Ultrafast dynamics of bright and dark excitons in monolayer WSe₂ and heterobilayer WSe₂/MoS₂

In order to establish the most direct experimental comparison of the exciton energy landscape of the WSe₂ monolayer and the twisted WSe₂/MoS₂ heterobilayer, we fabricate a single sample that contains distinct areas in which the monolayer WSe₂ flake and the WSe₂/MoS₂ heterostructure are found (figure 1(a)). We have chosen a doped silicon wafer with a native oxide layer as the substrate for the heterostructure, because it ensures high quality trARPES data that is not affected by sample charging (figure 1(b)). Moreover, the TMD flakes are stacked on 20–30 nm hexagonal boron nitride [66] for best interface quality [67]. Before the trARPES experiments, the sample is annealed for 1 h to 670 K. In the real-space-resolved photoemission electron microscopy image in figure 1(a), the boundaries of the WSe₂ and MoS₂ monolayers are traced by orange and dark red (dashed) polygons, respectively. The twist-angle of the heterostructure is quantified to 9.8 ± 0.8^∘ [46].

Time-resolved photoemission spectroscopy of exfoliated mono- and heterobilayers becomes possible by using our setup for femtosecond momentum microscopy (see [25, 68, 69]). We resonantly excite the bright A1s exciton of WSe₂ with 1.7 eV 40 fs light pulses (s-polarized). Photoemission from the occupied band structure and the excitons is induced with time-delayed 26.5 eV 20 fs light pulses (p-polarized) that are created in a table-top 500 kHz repetition rate high-harmonic generation beamline [25, 70, 71]. For each delay between the pump and the probe laser pulse, the ToF-MM (Surface Concept GmbH) collects three-dimensional data cubes that contain information on the two in-plane momenta k_x and k_y and the energy E of the detected photoelectrons [25, 42]. Notably, by inserting an aperture into the real-space plane of the microscope, the experiment is sensitive to the exciton dynamics in a sample region with a diameter of 10 µm (orange and red circles in figure 1(a)) [43–46].

The momentum microscopy experiment can be used to directly characterize and compare the occupied band structure of monolayer WSe₂ and heterobilayer WSe₂/MoS₂ (figure 2). In both sample areas, the spin-split valence bands at the WSe₂ $K_\textrm{W}$ valley can be identified (labelled (1) and (2) in the magenta energy-distribution-curves (EDCs)). For the characterization of the inhomogeneity of the heterostructure, we analyse the linewidth of the top WSe₂ valence band at the $K_\textrm{W}$ valley, and find a full width at half maximum of ≈280 meV (figure 2(b)). The linewidth is composed of the spectral width of the probe laser pulse (≈200 meV) and inhomogeneous broadening of about ≈200 meV due to imperfections and inhomogeneities within the probed sample area (≈100$\mu m^2$) [46, 72]. In the heterobilayer, in addition, the MoS₂ valence band is observed at $E-E_\textrm{VBM} = 0.94\pm0.05$ eV (labelled (3) in figure 2(b)). While the dispersion of the WSe₂ valence bands are similar at the $K_\textrm{W}$ valleys of the mono- and the heterobilayer, it is strikingly different at the Γ valley: In the monolayer, only a single band at the Γ valley is observed (horizontal arrow, figure 2(a)). In contrast, in the heterobilayer, we find two energetically separated bands that are a clear indication for interlayer hybridization (two horizontal arrows in figure 2(b)) [73–75].

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Having identified these distinct spectroscopic signatures of the electronic band structure that allow the direct discrimination of the mono- and the heterobilayer region in the trARPES experiment, in the next step, we probe the energetics of the optical excitations of the WSe₂ monolayer. Therefore, optical pump pulses with a centre energy of 1.7 eV are used in order to be resonant to the WSe₂ A1s exciton (fluence: 280 µJ cm², exciton density: 5.4$\times 10^{12}$ excitons cm²). We find spectral weight above the valence bands that we attribute to photoelectrons being emitted from excitons (figure 2(a)). Specifically, at a pump-probe delay of 1 ps, photoemission yield is detected at the $K_\textrm{W}$ and the $\Sigma_\textrm{W}$ valleys of the WSe₂ Brillouin zone (orange and grey hexagon in figure 3(a), respectively). These spectral signatures can be attributed to photoemission from intralayer K and Σ excitons, consistent with earlier reports [43, 44].

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When applying similar excitation conditions to the WSe₂/MoS₂ heterobilayer region, much richer spectral signatures are detected in the momentum microscopy experiment: A complex distribution of photoemission intensity is detected above the WSe₂ valence bands in an energy window ranging from 0.9 eV to 1.9 eV (figure 2(b), 1 ps pump-probe delay). The momentum-map centred at an energy of 1.7 eV above the WSe₂ VBM shows spectral weight at the momenta of the $K_\textrm{W}$ and the $\Sigma_\textrm{W}$ valleys that we attribute to photoemission signal from intralayer K and hybrid $h\Sigma$ excitons (figure 3(b), orange and grey hexagon, respectively). At a lower energy (figure 3(c), $E-E_\textrm{VBM}\approx1.1$ eV), we find a complex momentum structure of the photoemission intensity that can be attributed to ILX: Spectral weight is detected at the $K_\textrm{Mo}$ valley and the additional κ valleys that are described within the moiré mini Brillouin zone (mBz, red hexagon). This hallmark of the moiré superlattice imprinted onto the exciton photoemission signature from the interlayer ILX excitons is discussed in detail in [46].

Having identified the major photoemission spectral signatures of excitons, we aim to experimentally quantify the energy landscape of bright and dark excitons in the mono- and the heterobilayer sample. For this, first, we have to discuss at which energy the photoemission experiment detects single-particle photoelectrons that have initially been bound in the correlated exciton state. In the process of photoemission from an exciton, the Coulomb correlation between the exciton's electron and hole is broken at the cost of the exciton binding energy. As described by Weinelt et al [76] and others [35, 47, 77–84], the single-particle photoelectron from an exciton will be detected one exciton energy $E_{\mathrm{exc}}^{i}$ above the energy of the single-particle band where the former hole contribution to the exciton remains in the sample, i.e. at

$\begin{align} E_{\mathrm{elec}} = E_{\mathrm{hole}}+E^i_{\mathrm{exc}}+\hbar\omega \end{align} \tag{ 1 }$

with $E_\textrm{hole}$ and $E_\textrm{elec}$ as the single-particle energy of the hole- and the electron-state, respectively; furthermore with $E^i_{\mathrm{exc}}$ as the exciton energy and $\hbar\omega$ as the probe photon energy. Importantly, equation (1) sets the energy of the WSe₂ VBM at the $K_\textrm{W}$ valley as the natural reference point of the present experiment, because the single-particle hole of all probed excitons remains in this valley once photoemission has occurred (see figures 2(c) and (d)).

Hence, we can quantify the exciton energy $E_{\mathrm{exc}}^i$ of all contributing intralayer, hybrid and interlayer excitons by analysing the EDCs taken at the $K_\textrm{W}$, the $\Sigma_\textrm{W}$ and the $K_\textrm{Mo}$ (κ) valleys (figure 2). Following equation (1), we then calculate the energy difference between each exciton photoemission signal and the energy of the $K_\textrm{W}$ valley VBM. All exciton energies $E_{\mathrm{exc}}^i$ quantified for the WSe₂ mono- and the WSe₂/MoS₂ heterobilayer are summarized in table 1. In addition, previous experimentally determined exciton energies extracted by photoluminescence (PL) [62] and trARPES [43, 65] are summarized in table 1, and show an excellent agreement with our analysis.

Having experimentally measured the exciton energies $E_{\mathrm{exc}}^i$, we are now in the position to systematically compare those values. First, we find that, within the experimental error, the intralayer K exciton energy is comparable in the mono- and the heterobilayer region (1.67 ± 0.05 eV vs. 1.66 ± 0.05 eV). For WSe₂/MoS₂, this result strongly supports the expectation that excitons, where the electron- and hole-component are localized in the $K_\textrm{W}$ valleys, are not affected by interlayer hybridization [48, 51, 60]. In contrast, we find that the hybrid character of the $h\Sigma$ excitons indeed leads to a renormalization of the exciton energy: The interlayer hybridization leads to a reduction of the exciton energy from 1.60 ± 0.05 eV (Σ exciton, monolayer WSe₂) to 1.46 ± 0.05 eV ($h\Sigma$ exciton, heterobilayer WSe₂/MoS₂). This observation is a direct experimental verification of seminal photoluminescence experiments that reported a changed emission energy for hybrid excitons, if the degree of hybridization is controlled, e.g. by the twist angle [51, 85–87]. Moreover, it fully confirms the calculated energy landscape of excitons that predicts a reduction of the energy of the hybrid $h\Sigma$ exciton of the WSe₂/MoS₂ heterobilayer in comparison to the intralayer Σ exciton of the WSe₂ monolayer (table 1).

The femtosecond momentum microscopy experiment provides direct access to the ultrafast dynamics of bright and dark excitons. The symbols in the main panels of figure 4 show the pump-probe delay-dependent photoemission yield from the intralayer K (orange), intralayer Σ (grey), hybrid $h\Sigma$ (grey) and ILX (red) excitons. In addition, the femtosecond evolution of exciton occupation as calculated in our microscopic model is plotted as solid lines of the respective colour.

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In the WSe₂ monolayer (figure 4(a)), photoemission yield from the K exciton peaks at pump-probe delays close to 40 fs. Delayed to this process, we find that spectral weight from momentum-indirect Σ excitons (grey) increases on a 100 fs timescale. This rise of the photoemission yield from the intralayer Σ excitons is in agreement with momentum microscopy experiments by Madéo et al [43] and Wallauer et al [44]. Moreover, the rise time is also in agreement with our microscopic calculations that include exciton-light and exciton-phonon interaction. From the model, we therefore identify exciton-phonon scattering as the dominant mechanism for the formation of intralayer Σ excitons. Note that for pump-probe delays >100 fs, the exciton occupation calculated in the model overestimates the experimentally measured photoemisison intensity from both excitons. The reason for this deviation is that the model does not include decay processes and thus overestimates the exciton occupation for longer pump-probe delays.

The pump-probe delay-dependent photoemission yield from excitons measured in the WSe₂/MoS₂ heterobilayer is shown in figure 4(b). We find a direct hierarchy in the onset of rising photoemission yield from the three types of excitons, i.e.the K excitons (orange), the hybrid $h\Sigma$ excitons (grey), and the ILX (red). Again, the dynamics is in excellent agreement with our microscopic calculations, such that we can identify exciton-phonon scattering as the dominant mechanism for the formation of hybrid $h\Sigma$ excitons.

So far, we have found that the intervalley relaxation processes in monolayer WSe₂ and heterobilayer WSe₂/MoS₂ are phonon-mediated and lead to the formation of intralayer Σ and hybrid $h\Sigma$ excitons, respectively. However, even though the intervalley relaxation proceeds via the same mechanism, we find distinctly different decay dynamics of the contributing intralayer and hybrid excitons on the sub-ps timescale (figure 5 and table 2). In the following, we pinpoint the origin of the different dynamics to the relative energy alignment of the intralayer Σ and hybrid $h\Sigma$ excitons with respect to the intralayer K excitons, which has direct impact on the efficiency of exciton-phonon scattering processes.

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Table 2. Summary of the experimentally quantified rise and decay times of photoemission yield from excitons.

	Monolayer WSe2	Heterobilayer WSe2/MoS2
$\tau_\textrm{fast}^{\mathrm{K}}$ (fs)	70 ± 10	28 ± 2
$\tau_\textrm{slow}^{\mathrm{K}}$ (fs)	1500 ± 200	1900 ± 800
$\tau_{\textrm{WSe}_2}^{\Sigma}$ (fs)	1050 ± 60	—
$\tau_{\textrm{WSe}_2/\textrm{MoS}_2, \textrm{fast}}^{\textrm{h}\Sigma}$ (fs)	—	110 ± 40
$\tau_{\textrm{WSe}_2/\textrm{MoS}_2, \textrm{slow}}^{\textrm{h}\Sigma}$ (fs)	—	1600 ± 800
$\tau_\textrm{rise}^{\Sigma}$ (fs)	36 ± 3	—
$\tau_\textrm{rise}^{\textrm{h}\Sigma}$ (fs)	—	34 ± 3
$\tau_\textrm{rise}^{\textrm{ILX}}$ (fs)	—	120 ± 20

In monolayer WSe₂, the energy difference between the optically excited K and the intralayer Σ exciton is $\Delta E_{\mathrm{exc}}^{\textrm{WSe}_2} = E_{\mathrm{exc}}^{\mathrm{K}}-E_{\mathrm{exc}}^{\Sigma} = 0.07\pm0.10$ eV. Hence, phonon emission and absorption processes with typical energies of 0.03 eV [88] can efficiently create a steady state between both excitonic species, i.e. $K\rightleftharpoons\Sigma$, where the relative exciton occupation is given by degenerate Bose–Einstein distributions [21]. In order to identify this steady state in the photoemission data, we plot the sub-ps pump-probe delay-dependent photoemission intensity from K and Σ excitons on a logarithmic intensity axis in figures 5(a) and (b), respectively. As indicated by the yellow, green and blue marked areas, the sub-ps dynamics of K excitons can be divided into overall three characteristic timescales. On the sub-40-fs timescale (yellow, figure 5(a)), photoemission yield from K excitons increases due to the optical excitation. For increasing pump-probe delay, the decaying photoemission intensity can be approximated by a bi-exponential function. Here, the two decay times $\tau_{\textrm{WSe}_2, \textrm{fast}}^{\mathrm{K}} = 70\pm10$ fs and $\tau_{\textrm{WSe}_2, \textrm{slow}}^{\mathrm{K}} = 1.5\pm0.2$ ps describe the fast and the slow component of the dynamics that are dominant in the green and blue delay-regions, respectively. In direct comparison to time-resolved all-optical spectroscopies, the slow component $\tau_{\textrm{WSe}_2, \textrm{slow}}^{\mathrm{K}}$ can be attributed to radiative recombination processes of the bright excitons [50, 63, 89]. However, the interpretation of the fast time constant $\tau_{\textrm{WSe}_2, \textrm{fast}}^{\mathrm{K}}$ is more complex (green): First, it contains information on the decay of the coherent exciton polarization towards the incoherent K exciton population [44, 90], which is not the focus of our study. Second, and more importantly, $\tau_{\textrm{WSe}_2, \textrm{fast}}^{\mathrm{K}}$ is dominant in the delay-window that is necessary to establish a steady state between phonon absorption and emission events transferring K into Σ excitons and vice versa. In agreement with this assignment, we find that photoemission intensity from momentum-indirect Σ excitons, which are formed due to the decay of K excitons, rises on the same timescale and peaks at 100 fs (yellow and green delay-region in figure 5(b)). For longer delays (blue delay-region), the Σ exciton photoemission intensity decays and is described by a single-exponential fit with a decay time of $\tau_{\textrm{WSe}_2}^{\Sigma} = 1.1\pm0.1$ ps. Notably, it has already been suggested that the decay of momentum-indirect Σ excitons dominantly proceeds via phonon absorption processes that first transfer the Σ excitons into bright K excitons that can, subsequently, decay in a radiative process [15, 21, 91]. Our analysis verifies this proposition, because the experimentally quantified decay time $\tau_{\textrm{WSe}_2}^{\Sigma}$ of dark Σ excitons is in reasonable agreement with the radiative decay time $\tau_{\textrm{WSe}_2, \textrm{fast}}^{\mathrm{K}}$ of K excitons (cf table 2).

The situation is significantly different for the WSe₂/MoS₂ heterobilayer. The hybrid character of the $h\Sigma$ exciton leads to a reduction of its exciton energy and thus to an energy difference of $\Delta E_{\mathrm{exc}}^{\textrm{WSe}_2/\textrm{MoS}_2} = E_{\mathrm{exc}}^{\mathrm{K}}-E_{\mathrm{exc}}^{\textrm{h}\Sigma} = 0.20\pm0.10$ eV with respect to the intralayer K exciton. Hence, accompanied by the emission of a phonon, optically excited K excitons can effectively be transferred to hybrid $h\Sigma$ excitons. However, the large energy difference $\Delta E_{\mathrm{exc}}^{\textrm{WSe}_2/\textrm{MoS}_2}$ strongly suppresses backscattering events for which multiple phonon absorption processes would be required. The suppression of the backscattering channel in the heterobilayer in comparison to the monolayer is most evident by the much stronger reduction of photoemission intensity from K exctions to below 10% after only 100 fs (green delay-region in figure 5(a)). Photoemission intensity from hybrid $h\Sigma$ excitons, on the other side, rises on the same timescale, which is in agreement with the interpretation of an initially fast transfer of excitons from K to $h\Sigma$ excitons (yellow and green delay-regions in figure 5(b)).

Once the hybrid $h\Sigma$ excitons are formed, they can relax to the ILX by subsequent exciton-phonon scattering processes within the MoS₂ layer. For the analysis of this process, we fit the picosecond evolution of photoemission intensity from hybrid $h\Sigma$ excitons with a biexponential function (figure 5(b)) and extract a fast $h\Sigma\rightarrow$ILX decay time of $\tau_{\textrm{WSe}_2/\textrm{MoS}_2, \textrm{fast}}^{\textrm{h}\Sigma} = 110\pm40$ fs. Notably, this decay time is in excellent agreement with the rise time of photoemission intensity from ILX (figure 5(b), $\tau_{\textrm{WSe}_2/\textrm{MoS}_2, \textrm{rise}}^{\textrm{ILX}} = 120\pm 20$ fs, red data points), being thus a strong indication that ILX excitons are directly formed from hybrid $h\Sigma$ excitons. Again, because of the large energy difference between the hybrid $h\Sigma$ exciton and the ILX, i.e. $\Delta E_{\mathrm{exc}}^{\textrm{ILX}} = E_{\mathrm{exc}}^{\textrm{h}\Sigma}-E_{\mathrm{exc}}^{\textrm{ILX}} = 0.26\pm0.10$ eV (cf table 1), phonon absorption processes are nearly fully suppressed and backscattering events from ILX to hybrid $h\Sigma$ excitons can also be excluded.

Finally, we note that our experimental observation on the efficiency of forward and backward scattering in the WSe₂ monolayer and the WSe₂/MoS₂ heterobilayer are fully consistent with our microscopic model. Specifically, for the WSe₂ monolayer, the calculations reproduce the establishment of a steady state $K\rightleftharpoons\Sigma$ (blue arrows in figure 1(e)). Notably, the model here finds that especially the momentum-indirect excitons, where the hole- and the electron-component are momentum-offset in the $K_\textrm{W}$ and $K^{\prime}_\textrm{W}$ valleys, contribute to the establishment of the steady state, as detailed, e.g. in [15, 21]. In addition, for the WSe₂/MoS₂ heterobilayer, the microscopic model reproduces the negligible efficiency for backscattering as compared to the forward scattering leading to the formation of ILX (blue arrows in figure 1(f)).