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Shuo Dong, Samuel Beaulieu, Malte Selig, Philipp Rosenzweig, Dominik Christiansen, Tommaso Pincelli, Maciej Dendzik, Jonas D. Ziegler, Julian Maklar, R. Patrick Xian, Alexander Neef, Avaise Mohammed, Armin Schulz, Mona Stadler, Michael Jetter, Peter Michler, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Hidenori Takagi, Ulrich Starke, Alexey Chernikov, Martin Wolf, Hiro Nakamura, Andreas Knorr, Laurenz Rettig, Ralph Ernstorfer

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[Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der Waals heterostructure](https://mdr.nims.go.jp/datasets/aa041d00-20b0-4dbc-9f20-a71248149d55)

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Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der Waals heterostructureArticle https://doi.org/10.1038/s41467-023-40815-8Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der WaalsheterostructureShuo Dong 1,2 , Samuel Beaulieu1,3, Malte Selig4, Philipp Rosenzweig 5,Dominik Christiansen4, Tommaso Pincelli 1, Maciej Dendzik 1,6,Jonas D. Ziegler7,8, Julian Maklar 1, R. Patrick Xian 1,9, Alexander Neef 1,Avaise Mohammed5, Armin Schulz5, Mona Stadler10, Michael Jetter10,Peter Michler 10, Takashi Taniguchi 11, Kenji Watanabe 12,Hidenori Takagi5,13,14, Ulrich Starke 5, Alexey Chernikov 7, Martin Wolf 1,Hiro Nakamura5,15, Andreas Knorr4, Laurenz Rettig 1 &Ralph Ernstorfer 1,16Atomically thin layered van der Waals heterostructures feature exotic andemergent optoelectronic properties. With growing interest in these novelquantummaterials, themicroscopic understanding of fundamental interfacialcoupling mechanisms is of capital importance. Here, using multidimensionalphotoemission spectroscopy, we provide a layer- and momentum-resolvedview on ultrafast interlayer electron and energy transfer in a monolayer-WSe2/graphene heterostructure. Depending on the nature of the optically preparedstate, we find the different dominating transfer mechanisms: while electroninjection from graphene to WSe2 is observed after photoexcitation of quasi-free hot carriers in the graphene layer, we establish an interfacial Meitner-Auger energy transfer process following the excitation of excitons in WSe2. Byanalysing the time-energy-momentum distributions of excited-state carrierswith a rate-equation model, we distinguish these two types of interfacialdynamics and identify the ultrafast conversion of excitons in WSe2 to valenceband transitions in graphene. Microscopic calculations find interfacial dipole-monopole couplingunderlying theMeitner-Auger energy transfer todominateover conventional Förster- andDexter-type interactions, in agreementwith theexperimental observations. The energy transfer mechanism revealed heremight enable new hot-carrier-based device concepts with van der Waalsheterostructures.The unique physical properties of atomically thin two-dimensional(2D) materials1,2 and constantly improving fabrication methods3,4 haveled to a great interest in novel quantum materials based on van derWaals (vdW) heterostructures5. By stacking 2D materials, vdW het-erostructures inherit the properties from individual constituents, andexotic physical phenomena may emerge due to the interfacialinteraction5–7. An emblematic example is the emergence of super-conductivity in twisted bilayer graphene when stacked at the so-called“magic angle”8. As another example, interlayer excitons, which arespatially separated yet Coulomb-bound electron-hole pairs inReceived: 24 June 2023Accepted: 11 August 2023Check for updatesA full list of affiliations appears at the end of the paper. e-mail: dong@fhi-berlin.mpg.de; rettig@fhi-berlin.mpg.de; ernstorfer@fhi-berlin.mpg.deNature Communications |         (2023) 14:5057 11234567890():,;1234567890():,;http://orcid.org/0000-0002-7940-9583http://orcid.org/0000-0002-7940-9583http://orcid.org/0000-0002-7940-9583http://orcid.org/0000-0002-7940-9583http://orcid.org/0000-0002-7940-9583http://orcid.org/0000-0001-8426-9397http://orcid.org/0000-0001-8426-9397http://orcid.org/0000-0001-8426-9397http://orcid.org/0000-0001-8426-9397http://orcid.org/0000-0001-8426-9397http://orcid.org/0000-0003-2692-2540http://orcid.org/0000-0003-2692-2540http://orcid.org/0000-0003-2692-2540http://orcid.org/0000-0003-2692-2540http://orcid.org/0000-0003-2692-2540http://orcid.org/0000-0002-4179-0040http://orcid.org/0000-0002-4179-0040http://orcid.org/0000-0002-4179-0040http://orcid.org/0000-0002-4179-0040http://orcid.org/0000-0002-4179-0040http://orcid.org/0000-0003-4123-4455http://orcid.org/0000-0003-4123-4455http://orcid.org/0000-0003-4123-4455http://orcid.org/0000-0003-4123-4455http://orcid.org/0000-0003-4123-4455http://orcid.org/0000-0001-9895-6956http://orcid.org/0000-0001-9895-6956http://orcid.org/0000-0001-9895-6956http://orcid.org/0000-0001-9895-6956http://orcid.org/0000-0001-9895-6956http://orcid.org/0000-0002-2375-5970http://orcid.org/0000-0002-2375-5970http://orcid.org/0000-0002-2375-5970http://orcid.org/0000-0002-2375-5970http://orcid.org/0000-0002-2375-5970http://orcid.org/0000-0002-2949-2462http://orcid.org/0000-0002-2949-2462http://orcid.org/0000-0002-2949-2462http://orcid.org/0000-0002-2949-2462http://orcid.org/0000-0002-2949-2462http://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/0000-0003-1153-1862http://orcid.org/0000-0003-1153-1862http://orcid.org/0000-0003-1153-1862http://orcid.org/0000-0003-1153-1862http://orcid.org/0000-0003-1153-1862http://orcid.org/0000-0002-9213-2777http://orcid.org/0000-0002-9213-2777http://orcid.org/0000-0002-9213-2777http://orcid.org/0000-0002-9213-2777http://orcid.org/0000-0002-9213-2777http://orcid.org/0000-0001-7226-9592http://orcid.org/0000-0001-7226-9592http://orcid.org/0000-0001-7226-9592http://orcid.org/0000-0001-7226-9592http://orcid.org/0000-0001-7226-9592http://orcid.org/0000-0002-0725-6696http://orcid.org/0000-0002-0725-6696http://orcid.org/0000-0002-0725-6696http://orcid.org/0000-0002-0725-6696http://orcid.org/0000-0002-0725-6696http://orcid.org/0000-0001-6665-3520http://orcid.org/0000-0001-6665-3520http://orcid.org/0000-0001-6665-3520http://orcid.org/0000-0001-6665-3520http://orcid.org/0000-0001-6665-3520http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40815-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40815-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40815-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40815-8&domain=pdfmailto:dong@fhi-berlin.mpg.demailto:rettig@fhi-berlin.mpg.demailto:ernstorfer@fhi-berlin.mpg.desemiconducting transition metal dichalcogenide (TMDC) hetero-structures allow exceptional control of optoelectronic properties9–11.Out of the vdWheterostructure library, a basic optoelectronic buildingblock is a monolayer (ML) semiconducting TMDC in contact withgraphene12. This hybrid structure represents a model system as itcombines the strong light-matter coupling of TMDCs and the highmobility of massless Dirac carriers of graphene13. The gapless elec-tronic structureof graphene allows for harvesting low-energyphotons,extending the spectral range covered by conventional photodetectorsto the near-infrared wavelength, which is highly beneficial for photo-voltaic applications14.Optoelectronic functionality in vdW heterostructures arises fromcareful design and control of optical transitions and interfacial transferprocesses. Particularly, interfacial charge (ICT) and energy transfer(IET) are key processes that have triggered extensive experimental andtheoretical efforts15–20 Using time-resolved optical spectroscopies, astrong reduction of the exciton lifetime21 and optically active charge-transfer excitations of TMDC/graphene heterostructures have beenobserved22,23, suggesting strong interlayer coupling and the underlyingmechanisms have been discussed24–26. Moreover, the efficiency of IETprocesses like Förster-type coupling (based on electronic dipole-dipole interaction) has recently been investigated theoretically,pointing out the importance of energy-momentum conservationbetween participating quasiparticles15. These studies provide our cur-rent understanding of the mechanisms of interfacial interactions.However, it is still challenging to clearly distinguish and unravel theinvolved interlayer charge and energy transfer in vdW hetero-structures based on optical spectroscopies, primarily transientabsorption/reflection and terahertz spectroscopy, which are inher-ently sensitive to the selective spectral range and limited momentumaccessible. Therefore, a momentum-resolved probe is required tomonitor the dynamics directly and achieve a complete picture ofinterfacial charge and energy transfer processes, including thoseinvolving momentum-forbidden dark states.Here, we use time- and angle-resolved photoemission spectro-scopy (trARPES) to investigate ultrafast interlayer carrier interactionsin an epitaxially grown ML-WSe2/graphene heterostructure. OurtrARPES setup combines ahigh-repetition-rate (500 kHz) femtosecondextreme ultraviolet (XUV) source27 coupled to a time-of-flightmomentum microscope28 (see Methods). It allows the measurementof the four-dimensional (4D) photoemission intensity I(Ekin, kx, ky, Δt),where Ekin is the outgoing photoelectron kinetic energy, kx,ky are thein-plane momenta and Δt is the pump-probe delay, as shown in Fig. 1a,b. The probe photon energy of 21.7 eV allows accessing the entireBrillouin zone of the heterostructure and the variable pump wave-length allows us to photoexcite the heterostructure in a state-resolvedmanner. In the following, we present a time-, energy-, andmomentum-resolved study on the excited-state dynamics in the heterostructurewith two different pump photon energies: below the optical bandgapof WSe2 (1.2 eV) and in resonance with its first excitonic transi-tion (1.55 eV).ResultsInterlayer quasi-free carrier transferFirst, we photoexcite the heterostructure with the pump photonenergy centered at ℏωpump=1.2 eV (pump pulse duration 200 fsFWHM), well below the optical bandgap of WSe229. The NIR-pump/XUV-probe experiments were performed with a pump fluence ofF = 5.3 mJ/cm2 and at room temperature. Figure 2a–d shows energy-resolved photoemission signals along the K0 � K cut of the Brillouinzone, at selected time delays. The band mappings are contrast-enhanced using a multidimensional extension of the contrast limitedadaptive histogram equalization (MCLAHE)30,31 for better visualizationof the band structure. The momentum distributions above EF withinthe first 400 fs reveal that the excited states are localized in threedifferent types of valleys: the Dirac cones of graphene at its K points(KGr) and the K andQvalleys ofWSe2 (KWSe2,QWSe2), as shown in Fig. 2e.The QWSe2valley localizes between the KWSe2valley and the Γ point. Byperforming energy-momentum integration in selected regions ofinterest (ROIs), we extracted excited-state dynamicswithin these threevalleys (Fig. 2f). Upon arrival of the pump pulses, the excited-statepopulation rapidly builds up at KGr (black curve) and decays with atime scale of ~200 fs. Strikingly, the conduction band minima (CBMs)at KWSe2(red curve) and QWSe2valleys (green curve) are also beingpopulated, however, with a delay of Δt = 51 ± 9 fs (see SI) compared tothe rise of hot-carrier population in graphene. Since below-bandgappump photon energy does not allow the direct photoexcitation ofWSe2, the delayed electron populations in the conduction bands arisethrough charge transfer fromgraphene toWSe2. Two/multiple photonexcitation can safely be ruled out (details see SI). The excited-statepopulation of the QWSe2valleys (Fig. 2f) could be raised via ICT fromthe graphene layer and the intervalley scattering from the KWSe2valleys32,33.These observations support the following picture of the under-lying processes with a below-bandgap excitation: light is absorbed bygraphene and populates unoccupied states at EelGr = ED + _ωpump=2,leaving holes at EhGr = ED � _ωpump=2 (Dirac energy ED >0 for a p-dopedsystem or ED <0 for an n-doped system). The energy position of theDirac point in our heterostructure is estimated tobe ~ −0.1eVbelow theFermi level, obtained from the conical crossing34,35 (see SI). The pho-EFCBVBcenergy transfercharge transfer1.2 eV1.55 eVE-E F (eV)bmaxminKWSe2QWSe2k y (A-1 )kx (A -1)KGrWSe2GraML-WSe2SeWCtNIR pumpXUV probegraphenePhotoelectronsFig. 1 | Time- and angle-resolved photoemission measurement of interlayercharge and energy transfer in a ML-WSe2/graphene heterostructure.a Following the near-infrared pump, electrons are photoionized by the delayedXUV-probepulses and collected by a three-dimensional (3D) (Ekin, kx, ky) detector asa function of pump-probe delay Δt. b The 3D snapshot of the 4D data, I(Ekin, kx, ky,Δt =0 fs) presents the valence band structures from the Γ point to the Brillouinzone boundary of WSe2, as well as the linearly dispersing graphene bands. Theexcited state population can be clearly mapped at the KWSe2and QWSe2valleys, andthe π* band of graphene (KGr). c By changing the pump wavelength, we can selec-tively prepare different initial excited states: quasi-free carriers in graphene withbelow-bandgap excitation (red arrow) or excitons in WSe2 using excitation on theexcitonic resonance (blue arrow).Article https://doi.org/10.1038/s41467-023-40815-8Nature Communications |         (2023) 14:5057 2toexcited carriers quickly reach a quasi-thermalized states in ~10 fs36and could further increase their energy via intraband electron-electronscattering and interband Auger recombination in few tens offemtoseconds37,38. Once electrons gained a sufficient amount of energyto overcome the energy barrier, they scatter to WSe2 via a phonon-assisted tunneling process, filling the single-particle CBMs at KWSe2andQWSe2. This ICT mechanism is called interlayer hot-carrier injection,and is schematically illustrated in Fig. 2g. The excited electrons inWSe2may subsequently scatter back to graphene and relax down towardsthe Fermi energy (EF). Based on the observed carrier dynamics, weperformed microscopic calculations of the phonon-assisted interlayertunneling process, allowing us to estimate the electronic wavefunctionoverlapbetween the involved conduction bandsofWSe2 andgrapheneto be ~4% (see SI for details).Interlayer energy transferNext, we select a pumpphoton energy ofℏωpump = 1.55 eV (pumppulseduration: 35 fs FWHM, pump fluence: F = 1.7mJ/cm2), near-resonant tothe A-excitonic transition of WSe2. In this case, the pump photonenergy allows both the WSe2 and the graphene layer to be simulta-neously photoexcited. One striking observation is that the energydistribution of excited carriers at the KWSe2valleys is centered at0.63 eV (Fig. 3a), ~100meV lower than with below-bandgap excitation(Fig. 3b), as apparent from the energy distribution curves (EDCs) (first100 fs). As discussed above, with 1.2 eV excitation, the KWSe2valleys arefilled with quasi-free electrons that have tunneled from the graphenelayer. Therefore, this ~100meV energy difference is a direct photo-emission signature of exciton formation, when near-resonantlypumping using 1.55 eV photons39: the bound electron-hole (el-h) pairreduces the quasi-free particle bandgapby the exciton binding energy.In addition to this excitonic feature, we also observe a transient shift ofWSe2 valence bands. In Fig. 3d, EDCs at KWSe2are shown at Δt = 0 fs(red) andΔt = − 200 fs (black), in which the top two valence bands, VB1and VB2, are fitted using Gaussian lineshape functions (see SI). Thepeak position of VB1 shifts towards the conduction band within thefirst 100 fs, transiently shrinking the electronic bandgap. This is due tothe arrival of ICT-induced charge carriers from the graphene layer.With near-resonantly pumping the A-exciton, the occurrence of ICTand injectionof quasi-free carriers fromgraphene toWSe2 is expected,similar to the case of below-bandgap excitation. This could lead todynamical screening effect and the observed bandgap renormaliza-tion, as reported in highly-excited or doped ML TMDC materials40–44.As the magnitude of such a transient bandgap renormalization hasbeen shown to scale with the excited charge carrier density42,45, weutilize the VB shift in the following as a measure of the ICT transferredcarriers dynamics from graphene layer.In addition to the excited-state dynamics in WSe2, importantinsight can be drawn from the energy-momentum distribution of hotcarriers in graphene. As shown in the early-time 2D differential spec-trum ΔI(E, k, Δt = 0 fs) (Fig. 3c), obtained by subtracting the spectrumat the negative time, hot carriers distribute in a broad energy range.The momentum-integrated spectrum along the linearly dispersingband in Fig. 3e clearly features the energy distribution of net electrongain (positive; red area) and loss (negative; blue area) following near-resonant photoexcitation. Remarkably, besides themodification of thedistribution function near the Fermi level, we notice a strong negativepeak at E−EF = −1.8 eV. As noted earlier, for direct photoexcitation ingraphene the photoexcited carriers are expected to be spread ±0.77eV(ℏωpump/2) around the Dirac point and quickly relax back to the Fermilevel. Thus, this simple excitation mechanism cannot explain thispeculiar feature in the valence band spectrum. The electron-electronscattering and Auger recombination could lead to a transient broad-ening of the momentum-space carrier distribution, but without anypreferential energy localization38,46,47. hole transfer can also be ruledout, as the top valence band of WSe2 lies at E−EF = −1.0 eV. It wouldrequire a multi-phonon absorption to populate the hole-states loca-lized deeply in the valence band, taking the typical phonon energy of~0.17 eV in graphene48, a process of very low probability. However, theenergy difference of deep-lying valence holes (E−EF = −1.8eV) andstates near EF (E−EF = −0.2 eV) in graphene well matches the energy oftheA-exciton inWSe2 (Eex ~ 1.6eV). Combinedwith the fast depletion ofexciton population shown in Fig. 4a (black curve) extracted from thea b cE-E F (eV)kx (Å-1)de f gEnergy EFΓQWSe2xKGrKWSe2QWSe2 x12x20Time delay (fs)Intensity (norm.)minmaxK'WSe2K'Gr Γ KGrQ'WSe2KWSe2QWSe2KGr KWSe2K'Gr Γ KGr K'Gr Γ KGr K'Gr Γ KGrkx (Å-1) kx (Å-1) kx (Å-1)t=-400 fs t=0 fs t=200 fs t=400 fsky (Å-1)KGrQWSe2KWSe2kx (Å-1)minmaxky (Å-1)KGrQWSe2KWSe2kx (Å-1)minmaxFig. 2 | Layer- and valley-resolved ultrafast dynamics upon below-bandgappumping. a–d Energy-momentum cuts of the photoemission signal along the K0Gr-K0WSe2-Γ-KWSe2-KGr high symmetry direction, at selected pump-probe time delays.a The 2D spectrum at negative time delay reveals the equilibrium band structure ofML-WSe2 as well as the linearly dispersing π band of graphene. The gray linesrepresent the DFT-calculated band structures (details in methods). Snapshots ofthe energy-momentum cuts at time delays of b Δt =0 fs, c Δt = 200 fs, andd Δt = 400 fs, respectively. e Momentum map of the excited states (energyintegrated for E > EF and time integrated for thefirst 400 fs), showing the KGr pointsof graphene (black box) aswell as the KWSe2andQWSe2valleys (red and greenboxes,respectively). The dashed gray lines represent the hexagonal Brillouin zones ofboth layers. f Normalized population dynamics within the three ROIs defined in e:KWSe2(red) and QWSe2(green) are populated with a ~50 fs delay with respect to KGr(black). g Schematic of the early-time carrier dynamics upon below-bandgapexcitation: photo-generated hot carriers within the graphene layer are transferredto the conduction bandsofWSe2 via hot electron injection after the thermalization.Article https://doi.org/10.1038/s41467-023-40815-8Nature Communications |         (2023) 14:5057 3excited state of WSe2 (ROI1 in Fig. 3c), this brings about the followingscenario for the excitation of these carriers: annihilation of excitons inWSe2 drives the intraband excitation of deep-lying valence electrons ingraphene into empty hole states below the Dirac point. In more detail,this exciton energy transfer process, which we term Meitner-Augerenergy transfer49,50, considers recombination of excitons in WSe2 withcenter-of-mass (COM) momentum Q and exciton energy Eex. Thephotoexcitation prepares the required hot hole vacancy below EF ingraphene, thus enabling the intraband excitation. The photo-generated hole density plays an important role in the MA-type IETprocess (see the discussion of pump fluence dependence in SI).Besides the observation of the deep-lying hot holes, we also identify asubstantial suppression of hole-like spectral weight (Meitner-Augertype IET-induced hot electrons) below the Fermi level with near-resonant excitation, supporting the occurrence of intraband transitionin the graphene layer (details see SI, section Meitner-Auger type IET-induced hot electrons near the Fermi level). The momentum of thevalence electron-hole pair kGr is determined by the Fermi velocity ofthe graphene bands and the transition energy EGr. This requiredmomentum is provided by the optically pumped excitons which gainfinite COM momenta during the population formation process viaphonon-mediated dephasing and intravalley thermalization51–54 (seethe discussion in SI). The highly efficient IET of the excitons andintraband electron-hole pairs is thus possible under the conservationof energy andmomentum, i.e., Eex = EGr andQ = kGr. In a similar trARPESstudy of a ML WS2/graphene heterostructure, dominating interfacialcharge transfer has been observed17. Compared with our study, thedifferent charge transfer rates could be raised from the different bandstructure alignment near the interface and the density of defect sites26.While the additional exciton energy transfer was not excluded, itsrelative efficiencymight be reduceddue to the largerCOMmomentumrequired at the larger A-exciton energy of WS2 and the energy levelalignment of these specific samples.In order to gain information on the time scales of the energy andcharge transfer processes, next we analyze the dynamics of excited-state populations extracted from the ROIs shown in Fig. 3c, includingthe excited-state carriers in WSe2 (ROI1), VB1 shifting (ROI2), hot elec-trons in graphene (ROI3) and IET-driven deep valence band holes(ROI4). The time trace of hot carriers in the CBM of WSe2 (black curvein Fig. 4a) contains two types of quasiparticles dynamics: the photo-generated excitons NexT and the ICT-induced quasi-free electrons NelT .The decay of excitons excite the valence band electrons in graphenevia IET with a transfer time of τIET (Fig. 4f). On the other hand, thearrival of ICT-induced electrons transiently shifts the VBs of WSe2a bc d1.2 eV excitationI (%)0.73 eV ICTEDC1.55 eV excitationEFkx (Å-1)min maxKWSe2 KGr0.63 eVI (%)EDCEDCWSe2t=-200 fst=0 fsemaxminE-E F (eV)E-EF (eV)E-E F (eV)I (norm.)E-E F (eV)1.55 eV excitationKWSe2 KGrkx (Å-1)kx (Å-1)EFmin maxelectron gainelectron lossEDCGrEGrROI1ROI2ROI4ROI3I/C (%)x15Fig. 3 | Photoemission signatures of exciton formation and interfacial inter-actions. a With near-resonant A-exciton pump (1.55 eV), carriers within both theWSe2 and the graphene layer are photoexcited (time integration of 100 fs). Theenergy of the excited-states carriers at KWSe2is 0.63 eV, shown in the EDC (left panelfigure). b With below-bandgap excitation (1.2 eV), the local CBM of KWSe2is filledwith ICT-induced electrons and centered at 0.73 eV. c Differential energy-momentum cut with 1.55 eV pump at time zero, obtained by subtracting thenegative time delay spectrum. d The normalized EDC of KWSe2(momentum inte-gration of 0.2Å−1) at Δt = −200 fs (black) and Δt =0 fs (red). The VBs are fitted withtwo Gaussian functions (dashed curves) and the positions of VB1 are indicated bythe dash lines. e The momentum-integrated spectrum of graphene Dirac bands(between the dashed yellow lines in c) shows the electron gain (positive, red area)and loss (negative, blue area) following photoexcitation. The intensity is normal-ized by the total electron count C obtained from negative time delay spectrum.Apart from the carriers accumulation near the EF, the hole population formsanother prominent peak around E−EF = −1.8 eV, indicated between the dash lines.The EDC of graphene with 1.2 eV pump (green) is also shown as a comparison.Article https://doi.org/10.1038/s41467-023-40815-8Nature Communications |         (2023) 14:5057 4(green curve in Fig. 4a)which therefore represents the dynamics ofNelTas discussed before. We assume VB1 and VB2 shift in the same way(fitting details see SI). The VB1 shifting shows a time delay of ~65 fscompared to theCB signal, evidencing the occurrence of interlayer hotelectron injection after photoexcitation. The population of NelT sub-sequently relaxes back to KGr, refilling the excited states of graphene(Fig. 4h). From the graphene side, the photoexcited hot electrons NelGr(red curve in Fig. 4b) could either scatter to conduction bands ofWSe2or relax by interband decay channels in graphene. Therefore, therelaxation of NelGr could be characterized with the charge transfer timeof τICT and a decay time of τelGr . The deep valence band holes NhGr(blue curve in Fig. 4b) are populated by exciton energy transfer on atime scale of τIET, which would relax back to the Fermi level with alifetime of τhGr .The complete dynamics across the interface can be describedwith a set of coupled rate equations based on a multi-level scheme(details see SI). By numerically solving the rate-equationmodel, wedisentangle the dynamics of IET and ICT. Our global fit describesthe data well and yields the transfer times of τIET = 67 ± 7 fs andτICT = 118 ± 18fs. The lifetimes of electrons and IET-populated hotholes in graphene are simultaneously extracted as τelGr =84± 7 fsand τhGr = 7±4 fs. Combining all our observations and analysis ofthe energy-momentum dynamics in WSe2 and graphene, we sum-marize the interfacial phenomena governing the non-equilibriumbehavior of our heterostructure: first, the optical pump generatesexcitons in WSe2 and quasi-free carriers in graphene (Fig. 4e).Following photoexcitation, the exciton annihilation excites deepvalence electrons in graphene via an IET process (Fig. 4f, g).Simultaneously, hot electrons in graphene are injected to theconduction bands of WSe2 via ICT which transiently shift thevalence bands of WSe2 (Fig. 4h).DiscussionTo elucidate the interfacial coupling mechanism at play in ourexperiment, in particular the observed ultrafast energy transfer rate,we perform microscopic calculations of three types of IET mechan-isms: Meitner-Auger, Förster, and Dexter energy transfer. The inter-layer MA process is described by the dipole-monopole energy transferfrom excitons to valence band excitation, schematically shown inFig. 4e. The photoexcited hot holes in graphene quickly relax anddistribute below EF near a transient chemical potential μh*Gr . This allowsan MA-type transition from the deep valence band to the hot holevacancy by absorbing the exciton energy. The microscopically calcu-lated transfer rate is plotted as a function ofQ in Fig. 4c with differenttransient chemical potentials for the hole distributions μh*Gr . When thehole vacancy is located around μh*Gr = � 0:3 eV, the maximum transferrate reaches ΓIET = 2.4meV, corresponding to a τIET = 270 fs transfertime. The MA-type IET process could describe the observed energy-momentumdistribution of intraband transition of valence electrons ina reasonable quantitative agreement with the extracted transfer rate.As the transient chemical potential is subject to the doping level ofgraphene,we also calculate theMA-type IETwith n-doped graphenebyartificially increasing the Fermi energy. The IET-induced intrabandtransition in the valence bands is suppressed with decreased photo-generated hole vacancies. However, the intrinsically doped electronsabove the Dirac point enable theMA-type IET in the conduction bands(details see SI).Another IET mechanism is Förster energy transfer (Fig. 4f). Theenergy of the exciton excites an interband transition from valencebands to above Dirac point via the dipole-dipole coupling55. Incontrast to the MA-type IET process, the interband excitation viaFörster-type energy transfer populates the conduction bands ofgraphene above the Fermi level, independent of the photon-EGrEGr EexEexI (norm.)abTime delay (fs)I (norm.)Q (Å-1)d=1.0 nmd=0.5 nmd=0.0 nmΓ IET(meV)cdMeitner-AugerFörsterE VB1(meV)ROI1(NT, NT )ex elμGr=-0.3 eVh*μGr=-0.4 eVh*μGr=-0.5 eVh*Γ IET(meV)ICThKGrKWSe2EFτ IET (ps)τ IET (ps)Förster-type IETfkGrQEFg Dexter-type IETKGrKWSe2EFMA-type IETeQ kGrEGrEex μGrh*EFNGrhNTelROI2(NT )el(NGr)hROI4ROI3(NGr)elμGr=-0.2 eVh*μGr=-0.1 eVh*Fig. 4 | Interlayer charge and energy transfer upon near-resonant A-excitonexcitation. a By integrating the ROI1 in Fig. 3c, the time trace of the normalizedphotoemission intensity of excited-state carriers at the CBM of WSe2 (black) con-tains the dynamics of excitons (NexT ) and ICT-induced quasi-free carriers (NelT ). Theenergy shift of VB1 (green) mainly reflects the dynamic of NelT , which are extractedfrom time-dependent EDCs in ROI2.bThe time traces of hot electrons (red) andhotholes in the deep VB (blue) in graphene are extracted from the ROI3 and ROI4 inFig. 3c, respectively. The time traces in a, b are fitted globally based on a rate-equationmodel (see text). cCalculatedMeitner-Augermediated IET transfer rate asa function of COM momentum Q with different photo-induced hole vacancy atE =μh*Gr . d Calculated Förster coupling rate as a function ofQ with varied interlayerdistance of d. Sketch of the underlying carrier dynamics: eMeitner-Auger IET withcreation of intraband electron-hole pairs in graphene by absorbing the excitonenergy. f Förster-type energy transfer with the generation of interband electron-hole pairs in graphene. g Dexter-type energy transfer with electrons and holesinjection to graphene simultaneously. h ICT-induced hot electron injection intoWSe2 and transient energy shift of its valence band.Article https://doi.org/10.1038/s41467-023-40815-8Nature Communications |         (2023) 14:5057 5induced hot carriers distribution. The coupling strength is explicitlyevaluated (for derivation, see SI) and determined by themomentumQ and interlayer distance d. The strong exciton oscillator strengthand intrinsic in-plane exciton dipole moment in many 2D materialsfavor the Förster-type IET56. However, the calculated transfer rate isonly 0.08meV (a transfer time of ~8.1 ps), even assuming a tightlystacked heterostructure with interlayer distance of d = 0nm(Fig. 4d). Our calculations reveal that the IET process preferablyexcites an intraband rather than an interband transition. Theexperimentally observed energy-momentum distribution ofexcited-state hot holes supports this conclusion. To further distin-guish theMA- and Förster-type IET, we calculate the transfer rates ofthese two mechanisms as a function of layer distance, and identifythe distinct layer distance dependence (details see SI). In addition,we also performed calculations of Dexter-type IET (Fig. 4g), in whichscenario the electron and hole components of excitons in WSe2scatter to the graphene layer simultaneously. However, due to thesmall wavefunction overlap and the finite momentum distancebetween KWSe2and KGr, we found a very weak Dexter-type interlayercoupling strength, more than three orders of magnitude smallercompared to the other two mechanisms (see SI). Compared withFörster- and Dexter-type IET, the calculated transfer time of MA-type energy coupling is the closest to our experimental results. Wecan thus identify the MA-type conversion of excitons in WSe2 tointraband excitations in graphene as the dominant IET mechanism.In this work, we provide a detailed microscopic picture of inter-facial charge and energy transfer processes in photoexcitedML-WSe2/graphene heterostructures.Optical excitation of electrons in grapheneleads to interlayer charge transfer of quasi-free electrons from thegraphene layer to the K and Q valleys of the semiconductor’s con-duction bands on a time scale of ~50 fs. In contrast, excitons in WSe2decay through an interfacial Meitner-Auger energy transfer processwith a time constant of ~70 fs. This previously unidentified process isgoverned by interlayer dipole-monopole interactions leading to anni-hilation of an exciton inWSe2 and non-vertical intraband excitations ingraphene. The momentum of the electron-hole pair in graphene ori-ginates from the finite center of mass momentum of the hot excitonsin WSe2. The interfacial Meitner-Auger mechanism is found to dom-inate the energy transfer process over established mechanisms likeFörster- and Dexter-type transfer. This mechanism results in transienthole distributions as low as 2 eV below the Dirac points. These obser-vations enrich the physical toolbox for designing van der Waals het-erostructures and might be utilized in hot-carrier photovoltaic deviceconcepts to harness the ultrafast and efficient carrier transfer pro-cesses at interfaces57.MethodsTime- and angle-resolved photoemission spectroscopyWe used a 500 kHz tabletop femtosecond optical parametric chirpedpulse amplification (OPCPA) laser system operating at a center wave-length of 800nm and delivering average power up to 15W. The highharmonic generation is produced in a vacuum chamber by tightfocusing (10μm) the second harmonic (400 nm) of the OPCPA fun-damental on a thin and dense argon gas jet. We select the photons~21.7 eV (110meV FWHM bandwidth) as the probe arm for trARPESexperiment27. Concerning the pumparm,we used two different beamsfor this study. One pump beam is directly obtained from the OPCPA(800 nm, FWHM= 35 fs) and another one is the residual power of thecompressed fiber amplifier (1030nm, FWHM=200 fs). The pump andprobe beams are coupled into an ultra-high-vacuum (UHV) chamberand spatially overlapped at the sample position which is controlled bya six-axis manipulator (Carving, SPECS GmbH). The main UHV cham-ber is equippedwith a unique combinationof a hemispherical electronenergy analyzer (PHOIBOS150, SPECS GmbH) and time-of-flight (ToF)momentum microscope (METIS1000, SPECS GmbH)28. On the onehand, the hemispherical analyzer, which can work in a multi-electronsper laser shot regime, provides high statistic energy/momentum cutsalong a given momentum direction, as shown in Fig. 3. On the otherhand, the momentum microscope allows for efficient, parallel,momentum-resolveddetection of the full photoemissionhorizon fromthe surface as shown in Fig. 1b and Fig. 2a–e. All the experiments areperformed at room temperature.ML-WSe2/ML-graphene vdW heterostructure fabricationMonolayer graphene on SiC (Si-terminated surface) was grown usingthe well-established recipe of sublimation growth at elevated tem-peratures in an argon atmosphere4. Note that, on SiC58, the graphenemonolayer resides on top of a ð6ffiffiffi3p×6ffiffiffi3pÞR30∘ reconstructed carbonbuffer layer that is covalently bound to the SiC substrate. WSe2 filmswere grown on the thus prepared MLG/SiC substrates via hybrid-pulsed-laser deposition (hPLD) in ultra-high vacuum35. Pure tungsten(99.99%) was ablated using a pulsed KrF excimer laser (248 nm) with arepetition rate of 10 Hz, while pure selenium (99.999%) was evapo-rated from a Knudsen cell at a flux rate of around 1.5Å/s as monitoredby a quartz crystal microbalance. The deposition was carried out at450 °C for6h, followedby two-step annealing at 640 °Cand400 °C for1 h each.DFT band structure calculationsWe performed density functional theory (DFT) calculation of sus-pended ML WSe2 and graphene with the projector augmented wavecode GPAW59 using GLLB-SC xc-functional, separately. The GLLB-SC isan orbital-dependent exact exchange-based functional including thespin-orbital coupling60. The relaxed lattice constant of WSe2 isa = 3.25Å. We sample the Brillouin Zone with a (15 × 15 × 1) k-pointmesh, and set the cutoff energy for the plane-wave expansion at600 eV. The bandgap is adjusted to fit our data. The calculated bandstructures of both materials are superimposed on each other andshown in Fig. 2a.Data availabilityThe trARPES data generated in this study have been deposited in theZenodo database under accession code https://doi.org/10.5281/zenodo.8210835.Code availabilityThe source code for the trARPES data analysis is available on GitHub(https://github.com/mpes-kit). The data processing details are welldescribed in ref. 61.References1. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Neto, A. H. 2Dmaterials and van der Waals heterostructures. Science 353,6298 (2016).2. Akinwande, D. et al. Graphene and two-dimensional materials forsilicon technology. Nature 573, 507–518 (2019).3. Liu, F. et al. Disassembling 2D van der Waals crystals into macro-scopicmonolayers and reassembling into artificial lattices. Science367, 903–906 (2020).4. Emtsev, K. V. et al. Towards wafer-size graphene layers by atmo-spheric pressure graphitization of silicon carbide. Nat. Mater. 8,203–207 (2009).5. 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Data 7, 442 (2020).AcknowledgementsThisworkwas fundedby theMax Planck Society, the EuropeanResearchCouncil (ERC) under the European Union’s Horizon 2020 research andinnovation program (Grant No. ERC-2015-CoG-682843), the GermanResearch Foundation (DFG) within the Emmy Noether program (GrantNo. RE 3977/1), through Projektnummer 18208777-SFB 951 “HybridInorganic/Organic Systems for Opto-Electronics (HIOS)” (CRC 951 pro-ject B12, M.S., D.C., A.K.), and the SFB/TRR 227 “Ultrafast Spin Dynamics”(projects B07, project-ID: 328545488), and the Program DFG SPP2244(project-ID: 443366970). S.B. acknowledges financial support from theNSERC-Banting Postdoctoral Fellowships Program. M.D. acknowledgesfinancial support from the Göran Gustafsson Foundation and theSwedish Research Council under Grant No: 2022-03813. A.K. acknowl-edges financial support from DFG Projekt KN 427/14-1. A.C. and J.D.Z.acknowledge the financial support by the DFG SPP2244 (Project-ID:443405595) and the Würzburg-Dresden Cluster of Excellence onComplexity and Topology in Quantum Matter (ct.qmat) (EXC 2147,Project-ID 390858490). K.W. and T.T. acknowledge support from theJSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and WorldPremier International Research Center Initiative (WPI), MEXT, Japan.Author contributionsS.D., S.B., T.P., M.D., J.M., A.N., and L.R. performed the trARPES mea-surement. S.D. analyzed the data and wrote the first draft of the manu-script. R.E., L.R., and M.W. were responsible for developing all theexperimental infrastructures. M.S. and D.C. performed the microscopiccalculation with the guidance of A.K. R.P.X. and developed the 4D dataprocessing code. P.R. and H.N. provided the epitaxially grown hetero-structure, with support from U.S. and H.T. A.M., A.S., and M.S. con-ducted Raman and photoluminescence measurements, with guidancefrom M.J. and P.M. J.D.Z. and A.C. prepared the exfoliated ML samplewith the hBN substrate provided by K.W. and T.T. All authors contributedto the final version of the manuscript.FundingOpen Access funding enabled and organized by Projekt DEAL.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-40815-8.Correspondence and requests for materials should be addressed toShuo Dong, Laurenz Rettig or Ralph Ernstorfer.Peer review informationNature Communications thanks Hai Wang, andthe other, anonymous, reviewer(s) for their contribution to the peerreview of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 20231Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany. 2Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. 3Université de Bordeaux - CNRS - CEA, CELIA, UMR5107, F33405 Talence, France.4Nichtlineare Optik und Quantenelektronik, Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany. 5Max Planck Institute forSolid State Research, 70569 Stuttgart, Germany. 6Department of Applied Physics, KTH Royal Institute of Technology, Hannes Alfvéns väg 12, 114 19Stockholm, Sweden. 7Institute of Applied Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062Dresden, Germany. 8Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland. 9Department of Statistical Sciences, University of Toronto, 700 UniversityAvenue, Toronto, ON M5G 1Z5, Canada. 10Institute of Semiconductor Optics and Functional Interfaces, Research Center SCoPE and IQST, University ofStuttgart, 70569Stuttgart,Germany. 11International Center forMaterials Nanoarchitectonics, National Institute forMaterials Science, 1-1Namiki, Tsukuba 305-0044, Japan. 12Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.13Department of Physics, University of Tokyo, 113-0033 Tokyo, Japan. 14Institute for Functional Matter and Quantum Technologies, University of Stuttgart,70569 Stuttgart, Germany. 15Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA. 16Institut für Optik und Atomare Physik, TechnischeUniversität Berlin, 10623 Berlin, Germany. e-mail: dong@fhi-berlin.mpg.de; rettig@fhi-berlin.mpg.de; ernstorfer@fhi-berlin.mpg.deArticle https://doi.org/10.1038/s41467-023-40815-8Nature Communications |         (2023) 14:5057 8https://doi.org/10.1038/s41467-023-40815-8http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/mailto:dong@fhi-berlin.mpg.demailto:rettig@fhi-berlin.mpg.demailto:ernstorfer@fhi-berlin.mpg.de Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der Waals heterostructure Results Interlayer quasi-free carrier transfer Interlayer energy transfer Discussion Methods Time- and angle-resolved photoemission spectroscopy ML-WSe2/ML-graphene vdW heterostructure fabrication DFT band structure calculations Data availability Code availability References Acknowledgements Author contributions Funding Competing interests Additional information