Abstract
The equilibrium and nonequilibrium optical properties of singlelayer transition metal dichalcogenides (TMDs) are determined by strongly bound excitons. Exciton relaxation dynamics in TMDs have been extensively studied by timedomain optical spectroscopies. However, the formation dynamics of excitons following nonresonant photoexcitation of free electronhole pairs have been challenging to directly probe because of their inherently fast timescales. Here, we use extremely short optical pulses to nonresonantly excite an electronhole plasma and show the formation of twodimensional excitons in singlelayer MoS_{2} on the timescale of 30 fs via the induced changes to photoabsorption. These formation dynamics are significantly faster than in conventional 2D quantum wells and are attributed to the intense Coulombic interactions present in 2D TMDs. A theoretical model of a coherent polarization that dephases and relaxes to an incoherent exciton population reproduces the experimental dynamics on the sub100fs timescale and sheds light into the underlying mechanism of how the lowestenergy excitons, which are the most important for optoelectronic applications, form from higherenergy excitations. Importantly, a phononmediated exciton cascade from higher energy states to the ground excitonic state is found to be the ratelimiting process. These results set an ultimate timescale of the exciton formation in TMDs and elucidate the exceptionally fast physical mechanism behind this process.
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Introduction
Singlelayer (1L) TMDs are attracting growing interest because of their peculiar properties that make them highly suitable for optoelectronics applications^{1}. The reduced dielectric screening that is caused by the strong spatial confinement results in an optical response that is dominated even at room temperature by strongly bound excitons with large (hundreds of meV) binding energies^{2,3}. The enhanced Coulomb interaction gives rise to additional effects such as the occurrence of a Rydberg series of excitonic states^{4} and manybody complexes like trions^{5} and biexcitons^{6} whose physical properties can be tuned by changing the dielectric environment^{7} or by applying external stimula such as light^{8}, strain^{9}, electric^{10}, and magnetic fields^{11}. Ultrashort laser pulses offer an additional way to change and potentially control the properties of excitons on a fast timescale. The nonequilibrium optical response of TMDs has been extensively explored both experimentally and theoretically^{12,13}. The dynamical response of TMDs and, in general, all semiconductors can be divided into coherent and incoherent regimes^{14,15}. While the incoherent exciton dynamics of TMDs, including processes, such as exciton thermalization^{16}, radiative/non radiative recombination^{17}, intra and intervalley scattering^{18,19,20,21,22}, exciton dissociation^{23}, and exciton–exciton annihilation^{24}, have been extensively studied, the coherent exciton response and the corresponding early stage dynamics of the exciton formation process are still almost unexplored largely because the limited available temporal resolution (i.e., >100 fs for pumpprobe optical spectroscopy and >1 ps for timeresolved photoluminescence) has prevented the study of the primary early stage dynamics of exciton photogeneration processes^{17,25,26}.
Here, we push the temporal resolution of ultrafast differential reflectivity (ΔR/R) spectroscopy to the regime of less than 30 fs in order to investigate the dynamics of exciton formation in 1LMoS_{2}^{27}. Experimentally, we employ a pumpprobe technique that uses ΔR/R to monitor the evolution of the excited state population. Particularly, we elucidate how long it takes for an initial population of highenergy photoexcited electrons and holes to relax to the lowestenergy exciton states (i.e., the 1s states of the A and B excitons), and how this formation time depends upon the energy of the initial state (c.f. Fig. 1). The measured dynamics are found to be remarkably fast, suggesting that lowestenergy excitons form from these highenergy populations with a characteristic timescale as fast as 10 fs. Upon increasing the energy of the initial state of photoinjected carriers (i.e., by increasing the pump photon energy), we find that (1) the formation time of the excitons increases monotonically with increasing energy; (2) an initial, sub100 fs fast decay component of the excitons vanishes; and (3) the dynamics of a slower decay process (on the timescale of picoseconds) associated with the relaxation of a thermal population of excitons does not substantially change. Simulations based on the TMD Bloch equations attribute the excitation energy dependence of the formation dynamics to a phononinduced cascadelike relaxation process of highenergy incoherent excitons down to the excitonic ground state^{28}. This process, although extremely fast, is predicted to have a characteristic time constant between 20 and 30 fs, corroborating our experimental observations. The early sub100 fs relaxation dynamics are also well captured by the simulations, which reveal that they arise from the decay of the pumpinduced coherent optical polarization into ultimately thermal exciton populations (i.e., incoherent excitons). These results are of great relevance for optoelectronic applications of TMDs as they directly define a timescale for an efficient extraction of hot carriers in 1LTMDs and TMDbased heterostructures before the exciton formation process.
Results
Ultrafast exciton dynamics
Figure 1 schematically summarizes the exciton formation process (Fig. 1a) and the key optical excitonic transitions (Fig. 1b) of 1LMoS_{2}. The 1LMoS_{2} used here is grown by chemical vapor deposition on a SiO_{2}/Si substrate. All measurements were made on asgrown samples. From the steadystate reflectance measurements that are reported in Supplementary Fig. 1, the lowest energy A and B excitonic resonances that arise from optical transitions between the twohighest energy valence bands and the lowestenergy conduction bands at the K and K’ points in the Brillouin zone are centered at the energies of 1.88 eV and 2.03 eV, respectively (see sketch in Fig. 1b). As illustrated in Fig. 1c, both the A and B optical transitions form two manifolds of Rydberglike series of bound states that merge into a continuum of unbound electronhole states^{3,29}. These resonances correspond to the lowestenergy (or ground state) excitons in the A and B manifolds (i.e., the A_{1s} and B_{1s} states, respectively), possess the largest oscillator strengths, and dominate the optical response over the corresponding higherenergy unbound states. Based on previous experimental studies^{3,29} and refined theoretical models^{18}, we estimate that the exciton binding energy (i.e., the energetic difference between the 1s exciton and the lowest energy state in the exciton continuum) is of the order of 350 meV. In our measurements the pump photon energies span from 2.29 eV to 2.75 eV (with bandwidths spanning from 70 meV to 140 meV) and thus, at all energies, photoexcitation predominantly creates an initial population of excitons at or wellinto the exciton continuum for the A excitons (as well as for the B excitons at energies above ~2.4 eV). To monitor the formation dynamics and quantify the formation time (i.e., τ(E) in Fig. 1c), our probe energies monitor the rise and decay dynamics of the ΔR/R signals for the 1s states of the A and B excitons.
We use tunable pump pulses to photoinject electronhole pairs with increasing excess energy with respect to E_{G}. The timedelayed broadband probe pulses measure the buildup and early decay dynamics of both A_{1s} and B_{1s} excitons. The experimental temporal resolution of the setup is sub30fs (see Methods and Supplementary Fig. 5). Figure 2a and b reports ΔR/R(E_{probe},τ) maps as a function of the pumpprobe delay τ and the probe photon energy E_{probe} for two different pump photon energies: 2.29 eV and 2.75 eV, i.e., respectively, across and well above E_{G}. Due to the presence of the reflecting Si substrate, ΔR/R is equivalent to a doublepass differential transmission (ΔT/T). Both measurements show comparable qualitative responses: positive strong features associated with the A_{1s} (centered at E_{probe} = 1.88 eV) and B_{1s} (centered at E_{probe} = 2.03 eV) exciton states. The ΔR/R spectrum displays a symmetric profile around each excitonic resonance with no shift of the peak maximum, within the considered temporal window (i.e., from −100 to 200 fs). Weak and broad negative features are detected at higher and lower probe energies as better shown in Supplementary Fig. 4. These features are strongly quenched with respect to previously published pumpprobe measurements on 1LMoS_{2} performed in transmission geometry^{12}. We attribute the different intensities of these signals away from the excitonic transitions to a photonic effect caused by the interference of multiple reflections of the incoming beam in the thin SiO_{2} substrate.
In the temporal window explored in the experiment (i.e., ~200 fs), the ΔR/R spectrum displays a symmetric profile around each excitonic resonance with no shift of the peak maximum, showing that the signal is dominated by Pauli blocking (see Supplementary Fig. 2).
A closer inspection of the maps reveals that the formation time τ_{rise} of the ΔR/R signals of the A_{1s} and B_{1s} excitons is longer for higher pump photon energies. When the excitation energy is close to E_{G}, the signal displays a quasiinstantaneous (i.e., pulsewidth limited) buildup, while for increased pump photon energy, τ_{rise} significantly increases. We stress that this result can be observed only thanks to the high temporal resolution of the setup. To better quantify this effect, Fig. 2c reports the temporal cuts of the maps taken at the A_{1s} and B_{1s} exciton peak for increasing pump photon energies. The buildup times are estimated by fitting the temporal traces in the temporal window between −100 and 200 fs, to the function:
where H is the Heaviside function centered at τ = 0; τ_{1} and τ_{2} are decay constants and A_{1} and A_{2} are the amplitudes of each decay component. The fitting function is convoluted with a Gaussian profile corresponding to the instrumental response function, which is the experimentally measured crosscorrelation profile between the pump and the probe (see Methods and Supplementary Note 5 for the temporal characterization of the pulses). We stress that only after including a finite exponential rise time in the fitting function, we can satisfactorily reproduce the experimental formation time (see Supplementary Fig. 6). Figure 2d unambiguously shows that τ_{rise} monotonically increases with the initial excess energy of the photoinjected carriers. Interestingly, for a higher pump energy excitation (i.e., 3.75 eV), we observe that τ_{rise} sensitively deviates from the increasing energy trend reported in Fig. 2d (see Supplementary Note 3). We can tentatively explain this flattening of the formation dynamics as a result of different phononmediated scattering process involving electronic states far away from the K/K’ points. The weak negative dip observed for negative times in the B exciton signal for 2.29 eV excitation photon energy is attributed to the socalled pumpperturbed freeinduction decay (PPFID)^{30}. In this process that occurs when the probe pulse precedes the pump, the freeinduction decay field emitted by the sample excited by the probe pulse is perturbed by the interaction with the pump pulse, giving rise to oscillating signals at negative delays. The PPFID effect can be safely disregarded from the measured buildup timescale of the sample because its amplitude is more than one order of magnitude lower than the bleaching of the excitonic peak. Another interesting effect is the extremely fast decay observed at lower pump photon energy, which occurs on a timescale comparable to that of the buildup and fades away as the pump is tuned to higher photon energies. This effect is particularly clear on the A exciton ΔR/R trace (see Fig. 2c).
Theoretical model
To identify the essential mechanisms that underlie the earlytime nonequilibrium optical response of 1LMoS_{2}, we performed simulations based on the TMD Bloch equations^{31}. Our model describes the temporal dynamics of the excitons after the photoexcitation of free electronhole pairs above or close to E_{G}. The ΔR/R at the A/B exciton transitions due to the photoexcitation process is also calculated and compared with experimental results. Excitonic excitations are theoretically described by solving the Wannier equation (see Supplementary Note 8)^{31,32}. The exciton kinetics are determined by a set of coupled differential equations (TMD Bloch equations) describing the temporal evolution of the polarization (in our theory an excitonic scattering state) and the excitonic population (incoherent excitons) where the phononmediated relaxation from energetically higher densities is described with effective rates Γ_{ν+1→ν} determined by independent density functional theory calculations (see Methods section and the sketch in Fig. 3a). Solving the set of equations of motion for the coherent polarization as well as incoherent exciton population gives access to the temporal dynamics of the differential reflectance at the 1s exciton resonance frequencies.
The results of the simulations, reported in Fig. 3b, agree remarkably well with the experimental results. For all pump photon energies, the calculated ΔR/R exhibits sub100 fs buildup followed by a decay time on the picosecond timescale. At higher pump energies, the peak of the signal is progressively delayed as a result of a slower rise time. The timescale and the pump photon energy dependence of the buildup dynamics are in remarkable quantitative agreement with the experimental results. The slowing of τ_{rise} with increasing pump photon energy is the result of a highenergy exciton cascade scattering process down to the excitonic ground state. A sketch of the scattering processes involving photoexcited excitons is reported in Fig. 3a. The nonresonant pump pulse induces an almost instantaneous coherent interband exciton polarization which oscillates with the same frequency of the driving pulse. This polarization rapidly dephases by exciton–phonon scattering and leads to a delayed formation of an incoherent exciton population involving electronic states above E_{G}. These highenergy weakly bound excitons quickly lose their energy and scatter into lowerlying continuum and discrete excitonic states. The scattering process continues until most of the excitonic population reaches the lowest energy 1s exciton state. With increasing pump photon energy, the number of intermediate scattering events, required to complete the cascade process, increases. This increase in needed scattering events results in the experimentally observed delayed formation of the bleaching signal measured at the A_{1s}/B_{1s} optical transitions.
The simulations also capture the occurrence of a sub100 fs decay component, which is particularly evident in the ΔR/R temporal trace for the A_{1s} state and progressively vanishes at higher pump photon energies. We attribute this effect to an interplay between a coherent exciton polarization and an incoherent exciton density. The coherent contribution adiabatically follows the pump pulse and gives rise to an instantaneous coherent buildup, while the incoherent signal is characterized by a delayed formation time involving additional exciton–phonon scattering processes. Figure 4 compares the full transient signal incorporating both contributions (solid line) as well as the underlying coherent (shaded area) and incoherent (dashed line) contributions to the differential signal obtained by artificially turning off the coherent contribution for low and high pump photon energies. For low pump photon energies, the full signal and the incoherent part of the signal display different dynamics in the first tens of femtoseconds and almost overlap after ~100 fs. While the buildup dynamics are dominated by the coherent excitons, the energetically lowest incoherent exciton densities play a dominant role after the polarization to population transfer is complete. We stress that, in this excitation regime, coherent exciton contribution could be more clearly disentangled from the incoherent exciton dynamics by performing pumpprobe measurements that utilized extremely short, linearly, and circularly polarized pulses and polarization resolved detection schemes. However, the use of broadband polarization optics makes it difficult to preserve the extremely high temporal resolution needed to observe such a process.
For high pump photon energies, the difference between full and incoherent curves diminishes since the coherent part inversely depends on the detuning between pump and probe pulses. This difference is related to the polarization, which rapidly decays before a significant 1s exciton density builds up that can be detected by the probe pulse. Thus, the transient signal in this energy regime is strongly dominated by the dynamics of incoherent exciton densities. In this excitation regime, the extracted rise time (~30 fs) of the ΔR/R traces is a direct estimation of the timescale of the incoherent exciton formation process.
Discussion
Our combined experimental and theoretical work defines a different timescale for the exciton formation process in 1LTMDs, which is much faster than the one previously estimated by intraexcitonic midIR^{33,34} and interband visible optical spectroscopy^{25}. We also stress that this exciton formation process is faster than the ~1 ps trion formation time in TMDs^{5} and, remarkably, orders of magnitude faster than the formation time of excitons in quantum wells (i.e., ~1 ns) measured by timeresolved photoluminescence^{35} and transient terahertz spectroscopy^{36}. This result points to a correlation between the formation time and the binding energy of the excitons. The reduced Coulomb screening in TMDs makes this process more rapid and effective than for weakly bound excitons in quantum wells or trions. Two different mechanisms have been proposed to describe the exciton formation process in semiconductors: geminate and bimolecular^{37}. In the geminate mechanism excitons are directly created upon photoexcitation by simultaneous emission of phonons, while in the bimolecular process, excitons are created from thermalized electronhole pairs. The observed sub100 fs buildup dynamics suggests that the geminate mechanism mediated by strong exciton–phonon scattering is the dominant process responsible for the formation of excitons. This conclusion is further supported by the pump fluence dependent measurements (see Supplementary Fig. 8), where no change of τ_{rise} is observed for different densities of photoexcited excitons, contrary to what expected for a bimolecular formation process.
In summary, we have studied the exciton formation process in 1LMoS_{2} by measuring its transient optical response upon excitation with energy tunable sub30fs laser pulses. We resolve extremely fast and pump photon energydependent buildup dynamics of the ΔR/R signal around the A_{1s} and B_{1s} excitonic transitions. Microscopic calculations based on the TMD Bloch equations quantitatively reproduce the experimental results and explain the delayed formation of the transient signal as a result of a phononinduced cascadelike relaxation process of highenergy incoherent excitons down to the excitonic ground state. These results shed light on the poorly explored mechanism of the exciton formation in 2D semiconductors, redefining the timescale of this process and are extremely important in view of optoelectronic applications of these materials.
Methods
Sample preparation
The large area 1LMoS_{2} sample was grown by chemical vapor deposition on a SiO_{2}/Si substrate. The SiO_{2} layer thickness is 300 nm. The growth procedure was carried on in a dualzone tube furnace filled by sulfur and MoO_{3} precursors. Further details on the growth process are reported in ref. ^{3}. Contrast reflectivity and photoluminescence measurements have been carried out to characterize the static optical response of the sample (see Supplementary Fig. 1).
Pumpprobe setup
The ultrafast pumpprobe experiments were carried out using a regeneratively amplified Ti:Sapphire system (Coherent Libra II), emitting 100 fs pulses centered at 1.55 eV at 2 kHz repetition rate with 4W average power. The laser drives two homemade Noncollinear Optical Parametric Amplifiers (NOPAs), which serve, respectively, as the pump and the probe. The first NOPA (probe beam) is pumped at 3.1 eV by the second harmonic of the laser and is seeded by a whitelight continuum (WLC), generated in a 1mm thick sapphire plate. The seed is amplified in a 1mm thick betabarium borate (BBO) crystal and compressed to nearly transformlimited duration (i.e., 7 fs) by a pair of customdesigned chirped mirrors. The probe spectrum extends from 1.75 to 2.4 eV, covering the A/B excitonic resonances of 1LMoS_{2}. The second NOPA, used to produce the pump beam, is also pumped at 3.1 eV and uses a BBO crystal. It can be configured to amplify either the visible or the nearinfrared parts of the WLC. In the former case one obtains pulses tunable from 2 to 2.5 eV, compressed to sub20fs duration by chirped mirrors. In the latter case one obtains pulses tunable between 1.1 and 1.4 eV, which are compressed to a nearly transformlimited sub15fs duration by a pair of fused silica prisms. These pulses are then frequencydoubled in a 50μmthick BBO crystal to obtain pulses tunable between 2.29 and 2.75 eV. The overall temporal resolution of the setup is characterized via CrossFrequency Resolved Optical Gating (XFROG), as extensively explained in Supplementary Note 5. Pump and probe pulses are temporally synchronized by a motorized translation stage, and noncollinearly focused on the sample by a spherical mirror, resulting in spotsize diameters of ~100 μm and ~70 μm, respectively. After the interaction with the pumpexcited sample, the probe pulse is spectrally dispersed on a Silicon CCD camera with 532 pixels working at the same repetition rate as the laser. The pump beam is modulated at 1 kHz by a mechanical chopper. The detection sensitivity is on the order of 10^{4}–10^{5}, with an integration time of 2s. The fluence is ~5 μJcm^{−2} for different pump photon energies (i.e., well below the fluence threshold for the Mott transition measured for 1LTMDs^{38,39}). No pump fluence dependence of the buildup and the relaxation dynamics was observed in the pump fluence range between 1 and 20 μJcm^{−2} (see Supplementary Fig. 8). In all the experiments, pump and probe beams have parallel linear polarizations. No pumpprobe polarization dependence of the buildup dynamics was detected (see Supplementary Fig. 7).
Theory
To get insight into the static optical properties properties of 1LMoS_{2} on SiO_{2} substrate, we first solve the Wannier equation, obtaining a set of bound and continuum exciton wavefunctions φ_{λ,q} with energies ϵ_{λ}, cf. Supplementary Note 8. This allows to work in a convenient excitonic basis including coherent exciton polarizations P_{λ}, biexcitons and exciton–exciton scattering states B_{η}, as well as incoherent exciton populations \({N}_{{\lambda }_{1},{\lambda }_{2},q}\). The optical response is determined by the TMD Bloch equations for the exciton amplitude P_{λ} where λ as a compound index includes the exciton state with bound and continuum excitonic states and the valley and spins of involved electrons and holes^{31,40}:
The lefthand side of Eq. (2) describes the oscillation of the exciton transition damped by a dephasing rate \({\gamma }_{{\lambda }_{1}}\)^{41,42,43}. The first term on the righthand side represents the optical pump generating excitons with zero centerofmass motion at the corners of the hexagonal Brillouin zone with σ_{+} (ξ = K) or σ_{−} (ξ = K\(^{\prime}\)) circularly polarized light. Here, \({d}_{{\lambda }_{1}}\) is the optical transition matrix element and \({{\mathcal{E}}}_{{\sigma }_{\pm }}(t)\) the light field at the position of the monolayer. The latter is obtained by solving Maxwell’s wave equation, which determines the reflected light^{44,45}. The next contribution characterizes Pauli blocking by coherent excitons (~∣P∣^{2}) and incoherent densities (~N). The third term on the righthand side of Eq. (2) characterizes nonlinear exciton–exciton interactions on a Hartree–Fock level (~P∣P∣^{2}), which couples bound and continuum excitonic states. Finally, the last line of Eq. (2) describes the coupling of excitons to biexcitons B_{η=b}, and twoexciton scattering continua B_{η≠b}^{46}. Here, the index η serves as a compound index and includes the highsymmetry points and spins of the two electrons and two holes. All matrix elements are defined in ref. ^{18}.
In order to decrease the complexity of the problem for the description of the experiment, the excitonic occupations (N) are treated with effective occupation numbers λ_{2}, which average over the details of the complex momentum distribution of incoherent exciton occupations: \({\sum }_{{\lambda }_{2},{\lambda }_{3},q}{\hat{d}}_{{\lambda }_{1},{\lambda }_{2},{\lambda }_{3},q}\,{N}_{{\lambda }_{2},{\lambda }_{3},q}\approx {\sum }_{{\lambda }_{2}}{\tilde{d}}_{{\lambda }_{1},{\lambda }_{2}}\,{N}_{{\lambda }_{2}}\) with \({\tilde{d}}_{{\lambda }_{1},{\lambda }_{2}}={\hat{d}}_{{\lambda }_{1},{\lambda }_{2},{\lambda }_{2},0}/2\). However, the bleaching cross sections are explicitly evaluated as a function of the exciton state number λ_{1/2}. These cross sections exhibit a drastic decrease with increasing state number. The equations of motion of the exciton densities are given by:
Equations (3) and (4) describe the dynamics of the incoherent exciton densities associated with the energetically lowest A_{1s}/B_{1s} states \({N}_{{{\rm{A}}}_{{\rm{1s}}}/{{\rm{B}}}_{{\rm{1s}}}}\) and higher states N_{λ}, respectively. Γ_{decay} = 1 meV/ℏ characterizes the relaxation of the incoherent exciton densities into the ground state. Its value is adjusted to the experimental results. The first contributions to the righthand sides of Eqs. (3) and (4) represent the formation of incoherent exciton densities out of optically excited coherent excitations by exciton–phonon scattering^{47}. The terms proportional to Γ_{λ+1→λ} characterize the phononmediated relaxation from energetically higher densities with effective rates \({\Gamma }_{\lambda +1\to \lambda }=\frac{1\ {\rm{eV}}}{50\ {\rm{fs}}}\frac{1}{{\epsilon }_{\lambda +1}{\epsilon }_{\lambda }}\) adapted to density functional theory calculations^{48,49}. The solution of the Schrdinger equation for two electrons and two holes accesses biexcitons as well as exciton–exciton scattering continua^{18,50,51}. The Heisenberg equation of motion for bound biexcitons as well as continuous exciton–exciton scattering states B_{η} characterize damped (\({\gamma }_{{\lambda }_{1}}+{\gamma }_{{\lambda }_{2}}\)) oscillations (energy ϵ_{xx,η}), which are driven by two excitons \({P}_{{\lambda }_{1}}{P}_{{\lambda }_{2}}\) mediated by Coulomb interactions (\({\hat{W}}_{\eta ,{\lambda }_{1},{\lambda }_{2}}\)):
Solving the set of equations of motion, Eqs. (2)–(5), together with Maxwell’s wave equation^{44,45} gives access to the differential reflection signal. Our simulations include coherent exciton binding energy renormalizations and other manybody effects related to the transient variation of the Coulomb screening due to optically excited A_{1s} and B_{1s} excitons. For the incoherent contributions we restricted our model to the Pauli blocking effect of reduced complexity whereas incoherent Coulomb renormalizations in the TMD Bloch equations, originating from incoherent exciton populations, which are formed on a similar timescale were neglected. The agreement between the calculated and measured dynamics suggests that the outofequilibrium optical response of 1LMoS_{2} on a sub100 fs timescale is well captured by the incoherent dynamics to phasespace filling.
Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
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Acknowledgements
We thank Dominik Christiansen for many stimulating discussions. We gratefully acknowledge funding from the Deutsche Forschungsgemeinschaft via the Projects No. 420760124 (KN 427/111, F.K., A.K.) as well as No. 182087777SFB 951 (B12, M.S., A.K.). We also acknowledge support of the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 734690 (SONAR, A.K. and F.S.). This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie SkodowskaCurie (grant agreement no. 734690) and from the European Research Council (ERC, grant agreement no. 816313 F.S. and no. 850875 I.K.). G.C. and S.D.C. acknowledge support by the European Union Horizon 2020 Programme under Grant Agreement No. 881603 Graphene Core 3. S.D.C. and C.T. acknowledge financial support from MIUR through the PRIN 2017 Programme (Prot. 20172H2SC4). P.J.S. and K.Y. acknowledge support from Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DESC0019443. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DEAC0205CH11231. This research was supported in part by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DEAC0205CH11231, within the van der Waals Heterostructures Program (KCWF16), which provided for sample growth, and under the sp2bonded Materials Program (KC2207), which provided for SEM sample characterization (A.Z. and A.Y.). Support was also provided by the U.S. National Science Foundation under Grant No. DMR1807233 which provided for additional TEM sample characterization (A.Z. and A.Y.).
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N.J.B., S.D.C., G.C., and P.J.S. conceived the experiment. C.T. and S.D.C. designed the experiment and performed the measurements. R.B.V., I.K., and F.S. contributed to the experimental work. F.K., M.S., and A.K. performed the theoretical calculations. K.Y., A.Y., and A.Z. prepared and characterized the sample. All the authors wrote the manuscript.
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Trovatello, C., Katsch, F., Borys, N.J. et al. The ultrafast onset of exciton formation in 2D semiconductors. Nat Commun 11, 5277 (2020). https://doi.org/10.1038/s41467020188355
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DOI: https://doi.org/10.1038/s41467020188355
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