Observation of ultrafast interfacial Meitner-Auger energy transfer in a Van der Waals heterostructure

Atomically thin layered van der Waals heterostructures feature exotic and emergent optoelectronic properties. With growing interest in these novel quantum materials, the microscopic understanding of fundamental interfacial coupling mechanisms is of capital importance. Here, using multidimensional photoemission spectroscopy, we provide a layer- and momentum-resolved view on ultrafast interlayer electron and energy transfer in a monolayer-WSe2/graphene heterostructure. Depending on the nature of the optically prepared state, we find the different dominating transfer mechanisms: while electron injection 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. By analysing the time-energy-momentum distributions of excited-state carriers with a rate-equation model, we distinguish these two types of interfacial dynamics and identify the ultrafast conversion of excitons in WSe2 to valence band transitions in graphene. Microscopic calculations find interfacial dipole-monopole coupling underlying the Meitner-Auger energy transfer to dominate over conventional Förster- and Dexter-type interactions, in agreement with the experimental observations. The energy transfer mechanism revealed here might enable new hot-carrier-based device concepts with van der Waals heterostructures.

Atomically thin layered van der Waals heterostructures feature exotic and emergent optoelectronic properties.With growing interest in these novel quantum materials, the microscopic understanding of fundamental interfacial coupling mechanisms is of capital importance.Here, using multidimensional photoemission spectroscopy, we provide a layer-and momentum-resolved view on ultrafast interlayer electron and energy transfer in a monolayer-WSe 2 /graphene heterostructure.Depending on the nature of the optically prepared state, we find the different dominating transfer mechanisms: while electron injection from graphene to WSe 2 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 WSe 2 .By analysing the time-energy-momentum distributions of excited-state carriers with a rate-equation model, we distinguish these two types of interfacial dynamics and identify the ultrafast conversion of excitons in WSe 2 to valence band transitions in graphene.
Microscopic calculations find interfacial dipole-monopole coupling underlying the Meitner-Auger energy transfer to dominate over conventional Förster-and Dexter-type interactions, in agreement with the experimental observations.The energy transfer mechanism revealed here might enable new hot-carrier-based device concepts with van der Waals heterostructures.
The unique physical properties of atomically thin two-dimensional (2D) materials 1,2 and constantly improving fabrication methods 3,4 have lead to a great interest in novel quantum materials based on van der Waals (vdW) heterostructures 5 .By stacking 2D materials, vdW heterostructures inherit the properties from individual constituents, and exotic physical phenomena may emerge due to the interfacial interaction [5][6][7] .An emblematic example is the emergence of superconductivity in twisted bilayer graphene when stacked at the so-called 'magic angle' 8 .As another example, interlayer excitons, which are spatially separated yet Coulomb-bound electron-hole pairs in semiconducting transition metal dichalcogenide (TMDC) heterostructures allow exceptional control of optoelectronic properties [9][10][11] .Out of the vdW heterostructure library, a basic optoelectronic building block is a monolayer (ML) semiconducting TMDC in contact with graphene 12 .This hybrid structure represents a model system as it combines the strong light-matter coupling of TMDCs and the high mobility of massless Dirac carriers of graphene 13 .The gapless electronic structure of graphene allows for harvesting low-energy photons, extending the spectral range covered by conventional photodetectors to the near-infrared wavelength, which is highly beneficial for photovoltaic applications 14 .
Optoelectronic functionality in vdW heterostructures arises from careful design and control of optical transitions and interfacial transfer processes.Particularly, interfacial charge (ICT) and energy transfer (IET) are key processes which have triggered extensive experimental and theoretical efforts [15][16][17][18][19][20] Using time-resolved optical spectroscopies, a strong reduction of the exciton lifetime 21 and optically active charge-transfer excitations of TMDC/graphene heterostructures have been observed 22,23 , suggesting strong interlayer coupling and the underlying mechanisms have been discussed [24][25][26] .Moreover, the efficiency of IET processes like Förster-type coupling (based on electronic dipole-dipole interaction) has recently been investigated theoretically, pointing out the importance of energy-momentum conservation between participating quasiparticles 15 .
Therefore, a momentum resolved probe is required to directly monitor the dynamics and reveal the mechanism of interfacial transfer process in vdW heterostructures, including those involving momentum-forbidden dark states.
Here, we use time-and angle-resolved photoemission spectroscopy (trARPES) to investigate ultrafast interlayer carrier interactions in an epitaxially grown ML-WSe 2 /graphene heterostructure.
Our trARPES setup combines a high-repetition-rate (500 kHz) femtosecond extreme ultraviolet (XUV) source 27 coupled to a time-of-flight momentum microscope 28 (see Methods).It allows the measurement of the four-dimensional (4D) photoemission intensity I(E kin , k x , k y , ∆t), where E kin is the outgoing photoelectron kinetic energy, k x ,k y are the in-plane momenta and ∆t is the pump-probe delay, as shown in Fig. 1a,b.The probe photon energy of 21.7 eV allows accessing the entire Brillouin zone of the heterostructure and the variable pump wavelength allows us to photoexcite the heterostructure in a state-resolved manner.In the following, we present a time-, energy-, and momentum-resolved study on the excited-state dynamics in the heterostructure with two different pump photon energies: below the optical bandgap of WSe 2 (1.2 eV) and in resonance with its first excitonic transition (1.55 eV).as well as the linearly dispersing graphene bands.The excited state population can be clearly mapped at the K WSe 2 and Q WSe 2 valleys, and the π * band of graphene (K Gr ).c, By changing the pump wavelength, we can selectively prepare different initial excited states: quasi-free carriers in graphene with below-bandgap excitation (red arrow) or excitons in WSe 2 using excitation on the excitonic resonance (blue arrow).

Interlayer quasi-free carrier transfer
First, we photoexcite the heterostructure with the pump photon energy centred at hω pump =1.energy-momentum integration in selected regions of interest (ROIs), we extracted excited-state dynamics within these three valleys (Fig. 2f).Upon arrival of the pump pulses, the excited-state population rapidly builds up at K Gr (black curve) and decays with a time scale of ∼ 200 fs.Strikingly, the conduction band minima (CBMs) at K WSe 2 (red curve) and Q WSe 2 valleys (green curve) are also being populated, however, with a delay of ∆t = 51 ± 9 fs (see SI) compared to the rise of hot-carrier population in graphene.Since below-bandgap pump photon energy does not allow the direct photoexcitation of WSe 2 , the delayed electron populations in the conduction bands arise through charge transfer from graphene to WSe 2 .Two/multiple photon excitation can safely be ruled out (details see SI).The excited-state population of the Q WSe 2 valleys (Fig. 2f) could be raised via ICT from the graphene layer and the intervalley scattering from the K WSe 2 valleys 30,31 .
These observations support the following picture of the underlying processes with a belowbandgap excitation: light is absorbed by graphene and populates unoccupied states at E el Gr = tem or E D < 0 for an n-doped system).The energy position of the Dirac point in our heterostructure is estimated to be ∼ −0.1 eV below the Fermi level, obtained from the conical crossing 32,33 (see SI).The photoexcited carriers quickly reach a quasi-thermalized states in ∼ 10 fs 34 and could further increase their energy via intraband electron-electron scattering and interband Auger recombination in few tens of femtoseconds 35,36 .Once electrons gained a sufficient amount of energy to overcome the energy barrier, they scatter to WSe 2 via a phonon-assisted tunneling process, filling the single-particle CBMs at K WSe 2 and Q WSe 2 .This ICT mechanism is called interlayer hot carrier injection, and is schematically illustrated in Fig. 2g.The excited electrons in WSe 2 may subsequently scatter back to graphene and relax down towards the Fermi energy (E F ). Based on the observed carrier dynamics, we performed microscopic calculations of the phonon-assisted interlayer tunneling process, allowing us to estimate the electronic wavefunction overlap between the involved conduction bands of WSe 2 and graphene to be around 4% (see SI for details).Interlayer energy transfer: from excitons in WSe 2 to intraband transitions in graphene Next, we select a pump photon energy of hω pump =1.55 eV (pump pulse duration: 35 fs FWHM, pump fluence: F = 1.7 mJ/cm 2 ), near-resonant to the A-excitonic transition of WSe 2 .In this case, the pump photon energy allows both the WSe 2 and the graphene layer to be simultaneously photoexcited.One striking observation is that the energy distribution of excited carriers at the K WSe 2 valleys is centred at 0.63 eV (Fig. 3a), ∼100 meV lower than with below-bandgap excitation (Fig. 3b), as apparent from the energy distribution curves (EDCs) (first 100 fs).As discussed above, with 1.2 eV excitation, the K WSe 2 valleys are filled with quasi-free electrons that have tunneled from the graphene layer.Therefore, this ∼ 100 meV energy difference is a direct photoemission signature of exciton formation, when near-resonantly pumping using 1.55 eV photons 37 : the bound electron-hole (el-h) pair reduces the quasi-free particle bandgap by the exciton binding energy.In addition to this excitonic feature, we also observe a transient shift of WSe 2 valence bands.In Fig. 3d, EDCs at K WSe 2 are shown at ∆t = 0 fs (red) and ∆t = −200 fs (black), in which the top two valence bands, VB1 and VB2, are fitted using Gaussian lineshape functions (see SI).The peak position of VB1 shifts towards the conduction band within the first 100 fs, transiently shrinking the electronic bandgap.This is due to the arrival of ICT-induced charge carriers from the graphene layer.With near-resonantly pumping the A-exciton, the occurrence of ICT and injection of quasi-free carriers from graphene to WSe 2 is expected, similar to the case of below-bandgap excitation.This could lead to dynamical screening effect and the observed bandgap renormalization, as reported in highly-excited or doped ML TMDC materials [38][39][40][41][42] .As the magnitude of such a transient bandgap renormalization has been shown to scale with the excited charge carrier density 40,43 , we utilize the VB shift in the following as a measure of the ICT transferred carriers dynamics from graphene layer.
In addition to the excited-state dynamics in WSe is provided by the optically pumped excitons which gain finite COM momenta during the population formation process via phonon-mediated dephasing and intravalley thermalization [49][50][51][52] (see the discussion in SI).The highly efficient IET of the excitons and intraband electron-hole pairs is thus possible under the conservation of energy and momentum, i.e., E ex = E Gr and Q = k Gr .
In a similar trARPES study of a ML WS 2 /graphene heterostructure, dominating interfacial charge transfer has been observed 17 .Compared with our study, the different charge transfer rates could be raised from the different band structure alignment near the interface and the density of defectsites 26 .While the additional exciton energy transfer was not excluded, its relative efficiency might be reduced due to the larger COM momentum required at the larger A-exciton energy of WS 2 and the energy level alignment of these specific samples.In order to gain information on the time scales of the energy and charge transfer processes, next we analyze the dynamics of excited-state populations extracted from the ROIs shown in Fig. 3c, including the excited-state carriers in WSe 2 (ROI 1 ), VB1 shifting (ROI 2 ), hot electrons in graphene (ROI 3 ) and IET-driven deep valence band holes (ROI 4 ).The time trace of hot carriers in the CBM of WSe 2 (black curve in Fig. 4a) contains two types of quasi-particles dynamics: the photo-generated excitons N ex T and the ICT-induced quasi-free electrons N el T .The decay of excitons excite the valence band electrons in graphene via IET with a transfer time of τ IET (Fig. 4f).On the other hand, the arrival of ICT-induced electrons transiently shifts the VBs of WSe 2 (green curve in Fig. 4a) which therefore represents the dynamics of N el T as 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 fs compared to the CB signal, evidencing the occurrence of interlayer hot electron injection after pho-toexcitation.The population of N el T subsequently relaxes back to K Gr , refilling the excited-states of graphene (Fig. 4h).From the graphene side, the photoexcited hot electrons N el Gr (red curve in Fig. 4b) could either scatter to conduction bands of WSe 2 or relax by interband decay channels in graphene.Therefore, the relaxation of N el Gr could be characterized with the charge transfer time of τ ICT and a decay time of τ el Gr .The deep valence band holes N h Gr (blue curve in Fig. 4b) are populated by exciton energy transfer on a time scale of τ IET , which would relax back to the Fermi level with a lifetime of τ h Gr .
The complete dynamics across the interface can be described with a set of coupled rate equations based on a multi-level scheme (details see SI).By numerically solving the rate equation model, we disentangle the dynamics of IET and ICT.Our global fit describes the data well and yields the transfer times of τ IET = 67 ± 7 fs and τ ICT = 118 ± 18 fs.The lifetimes of electrons and IET-populated hot holes in graphene are simultaneously extracted as τ el Gr = 84 ± 7 fs and τ h Gr = 7 ± 4 fs.Combining all our observations and analysis of the energy-momentum dynamics in WSe 2 and graphene, we summarize the interfacial phenomena governing the non-equilibrium behaviour of our heterostructure: first, the optical pump generates excitons in WSe 2 and quasi-free carriers in graphene (Fig. 4e).Following photoexcitation, the exciton annihilation excites deep valence electrons in graphene via an IET process (Fig. 4f-g).Simultaneously, hot electrons in graphene are injected to the conduction bands of WSe 2 via ICT which transiently shift the valence bands of WSe 2 (Fig. 4h).Another IET mechanism is Förster energy transfer (Fig. 4f).The energy of the exciton excites an interband transition from valence bands to above Dirac point via the dipole-dipole coupling. 53 contrast to the MA-type IET process, the interband excitation via Förster-type energy transfer populates the conduction bands of graphene above the Fermi level, independent of the photoninduced hot carriers distribution.The coupling strength is explicitly evaluated (for derivation, see SI) and determined by the momentum Q and interlayer distance d.The strong exciton oscillator strength and intrinsic in-plane exciton dipole moment in many 2D materials favor the Förster-type IET 54 .However, the calculated transfer rate is only 0.08 meV (a transfer time of ∼ 8.1 ps), even assuming a tightly stacked heterostructure with interlayer distance of d = 0 nm (Fig. 4d).Our calculations reveal that the IET process preferably excites an intraband rather than an interband transition.The experimentally observed energy-momentum distribution of excited-state hot holes supports this conclusion.In addition, we also performed calculations of Dexter-type IET (Fig. 4g), in which scenario the electron and hole components of excitons in WSe 2 scatter to the graphene layer simultaneously.However, due to the small wavefunction overlap and the finite momentum distance between K WSe 2 and K Gr , we found a very weak Dexter-type interlayer coupling strength, more than three orders of magnitude smaller compared to the other two mechanisms (see SI).We can thus identity the MA-type conversion of excitons in WSe 2 to intraband excitations in graphene as the dominant IET mechanism.
In this work, we provide a detailed microscopic picture of interfacial charge and energy trans-

Methods
Time-and angle-resolved photoemission spectroscopy We used a 500kHz tabletop femtosecond optical parametric chirped pulse amplification (OPCPA) laser system operated at a center wavelength of 800 nm and delivering average power up to 15 W. The high harmonic generation is produced in a vacuum chamber by tight focusing (10 µm) the second harmonic (400 nm) of the OPCPA fundamental on a thin and dense argon gas jet.We select the photons around 21.7 eV (110 meV FWHM bandwidth) as the probe arm for trARPES experiment 27 .Concerning the pump arm, we used two different beams for this study.One pump beam is directly obtained from the OPCPA (800 nm, FWHM=35 fs) and another one is the residual power of the compressed fiber amplifier (1030 nm, FWHM=200 fs).The pump and probe beams are coupled into an ultra-high-vacuum (UHV) chamber and spatially overlapped at the sample position which is controlled by a six-axis manipulator (Carving, SPECS GmbH).The main UHV chamber is equipped with an unique combination of a hemispherical electron energy analyzer (PHOIBOS150, SPECS GmbH) and time-of-flight (ToF) momentum microscope (METIS1000, SPECS GmbH) 28 .On the one hand, the hemispherical analyzer, which can work in a multi-electrons per laser shot regime, provides high statistic energy/momentum cuts along a given momentum direction, as shown in Fig. 3. On the other hand, the momentum microscope allows for efficient, parallel, momentum-resolved detection of the full photoemission horizon from the surface as shown in Fig. 1b and Fig. 2a-e.All the experiments are performed at room temperature.
ML-WSe 2 /ML-Graphene vdW heterostructure fabrication Monolayer graphene on SiC (Siterminated surface) was grown using the well-established recipe of sublimation growth at elevated temperatures in an argon atmosphere 4 .Note that, on SiC 56 , the graphene monolayer resides on top of a (6 √ 3 × 6 √ 3)R30°reconstructed carbon buffer layer that is covalently bound to the SiC substrate.WSe 2 films were grown on the thus prepared MLG/SiC substrates via hybrid-pulsedlaser deposition (hPLD) in ultra-high vacuum 33 .Pure tungsten (99.99%) was ablated using a pulsed KrF excimer laser (248 nm) with a repetition rate of 10 Hz, while pure selenium (99.999%) was evaporated from a Knudsen cell at a flux rate of around 1.5 Å/s as monitored by a quartz crystal microbalance.The deposition was carried out at 450°C for 6 h, followed by two-step annealing at 640°C and 400°C for 1 h each.
DFT calculation of band structure We performed density functional theory (DFT) calculation of suspended ML WSe 2 and graphene with the projector augmented wave code GPAW 57 using and JP20H00354).Competing Interests The authors declare that they have no competing financial interests.
Correspondence Correspondence and requests for materials should be addressed to dong@fhi-berlin.mpg.de,rettig@fhi-berlin.mpg.de and ernstorfer@fhi-berlin.mpg.de.

Fig. 1 :
Fig. 1: Time-and angle-resolved photoemission measurement of interlayer 2 eV (pump pulse duration 200 fs FWHM), well below the optical bandgap of WSe 2 29 .The NIR-pump/XUV-probe experiments were performed with a pump fluence of F = 5.3 mJ/cm 2 and at room temperature.Fig.2a-d show energy-resolved photoemission signals along the K − K cut of the Brillouin zone, at selected time delays.The momentum distributions above E F within the first 400 fs reveal that the excited states are localized in three different types of valleys: the Dirac cones of graphene at its K points (K Gr ) and the K and Q valleys of WSe 2 (K WSe 2 , Q WSe 2 ), as shown in Fig.2e.The Q WSe 2 valley localizes between the K WSe 2 valley and the Γ point.By performing

Fig. 4 :
Fig. 4: Interlayer charge and energy transfer upon near-resonant A-exciton excita- fer processes in photoexcited ML-WSe 2 /graphene heterostructures.Optical excitation of electrons in graphene leads to inter-layer charge transfer of quasi-free electrons from the graphene layer to the K and Q valleys of the semiconductor's conduction bands on a time scale of ∼50 fs.In con-trast, excitons in WSe 2 decay through an interfacial Meitner-Auger energy transfer process with a time constant of ∼70 fs.This previously unidentified process is governed by inter-layer dipolemonopole interactions leading to annihilation of an exciton in WSe 2 and non-vertical intraband excitations in graphene.The momentum of the electron-hole pair in graphene originates from the finite center of mass momentum of the hot excitons in WSe 2 .The interfacial Meitner-Auger mechanism is found to dominate the energy transfer process over established mechanisms like Försterand Dexter-type transfer.This mechanism results in transient hole distributions as low as 2 eV below the Dirac points.These observations enrich the physical toolbox for designing van der Waals heterostructures and might be utilized in hot-carrier photovoltaic device concepts to harness the ultrafast and efficient carrier transfer processes at interfaces55 .
Author contributions S.D., S.B., T.P., M.D., J.M., A.N. and L.R. performed the trARPES measurement.S.D. analyzed the data and wrote the first draft of the manuscript.R.E., L.R. and M.W. were responsible for developing all the experimental infrastructures.M.S. and D.C. performed the microscopic calculation with the guidance of A.K.. R.P.X.developed the 4D data processing code.P.R. and H.N. provided the epitaxially-grown heterostructure, with support from U.S. and H.T.. A.M., A.S., and M.S. conducted Raman and photoluminescence measurements, with guidance from M.J and P.M.. J.D.Z and A.C. prepared the exfoliated ML sample with the hBN substrate provided by K.W. and T.T..All authors contributed to the final version of the manuscript.