (orange) andΣ (grey)excitons is detected. (b) The occupied valence band structure of heterobilayer WSe2/MoS2 is characterized by the WSe2 spin-splitvalence bands at the KW valley (labelled (1) and (2) in the EDCs) and the valence band of MoS2 (3), for which the spin-splitting isnot resolved. At the Γ valley, interlayer hybridization leads to the formation of two bands (horizontal black arrows). At apump-probe delay of 1 ps, exciton photoemission yield is detected from the intralayer K excitons (orange), hybrid hΣ excitons(grey) and ILX (red). The photoemission energy from hybrid hΣ exciton’s is significantly reduced when compared to theintralayer K (monolayer and heterobilayer) andΣ (monolayer) excitons. The energy-momentum cuts are obtained bysummation of all six measured Γ–KW (Γ–K ′W) directions.KW and the ΣW valleys of the WSe2 Brillouin zone(orange and grey hexagon in figure 3(a), respectively).These spectral signatures can be attributed to photoe-mission from intralayer K and Σ excitons, consistentwith earlier reports [43, 44].When applying similar excitation conditions tothe WSe2/MoS2 heterobilayer region, much richerspectral signatures are detected in the momentummicroscopy experiment: A complex distribution ofphotoemission intensity is detected above the WSe2valence bands in an energy window ranging from0.9 eV to 1.9 eV (figure 2(b), 1 ps pump-probe delay).The momentum-map centred at an energy of 1.7 eVabove the WSe2 VBM shows spectral weight at themomenta of the KW and the ΣW valleys that weattribute to photoemission signal from intralayer Kand hybrid hΣ excitons (figure 3(b), orange and greyhexagon, respectively). At a lower energy (figure 3(c),E− EVBM ≈ 1.1 eV), we find a complex momentumstructure of the photoemission intensity that canbe attributed to ILX: Spectral weight is detected atthe KMo valley and the additional κ valleys that aredescribedwithin themoirémini Brillouin zone (mBz,red hexagon). This hallmark of the moiré superlatticeimprinted onto the exciton photoemission signaturefrom the interlayer ILX excitons is discussed in detailin [46].3.3. Energy landscape of excitons inWSe2 andWSe2/MoS2Having identified the major photoemission spec-tral signatures of excitons, we aim to experiment-ally quantify the energy landscape of bright and darkexcitons in the mono- and the heterobilayer sample.For this, first, we have to discuss at which energythe photoemission experiment detects single-particlephotoelectrons that have initially been bound in thecorrelated exciton state. In the process of photoe-mission from an exciton, the Coulomb correlationbetween the exciton’s electron and hole is broken atthe cost of the exciton binding energy. As describedby Weinelt et al [76] and others [35, 47, 77–84], thesingle-particle photoelectron from an exciton will bedetected one exciton energy Eiexc above the energy ofthe single-particle band where the former hole con-tribution to the exciton remains in the sample, i.e. atEelec = Ehole + Eiexc + h̄ω (1)52D Mater. 10 (2023) 035039 J P Bange et alFigure 3.Momentum-resolved photoemission maps at the energies of the intralayer, hybrid and interlayer excitons in monolayerWSe2 and heterobilayer WSe2/MoS2. The pump-probe delay and the photoemission energy with respect to the WSe2 VBM aregiven in the figure. All momentum maps are integrated in an energy window ± 0.3 eV around the centre energy. (a) In the WSe2monolayer, the exciton photoemission momentum fingerprints of intralayer K (orange) and Σ (grey) show spectral weight at theK( ′)W andΣ( ′)W valleys of the WSe2 hexagonal Brillouin zone. (b) In the WSe2/MoS2 heterobilayer, exciton photoemission from theintralayer K (orange) and the hybrid hΣ (grey) excitons is found at the K( ′)W andΣ( ′)W valleys of the WSe2 hexagonal Brillouinzones. (c) The momentum-misalignment of the Brillouin zones of WSe2 (orange hexagon) and MoS2 (dark red dashed hexagon)leads to a complex photoemission signature from ILX that can be described within the moiré mini Brillioun zone (mBZ, redhexagon).with Ehole and Eelec as the single-particle energy ofthe hole- and the electron-state, respectively; fur-thermore with Eiexc as the exciton energy and h̄ω asthe probe photon energy. Importantly, equation (1)sets the energy of the WSe2 VBM at the KW valleyas the natural reference point of the present experi-ment, because the single-particle hole of all probedexcitons remains in this valley once photoemissionhas occurred (see figures 2(c) and (d)).Hence, we can quantify the exciton energy Eiexcof all contributing intralayer, hybrid and interlayerexcitons by analysing the EDCs taken at the KW, theΣW and the KMo (κ) valleys (figure 2). Followingequation (1), we then calculate the energy differencebetween each exciton photoemission signal and theenergy of theKW valley VBM.All exciton energies Eiexcquantified for the WSe2 mono- and the WSe2/MoS2heterobilayer are summarized in table 1. In addition,previous experimentally determined exciton ener-gies extracted by photoluminescence (PL) [62] andtrARPES [43, 65] are summarized in table 1, and showan excellent agreement with our analysis.Having experimentally measured the excitonenergies Eiexc, we are now in the position to systemat-ically compare those values. First, we find that, withinthe experimental error, the intralayer K excitonenergy is comparable in the mono- and the het-erobilayer region (1.67± 0.05 eV vs. 1.66± 0.05 eV).For WSe2/MoS2, this result strongly supports theexpectation that excitons, where the electron- andhole-component are localized in the KW valleys, arenot affected by interlayer hybridization [48, 51, 60].In contrast, we find that the hybrid character of thehΣ excitons indeed leads to a renormalization of theexciton energy: The interlayer hybridization leads toa reduction of the exciton energy from 1.60± 0.05 eV(Σ exciton, monolayer WSe2) to 1.46± 0.05 eV (hΣexciton, heterobilayer WSe2/MoS2). This observationis a direct experimental verification of seminal pho-toluminescence experiments that reported a changedemission energy for hybrid excitons, if the degree ofhybridization is controlled, e.g. by the twist angle[51, 85–87].Moreover, it fully confirms the calculatedenergy landscape of excitons that predicts a reduc-tion of the energy of the hybrid hΣ exciton of theWSe2/MoS2 heterobilayer in comparison to the int-ralayer Σ exciton of the WSe2 monolayer (table 1).4. Ultrafast exciton dynamics inWSe2 andWSe2/MoS2Having characterized the energy landscape ofexcitons, we now turn to the exciton scatteringdynamics. Specifically, the goal of the analysis is topinpoint the impact of the intralayerΣ and hybrid hΣexcitons on the relaxation dynamics. Therefore, first,we compare the experimentally measured excitondynamics with microscopic many-particle calcula-tions that allow us to identify exciton-phonon scat-tering as the dominant mechanism for intervalleythermalization and the formation of the intralayer Σand hybrid hΣ excitons. Second, we focus on the sub-ps dynamics in order to elucidate the impact of thedifferent exciton energies of the intralayer Σ and thehybrid hΣ exciton on the exciton relaxation cascade.4.1. Exciton-phonon scattering: Formation ofintralayerΣ and hybrid hΣ excitonsThe femtosecond momentum microscopy experi-ment provides direct access to the ultrafast dynam-ics of bright and dark excitons. The symbols in themain panels of figure 4 show the pump-probe delay-dependent photoemission yield from the intralayerK (orange), intralayer Σ (grey), hybrid hΣ (grey)62D Mater. 10 (2023) 035039 J P Bange et alFigure 4. Direct comparison of the ultrafast exciton dynamics in (a) monolayer WSe2 and (b) heterobilayer WSe2/MoS2. Thesymbols show the pump-probe delay-dependent photoemission yield from excitons, and the solid lines are based on microscopiccalculations. The exciton photoemission yield is filtered in the black-circled regions-of-interest indicated in the momentum-maps.and ILX (red) excitons. In addition, the femtosecondevolution of exciton occupation as calculated in ourmicroscopic model is plotted as solid lines of therespective colour.In the WSe2 monolayer (figure 4(a)), photoemis-sion yield from the K exciton peaks at pump-probedelays close to 40 fs. Delayed to this process, wefind that spectral weight frommomentum-indirectΣexcitons (grey) increases on a 100 fs timescale. Thisrise of the photoemission yield from the intralayerΣ excitons is in agreement with momentum micro-scopy experiments by Madéo et al [43] and Wallaueret al [44]. Moreover, the rise time is also in agree-ment with our microscopic calculations that includeexciton-light and exciton-phonon interaction. Fromthemodel, we therefore identify exciton-phonon scat-tering as the dominant mechanism for the formationof intralayer Σ excitons. Note that for pump-probedelays >100 fs, the exciton occupation calculated inthe model overestimates the experimentally meas-ured photoemisison intensity fromboth excitons. Thereason for this deviation is that the model does notinclude decay processes and thus overestimates theexciton occupation for longer pump-probe delays.The pump-probe delay-dependent photoemis-sion yield from excitons measured in the WSe2/MoS2heterobilayer is shown in figure 4(b). We find a directhierarchy in the onset of rising photoemission yieldfrom the three types of excitons, i.e.the K excitons(orange), the hybrid hΣ excitons (grey), and the ILX(red). Again, the dynamics is in excellent agreementwith our microscopic calculations, such that we canidentify exciton-phonon scattering as the dominantmechanism for the formation of hybrid hΣ excitons.4.2. MonolayerWSe2: Steady state of phononemission and absorption processesSo far, we have found that the intervalley relaxa-tion processes in monolayer WSe2 and heterobilayerWSe2/MoS2 are phonon-mediated and lead to theformation of intralayer Σ and hybrid hΣ excitons,respectively. However, even though the interval-ley relaxation proceeds via the same mechanism,we find distinctly different decay dynamics of thecontributing intralayer and hybrid excitons on thesub-ps timescale (figure 5 and table 2). In the fol-lowing, we pinpoint the origin of the differentdynamics to the relative energy alignment of the int-ralayer Σ and hybrid hΣ excitons with respect tothe intralayer K excitons, which has direct impacton the efficiency of exciton-phonon scatteringprocesses.In monolayer WSe2, the energy differencebetween the optically excited K and the intralayerΣ exciton is ∆EWSe2exc = EKexc − EΣexc = 0.07± 0.10 eV.Hence, phonon emission and absorption processeswith typical energies of 0.03 eV [88] can efficientlycreate a steady state between both excitonic species,i.e. K⇌ Σ, where the relative exciton occupationis given by degenerate Bose–Einstein distributions[21]. In order to identify this steady state in the pho-toemission data, we plot the sub-ps pump-probedelay-dependent photoemission intensity from Kand Σ excitons on a logarithmic intensity axis infigures 5(a) and (b), respectively. As indicated bythe yellow, green and blue marked areas, the sub-psdynamics of K excitons can be divided into over-all three characteristic timescales. On the sub-40-fstimescale (yellow, figure 5(a)), photoemission yield72D Mater. 10 (2023) 035039 J P Bange et alFigure 5. Quantitative analysis of the intralayer and hybrid exciton dynamics. In the yellow, green and blue shaded delay regions,excitons are optically excited, thermalize and radiatively recombine, respectively. (a) Pump-probe-delay evolution ofphotoemission signal from K excitons in monolayer WSe2 (empty triangles) and heterobilayer WSe2/MoS2 (filled triangles); thedashed and solid lines are bi-exponential decay fits to the data. (b) Quantitative evaluation of the formation and relaxationdynamics of intralayerΣ excitons (empty squares, grey) and hybrid hΣ excitons (filled squares, grey). The rise time of theexcitons is evaluated with a one-level rate equation model (blue dashed and solid line, respectively). The decay dynamics isapproximated by bi- and single-exponential fits, respectively. The rise time of the ILX (red circles) is fitted with a singleexponential function (red line). All rise and decay constants are summarized in table 2.from K excitons increases due to the optical excita-tion. For increasing pump-probe delay, the decayingphotoemission intensity can be approximated by abi-exponential function. Here, the two decay timesτKWSe2,fast= 70± 10 fs and τKWSe2,slow= 1.5± 0.2 psdescribe the fast and the slow component of thedynamics that are dominant in the green and bluedelay-regions, respectively. In direct comparison totime-resolved all-optical spectroscopies, the slowcomponent τKWSe2,slowcan be attributed to radiat-ive recombination processes of the bright excitons[50, 63, 89]. However, the interpretation of the fasttime constant τKWSe2,fastis more complex (green):First, it contains information on the decay of thecoherent exciton polarization towards the incoher-ent K exciton population [44, 90], which is not thefocus of our study. Second, and more importantly,τKWSe2,fastis dominant in the delay-window that isnecessary to establish a steady state between phononabsorption and emission events transferringK intoΣexcitons and vice versa. In agreement with this assign-ment, we find that photoemission intensity frommomentum-indirect Σ excitons, which are formeddue to the decay of K excitons, rises on the sametimescale and peaks at 100 fs (yellow and green delay-region in figure 5(b)). For longer delays (blue delay-region), theΣ exciton photoemission intensity decaysand is described by a single-exponential fit with adecay time of τΣWSe2 = 1.1± 0.1 ps. Notably, it hasalready been suggested that the decay of momentum-indirect Σ excitons dominantly proceeds via phononabsorption processes that first transfer theΣ excitonsinto bright K excitons that can, subsequently, decayin a radiative process [15, 21, 91]. Our analysis verifiesthis proposition, because the experimentally quanti-fied decay time τΣWSe2 of dark Σ excitons is in reason-able agreement with the radiative decay time τKWSe2,fastof K excitons (cf table 2).4.3. HeterobilayerWSe2/MoS2: Phonon emissionprocesses and formation of interlayer excitonsThe situation is significantly different for theWSe2/MoS2 heterobilayer. The hybrid charac-ter of the hΣ exciton leads to a reduction of itsexciton energy and thus to an energy difference of∆EWSe2/MoS2exc = EKexc − EhΣexc = 0.20± 0.10 eV withrespect to the intralayer K exciton. Hence, accom-panied by the emission of a phonon, opticallyexcited K excitons can effectively be transferred tohybrid hΣ excitons. However, the large energy differ-ence ∆EWSe2/MoS2exc strongly suppresses backscatteringevents for which multiple phonon absorption pro-cesses would be required. The suppression of thebackscattering channel in the heterobilayer in com-parison to themonolayer is most evident by themuchstronger reduction of photoemission intensity fromKexctions to below 10% after only 100 fs (green delay-region in figure 5(a)). Photoemission intensity fromhybrid hΣ excitons, on the other side, rises on thesame timescale, which is in agreement with the inter-pretation of an initially fast transfer of excitons fromK to hΣ excitons (yellow and green delay-regions infigure 5(b)).82D Mater. 10 (2023) 035039 J P Bange et alTable 2. Summary of the experimentally quantified rise and decay times of photoemission yield from excitons.Monolayer WSe2 Heterobilayer WSe2/MoS2τKfast (fs) 70± 10 28± 2τKslow (fs) 1500± 200 1900± 800τΣWSe2 (fs) 1050± 60 —τ hΣWSe2/MoS2,fast (fs) — 110± 40τ hΣWSe2/MoS2,slow (fs) — 1600± 800τΣrise (fs) 36± 3 —τ hΣrise (fs) — 34± 3τ ILXrise (fs) — 120± 20Once the hybrid hΣ excitons are formed, they canrelax to the ILX by subsequent exciton-phonon scat-tering processes within the MoS2 layer. For the ana-lysis of this process, we fit the picosecond evolutionof photoemission intensity from hybrid hΣ excitonswith a biexponential function (figure 5(b)) andextract a fast hΣ→ILX decay time of τ hΣWSe2/MoS2,fast=110± 40 fs. Notably, this decay time is in excel-lent agreement with the rise time of photoemis-sion intensity from ILX (figure 5(b), τ ILXWSe2/MoS2,rise=120± 20 fs, red data points), being thus a strongindication that ILX excitons are directly formed fromhybrid hΣ excitons. Again, because of the large energydifference between the hybrid hΣ exciton and the ILX,i.e.∆EILXexc = EhΣexc − EILXexc = 0.26± 0.10 eV (cf table 1),phonon absorption processes are nearly fully sup-pressed and backscattering events from ILX to hybridhΣ excitons can also be excluded.Finally, we note that our experimental observa-tion on the efficiency of forward and backward scat-tering in the WSe2 monolayer and the WSe2/MoS2heterobilayer are fully consistent with our micro-scopic model. Specifically, for the WSe2 monolayer,the calculations reproduce the establishment of asteady state K⇌ Σ (blue arrows in figure 1(e)).Notably, the model here finds that especially themomentum-indirect excitons, where the hole- andthe electron-component are momentum-offset in theKW andK ′W valleys, contribute to the establishment ofthe steady state, as detailed, e.g. in [15, 21]. In addi-tion, for the WSe2/MoS2 heterobilayer, the micro-scopic model reproduces the negligible efficiency forbackscattering as compared to the forward scatteringleading to the formation of ILX (blue arrows infigure 1(f)).5. ConclusionIn a joint experiment-theory effort, we have usedfemtosecond momentum microscopy and micro-scopic modelling to characterize the energy land-scape of bright and dark excitons and the result-ing scattering dynamics in monolayer WSe2 and het-erobilayer WSe2/MoS2. First, we find that interlayerhybridization in WSe2/MoS2 leads to a reduction ofthe energy of the optically dark hybrid exciton whencompared to monolayer WSe2, where the exciton islocalized in the layer. Second, in direct comparisonto microscopic modelling, we demonstrate that thehybrid hΣ and the intralayer Σ excitons are formedvia exciton-phonon scattering. And third, we showthat the relative efficiency of phonon absorption andemission processes are the dominant parameter forthe different exciton dynamics in monolayer WSe2and heterobilayer WSe2/MoS2. Specifically, in mono-layer WSe2, we showed that the occupation of int-ralayerK andΣ evolves into a steady state, i.e.K⇌ Σ,and the overall exciton occupation decays via radi-ative processes of the bright K excitons. In contrast,in the WSe2/MoS2 heterobilayer, we found that theenergy level alignment of the contributing excitonsstrongly suppresses phonon-absorption processesand leads to a true exciton cascade K→ hΣ→ILXwith negligible contributions of backscattering.Data availability statementThe data that support the findings of this study areavailable upon reasonable request from the authors.AcknowledgmentsThis work was funded by the DeutscheForschungsgemeinschaft (DFG, German ResearchFoundation) - 432680300/SFB 1456, Project B01,217133147/SFB 1073, Projects B07 and B10, and223848855/SFB 1083, Project B9. A A and S Hacknowledge funding from EPSRC (EP/T001038/1,EP/P005152/1). A A acknowledges financial sup-port by the Saudi Arabian Ministry of HigherEducation. E M acknowledges support from theEuropeanUnions Horizon 2020 research and innova-tion programme under Grant Agreement No. 881603(Graphene Flagship). K W and T T acknowledgesupport from the JSPS KAKENHI (Grant Numbers20H00354, 21H05233 and 23H02052) and World92D Mater. 10 (2023) 035039 J P Bange et alPremier International Research Center Initiative(WPI), MEXT, Japan.ORCID iDsJan Philipp Bange https://orcid.org/0000-0002-7355-8641Wiebke Bennecke https://orcid.org/0000-0001-9963-7527Giuseppe Meneghini https://orcid.org/0000-0002-1889-2380Marco Merboldt https://orcid.org/0000-0002-8958-7711Kenji Watanabe https://orcid.org/0000-0003-3701-8119Daniel Steil https://orcid.org/0000-0001-7448-1167R Thomas Weitz https://orcid.org/0000-0001-5404-7355Stephan Hofmann https://orcid.org/0000-0001-6375-1459G S Matthijs Jansen https://orcid.org/0000-0003-4753-3173Samuel Brem https://orcid.org/0000-0001-8823-1302Marcel Reutzel https://orcid.org/0000-0002-1085-2931Stefan Mathias https://orcid.org/0000-0002-1255-521XReferences[1] Jin C, Ma E Y, Karni O, Regan E C, Wang F and Heinz T F2018 Ultrafast dynamics in van der Waals heterostructuresNat. 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Introduction 2. Bright and dark excitons in WSe2 and WSe2/MoS2 3. Momentum microscopy: energy landscape of excitons 3.1. Femtosecond momentum microscopy of exfoliated TMDs 3.2. Spectroscopy of excitons in monolayer WSe2 and heterobilayer WSe2/MoS2 3.3. Energy landscape of excitons in WSe2 and WSe2/MoS2 4. Ultrafast exciton dynamics in WSe2 and WSe2/MoS2 4.1. Exciton-phonon scattering: Formation of intralayer Σ and hybrid hΣ excitons 4.2. Monolayer WSe2: Steady state of phonon emission and absorption processes 4.3. Heterobilayer WSe2/MoS2: Phonon emission processes and formation of interlayer excitons 5. Conclusion References