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Hansol Kim, Gyusu Lee, Jinjae Kim, Jiwon Park, Andrew S. Kim, Jongyun Choi, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Moon-Ho Jo, Hyunyong Choi

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[Exciton dynamics in marginally twisted <math>  <mrow>    <mi>WS</mi>    <msub>      <mi>e</mi>      <mn>2</mn>    </msub>  </mrow></math> homobilayer: Role of interlayer coupling, phonons,&nbsp;and intervalley scattering](https://mdr.nims.go.jp/datasets/b98cc1f8-4f16-46df-9a7d-b114ded9159a)

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Exciton dynamics in marginally twisted WSe2 homobilayer: role of interlayer coupling, phonons, and intervalley scatteringHansol Kim1,2, Gyusu Lee1, Jinjae Kim1,3, Jiwon Park1,3, Andrew S. Kim1,2,3, Jongyun Choi4,5, Kenji Watanabe6, Takashi Taniguchi6, Moon-Ho Jo4,5 and Hyunyong Choi1,3,*1Department of Physics, Seoul National University, Seoul 08826, Korea2Research Institute of Basic Sciences, Seoul National University, Seoul 08826, Korea3Institute of Applied Physics, Seoul National University, Seoul 08826, Korea4Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 37673, Korea5Center for Van der Waals Quantum Solids, Institute for Basic Science (IBS), Pohang 37673, Korea6Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan*Corresponding author: hy.choi@snu.ac.krAbstract In moiré materials, excitons serve as optical probes because of the sensitivity to both valley-dependent electronic structure and many-body excitonic interactions. For angle-tuned twisted bilayers, lattice reconstruction becomes significant at marginal twist angles, raising interesting questions about the optical characteristics of excitons both in the steady-state and nonequilibrium regimes. In this work, we investigate both the steady-state and the ultrafast transient exciton behaviors in a twisted WSe2​ homobilayer (t-WSe2) using reflection contrast (RC), polarization-resolved photoluminescence (PL), and ultrafast pump–probe spectroscopy. We report the emergence of two distinct intralayer excitons in the lattice reconstructed t-WSe2, which are used to probe local electronic asymmetries and interlayer coupling in moiré domains. These excitons possess distinct temperature- and doping-dependent valley coherence and population dynamics, arising from the asymmetric interlayer coupling. Theoretical modeling via Lindblad master equation highlights that the pure-dephasing rate increases with hole doping, attributed to the enhanced electron-hole interactions. Ultrafast degenerate pump-probe spectroscopy reveals distinct fast decaying dynamics (<1 picosecond, ps) for the two intralayer excitonic absorption species,  and , where the asymmetric interlayer coupling contributes more to the faster  decay than . Optical-pump and white-light probe spectroscopy further unveils a biexponential decay, where the fast component () signifies rapid radiative recombination with repopulation effects in the optical light cone. The slow component () is linked to exciton-phonon scattering and population relaxation via interlayer breathing phonons. We also present that intervalley scattering pathways, i.e. mediated by the  transitions, are distinct from the monolayer counterpart. This work provides detailed insights into the exciton population dynamics in twisted homobilayers, highlighting the role of intervalley and exciton-phonon interactions in the transient multiple exciton complex behaviors.I. IntroductionTransitional metal dichalcogenide (TMD) monolayers have garnered significant attention due to their strong light-matter interaction. [1,2] The reduced screening of Coulomb interactions, resulting from the two-dimensional confinement, leads to the strong light-matter interaction, larger exciton binding energies up to few hundred meV compared to the quasi-two-dimensional systems such as III-V quantum wells. WSe2 is an exemplary member of the TMD materials, which is composed of covalently bonded one W and two Se atoms forming two-dimensional sheets that are coupled by van der Waals forces. In the bulk form, WSe2 is an indirect bandgap semiconductor, while monolayer features a direct gap with bright exciton composed of electrons and holes possessing equivalent spins at  and  point of the Brillouin zone. [3] Spin-orbit coupling leads to a splitting of conduction and valence bands such that the lowest-lying exciton transition is the spin-dark state in W-based TMD materials. [4,5] Recent advances in fabrication of various ultrathin layered materials enabled the exploration of the twisted bilayer system, i.e. vertically stacked TMDs on top of each monolayer with a small twist angle or lattice mismatch. These materials host various emergent phenomena including correlated fermionic and bosonic phases [6–8], fractional quantum anomalous Hall effect [9–11], generalized Wigner crystals [12–14] and exciton condensates [15–17], to name a few. Furthermore, superconducting phases in twisted WSe2 homobilayer (t-WSe2) have been experimentally observed [18,19], where the moiré periodicity—tunable via the twist angle—enables unprecedented control over electrical band and topology. For the case of t-WSe2, it has been established that the emergent multiple excitonic responses are sensitive to the twist angle and layer stacking order, in which the lattice reconstruction further complicates in identifying the role of multiple excitons, as revealed in the recent discrepancies between theoretical predictions and experimental observations. [20,21] In marginally twisted t-WSe2, for instance, two nondegenerate A excitons with distinct valley coherence properties have been observed experimentally. [21] While some theoretical studies combined with optical experiments predict the stacking-order dependent optical properties in bilayer WSe2, [22–24] other works when considered reconstruction effects in rhombohedral-stacked t-WSe2 suggest the emergence of only a single A exciton. [20] This suggests that more investigations are necessary in understanding of how the reconstruction influences the optical spectra from both theoretical and experimental perspectives. For the photoexcited transient behaviors of excitons, the relaxation dynamics are accompanied by various dephasing phenomena with different timescales. Prior studies have demonstrated long exciton optical coherence times , suggesting TMDs hold promise for quantum information science application. [25,26] In particular, the coherent exciton dephasing time  and population lifetime  are influenced by various incoherent effects in the conventional pump-probe measurements. These include exciton thermalization, intra- /intervalley scattering, exciton-exciton annihilation, and phonon bottleneck effects [27]. These processes contribute to the ultrafast dynamics on the order of , which is also on the order of the population lifetime of excitons. Beyond these fast dynamics, exciton dynamics also exhibit longer timescales; exciton transport and diffusion occur over tens to hundreds of picoseconds, influenced by phonon-assisted indirect recombination or by exciton-exciton interactions. While there exist experimental studies on optical properties of monolayer TMDs, no corresponding time-resolved dynamics have been reported in the reconstructed t-WSe2. Given the fact that the lattice reconstruction significantly influences the optical responses of excitons, understanding their nonequilibrium dynamics may provide further insights into the exciton coherence, interlayer coupling, and emergent correlated phenomena in these twisted TMD systems. In this aspect, conventional methods such as time-resolved photoluminescence (PL) and pump-probe spectroscopy face temporal resolution limits  and , respectively), complicating the measurements of ultrafast radiative decay dynamics (~100s of fs)  [28], [29]. Furthermore, electrostatic doping introduces charged excitons (or polarons), where the gate-dependent PL shows the suppressed degree of linear polarization (DOLP) in charged excitons indicating the loss of valley coherence due to electron-hole exchange interaction. [30] These interactions enhance the pure-dephasing rate , posing a challenge in maintaining the valley coherence. While polarization-resolved PL captures the intervalley scattering pathways, it often fails to quantify the dephasing rates, necessitating complex techniques, such as resonant four-wave mixing (FWM) [26,31–33], to investigate the exciton valley coherence. [31,34] To address the above issues, we develop a theoretical framework based on the Lindblad master equation to interpret the polarization-resolved PL and extract  and  using the transfer matrix method (TMM). In this approach, we incorporate radiative decay, nonradiative decay, intervalley scattering, and a correction for pure dephasing. The developed theories are applied to understand the degree of linear and circular polarization of excitons. Then we incorporate the inhomogeneous broadening to ensure the homogeneous linewidth for steady-state optical linewidth analysis. While the FWM spectroscopy serves as a direct probe of excitonic coherence in deriving the homogeneous linewidth, we show that the RC measurement offers a complementary approach by enabling a broader range of steady-state optical measurement conditions. We have also investigated the optical responses of the hBN- encapsuled monolayer WSe2, allowing the RC measurements to reach the homogeneous linewidth limit, from which we are able to extract the  and  times. [35,36] Although the steady-state linewidth analysis provides access to  and , ultrafast pump-probe spectroscopy remains an essential tool for observing the population dynamics. Therefore, we systematically compare steady-state linewidth analysis with the time-resolved transients to establish a comprehensive understanding of exciton-population decaying mechanisms.In our experiments we employ RC, polarization-resolved PL and pump-probe differential reflectivity to investigate exciton dynamics in near-zero-angle t-WSe2 (twist angle of ). By fabricating a rhombohedral-stacked structure, we confirm the emergence of two distinct intralayer exciton species. The doping density is controlled by applying a back gate () structure. Through the -dependent RC and polarization-resolved PL measurements, we determine the band alignment of t-WSe2 and elucidate the origin of these excitonic species. Using degenerate pump-probe spectroscopy, we directly confirm the impact of asymmetric interlayer coupling on the early exciton dynamics. The interlayer coupling enhances the decay of excitons localized in the top layer, while it weakens the decay of excitons localized in the bottom layer for the BA stacking configuration. In addition, by analyzing the temperature- and -dependent exciton dynamics in both RC and pump-probe spectroscopy, we disentangle radiative recombination from the other scattering processes. Our data show that the exciton recombination in t-WSe2 follows a biexponential decay, with a fast component governed by radiative recombination due to the intervalley  scattering within the excited optical light cone and a slow component coupled to the interlayer breathing phonon-assisted recombination.The rest of this paper is organized as follows. In Sec. II, we describe the theoretical model consisted of a Lindblad master equation for TMD materials. In the steady-state limit, we derive the analytical form for interpreting the degree of circular polarization (DOCP) and DOLP results. In Sec. III, we present the results for the steady-state optical spectroscopy of t-WSe2 as well as monolayer WSe2. The measured RC and polarization-resolved PL are compared to the theoretical analysis presented in Sec. II. Sec. IV is devoted to the time-resolved spectroscopy of t-WSe2 with varying the pump fluence, the pump excitation wavelength, the temperature, and the doping dependence. We compare the results from the steady-state spectroscopy and the nonequilibrium spectroscopy. Sec. V contains the concluding remarks and summary.II. TheoryA. Lindbladian quantum master equation To theoretically investigate the dynamical feature of excitons, we perform nonperturbative density matrix analysis on TMD monolayers using the Lindblad master equation. [37–39] Considering the minimal model Hamiltonian for the interaction within a photonic bath, we have considered a valley specific Jaynes-Cummings model. Excitons in two different valleys (so called  and  valley) forms an energy degenerate V-type three level atomic system, and are individually coupled to the helicity-resolved photon modes, i.e. right-circular polarized and left-circular polarized photon. [38–41] The Hamiltonian reads,The first term stands for the exciton Hamiltonian, where  is the excitonic resonance energy and  is the exciton annihilation (creation) operator of the  and  valley, which obey the bosonic commutation rule. The second term is the photon Hamiltonian, where  is the photon resonance energy and  is the photon annihilation (creation) operator coupled to  and  valley, which also obeys the bosonic commutation rule. The last term describes the exciton-photon coupling, where  is the exciton-photon coupling constant between the ground state and the  or  valley. H.c. is the Hermitian conjugate.We employ a quantum master equation to solve the steady-state solution of the standard time-dependent density matrix, where  is the Liouvilian superoperator. [38–43] This operator includes exciton recombination, pure-dephasing and intervalley scattering process. It also encompasses incoherent pumping, which considers both valley-selective excitation and simultaneous excitation of two separate valleys. [41,44] The Liouvillian is explicitly expressed as,where . In this formulation, the first term describes the exciton recombination with recombination decay rate . The second term accounts for the pure-dephasing with a pure-dephasing rate of , leading to decoherence without affecting the exciton population. The third term models the intervalley scattering between  and  valley with intervalley scattering rate . The final term represents the contributions from the incoherent pump, with  and  governing the valley-selective and the valley-independent pumping, respectively. We formulate the density matrix as a basis of three occupied states  as Fock-Liouville space and express the evolution of motion for the elements of density matrix, as a set of coupled differential equations. Then we obtain the following set of equations for the density matrix elements. where  is the detuning from the exciton resonance frequency. We assume , ,  and Rabi frequency for each transition is equivalent. Solving Eq. (4) in the steady-state regime () assuming a weak pump limit of , the degree of linear polarization (DOLP)  and degree of circular polarization (DOCP)  can be expressed as, Whereas Eq. (1) refers to only coherent interactions, valley pumping is an incoherent process. The pumping of incident photons with a certain helicity with the photon energy higher than the excitonic bandgap, the carriers are injected into the higher-energy states and then relax to the lower-energy excitonic states before recombining radiatively; a process occurs in the conventional PL spectroscopy. This enables both valley-selective pumping and valley-independent pumping of excitons. Thus, since Eq. (5) is derived under the assumption of weak pumping, we can extract the valley coherence and interpret it as a measurable quantity through DOLP. For more details for the derivation, see the Supplemental Material S1 [45]. Therefore, the PL spectroscopy involves a continuous supply of light that repeatedly pumps the material under investigation. For the pulsed experiments, such as FWM or ultrafast pump–probe spectroscopy, the sample is excited only once at . As a result, the pulsed experiments do not sustain a nonzero linear or circular polarization; instead, any initial polarization decays over a characteristic valley coherence or valley lifetime. B. Modified Transfer Matrix Method (TMM)Linear susceptibility  serves as a fundamental quantity linking the material’s microscopic excitonic response to the macroscopic optical observables, such as reflectance contrast in our case. Specifically, in the framework of macroscopic electrodynamics, the susceptibility determines the excitonic polarization, which acts as a secondary source of modifying the electromagnetic field through Maxwell equations. This polarization contributes to the scattered field via Green’s function, and appears in the reflected electric field. Consequently,  implicitly governs the RC spectra, enabling a link between quantum properties of excitons and measurable optical signals. can be expressed as a Lorentzian function by solving the Maxwell equations. Considering an exciton as an individual oscillator [60], it can be written in the formHere,  is the speed of light,  is the exciton resonance frequency,  is the thickness of the TMD layer, and  represent the radiative, nonradiative, and pure-dephasing rates, respectively.To calculate the RC spectra of the t-WSe2, we consider a dielectric stack consisted of the three following layers: a top hBN layer, t-WSe2, and a bottom hBN layer. Under normal incidence, the positive frequency part of the electric field operator at position  within Born-Markov approximation is given bywhere  is the reflection of the background,  is the incident field operator,  is the wavenumber at the exciton resonance, and  is the Green’s function that describes the electric field at position  due to the exciton located at . To describe the exciton dynamics for the linear spectroscopy, we extract the  and  from the density matrix formalism and consider the distinct  and  valley states—both of which share the same energy—into a single state. The equation of motion for the expectation values of the exciton operators in the Heisenberg picture reads,where  is the dipole moment of the exciton resonance, and the product  corresponds to the Rabi frequency associated with the optical transition between the  and  excitonic state and the ground state, which characterizes the light–matter coupling strength. [61] By solving the steady-state solutions of the Eqs. (9A) and (9B), the total reflectance, defined as , is obtained aswhere  is a shift of the exciton resonance due to the presence of the substrate,  is the modified radiative decay rate due to the substrate,  is the population decay rate, and  is the dephasing rate. Spectral interference between the excitons is neglected, as we consider steady-state solutions where phase coherence between distinct excitonic transition is lost, and the excitons behave as independent oscillators. The RC formula is defined aswhere is the reflectance of the substrate stack. This approach captures the interference between the substrate and the TMD layer, with the influence of the  playing a role in shaping excitonic linewidth. The analysis is performed within the linear response of susceptibility, assuming low excitation power where perturbative quantum electrodynamic approach remains valid.  [35,62]The presence of disorder in TMD materials influences their optical response, as evidenced in both the steady-state and nonequilibrium time-resolved spectroscopy. Analogous to well-studied semiconductor quantum wells, the disorder leads to spectral features such as inhomogeneous broadening of exciton resonances, mixed Lorentzian-Gaussian spectra [26,63], and modification of exciton radiative lifetime. [64] We consider that the inhomogeneous broadening of the exciton resonance frequency  is spectrally distributed by a Gaussian function [63], and where no phase coherence (i.e., no interference) between excitons is assumed among different ’s. In this case, the susceptibility becomes a convolution of a Lorentzian and Gaussian distributionwhereandHere,  represents the inhomogeneous broadening,  is the Gaussian distribution for the inhomogeneous broadening of exciton resonance,  is the Faddeeva function, and  denotes the complementary error function. Incorporating the effect of inhomogeneous broadening to the RC spectra modifies Eq. (11), yielding the following expressionwith the modified argument of the Faddeeva function to To compute the Green’s functions  and , we follow the standard transfer matrix method, [46,47] where  corresponds to the electric field amplitude at position  inside the multilayer stack. For detailed derivation of the Green’s functions, see Supplemental Material S2 [45]. As discussed in Sec. I, we have used Eq. (15) to fit the measured RC spectra using a global mean-square minimization, from which we extract the ratio between the homogeneous linewidth (Lorentzian component ) and the inhomogeneous linewidth (Gaussian component ), and thereby isolate the contribution of each decay rate. More detailed methods for the RC spectra fitting are provided in Supplemental Material S3 [45].From these extracted quantities, we can further evaluate the exciton dephasing time using the standard relation, (setting  for simplicity)  [32,35,65,66]This formalism allows us to quantify the homogeneous and inhomogeneous contributions to the excitonic linewidth. By performing the RC spectroscopy under varying temperature and gate voltage ​ (Sec. IV.A and IV.B), we can monitor the evolution of ​ and , thereby revealing signatures of exciton–phonon and exciton–electron coupling mechanisms.III. Experiment methodsSample fabrication. In our experiment, we have used the tear-and-stack method to fabricate a rhombohedral stacked t-WSe2 using mechanically exfoliated WSe2 monolayers (HQ graphene). The full device structure [Fig. 1 (a)] comprises the following layers: 10 nm hexagonal boron nitride (hBN) as a top encapsulation layer to suppress the inhomogeneous broadening, t-WSe2, few-layer-graphene (FLG) acting as an electric contact, and 15 nm hBN as a bottom dielectric spacer. The encapsulation of hBN enhances the excitonic optical responses by narrowing exciton linewidths, [55,56] which enables to reach the homogeneous linewidths at the cryogenic temperatures [69]. This device design enhances the signal-to-noise ratio in the pump-probe spectroscopy and minimizes potential artifacts caused by graphene-derived hot carriers. A twist angle  of t-WSe2 is confirmed via the polarization-resolved second harmonic generation spectroscopy [Fig. S1 [45]]. Further details of the device fabrication are provided in Supplemental Material S4 [45].Steady-state and ultrafast optical measurements. RC spectra were acquired using a broadband tungsten-halogen lamp, PL was measured with a 632.8 nm continuous-wave laser. The incident light was focused onto the sample by a 50× objective, and signals were dispersed by a spectrometer and detected using a charge-coupled device camera. Time-resolved reflectivity measurements were conducted using a 250 kHz Ti:Sapphire regenerative amplifier. The pump pulses, tunable from 1.65 eV to 2.3 eV, were generated by an optical parametric amplifier, and the broadband white-light probe pulses were generated by focusing the 50 fs, 1.55 eV pulses onto a 0.5 mm thick sapphire disk. The reflected probe beam was spectrally filtered by a monochromator, detected using an avalanche photodiode, and the recorded signals were measured by the phase-sensitive lock-in amplifier. Further details of the experimental setup and data extraction are available in Supplemental Materials S5 and S6 [45].IV. Results and DiscussionsA. Steady-state optical measurements1. Reflection contrast spectroscopyFirst, we have conducted the RC spectroscopy at a base temperature of 4 K to probe intralayer excitons of monolayer WSe2 and t-WSe2. Unlike monolayer WSe2, which exhibits a single intralayer A exciton peak (resonant at 1.745 eV), t-WSe2 has two distinct intralayer exciton peaks, denoted as  (resonant energy 1.685 eV) and , (resonant energy 1.702 eV) in the charge-neutral regime [Fig 1. (b)]. These peaks are separated by approximately 17 meV in the resonance energy, which is reported in prior study. [21] In Fig. 1 (c), we show the -dependent RC spectra in monolayer WSe2 (top panel), and t-WSe2 (bottom panel). For WSe2, the -dependent RC spectra exhibit the A exciton () at charge-neutral point () and the negative (positive) charged excitons  (), above (below)  of . [48,70] For the t-WSe2 RC measurements,  charged exciton () emerges in the hole-doped regime () with reduced intensity, while  remains its oscillator strength. In the electron-doped regime, both   and  charged excitons  or attractive polarons exhibit significant spectral shifts. This characteristic is observed in monolayer WSe2 as well as t-WSe2. In contrast to the single exciton peak in monolayer WSe2, the emergence of two non-degenerate A excitons in t-WSe2, is attributed to the structural reconstruction of the twisted bilayer; spatial distribution of AB/BA stacking order is formed, which is a well-known reconstruction pathway occurring due to the energetic lattice instability [Fig. 1 (d)].  [21,71–74] The lateral shift of the top layer disrupts the mirror symmetry of the parallel (AA-stacked) configuration, reducing the structural symmetry to . This displacement modifies the azimuthal quantum number of the electronic states at the high-symmetry  and  points, thereby altering the rotational symmetry. As a result, electronic states in the bottom layer acquire an additional Berry phase [75], leading to the asymmetric interlayer coupling. This asymmetry induces a level repulsion between the coupled bands—the valence band of the bottom layer and the conduction band of the top layer—analogous to observations in 3R-MoS2. [76] In addition, the direct band gap at  valley for the top and bottom layer is different due to the variations of the local chemical environment [Fig. 1 (e)]. In one case, the metal atom vertically overlaps with a chalcogen atom from the opposing layer; whereas in the other case, the chalcogen atom in the same layer as the metal lacks vertical overlap with a metal atom. This difference induces asymmetry of the local chemical environment, [22,71,77] which is clearly reflected in the RC spectra where distinct exciton peaks in t-WSe₂ arise due to this reconstruction with comparable linewidth for each exciton [Fig. 1 (b)]. The corresponding reconstructed domains are confirmed by performing piezoelectric force microscopy (PFM) measurements on an additional t-WSe2 without hBN encapsulation, where we have observed a modulation of PFM signal at a spatial period approximately 100 - 200 nm, as expected [Fig. S2 [45]]. The above structural picture also accounts for the doping-dependent RC spectra for the two excitons. With increasing the hole doping density, the oscillator strength of  is weakened but that of  is increased. This behavior is attributed to the interaction of excitons and excess charge carriers near the Fermi Sea (FS).  exciton is dressed by the FS hole and split into attractive polaron  and repulsive polaron . Upon further increasing the hole density (), the exciton-FS interaction becomes more significant, resulting in a redshift of  and a blueshift of . At a critical hole density (), the repulsive polaron branch transfers its oscillator strength to the attractive one, which is consistent with other TMD materials. [70,76] However, unlike such strong spectral reshaping of  with hole doping,  remains largely unchanged other than a little red shift of spectrum; this might be due to the weak screening of the other layer of . The above -dependent responses suggest that holes primarily populate , which aligns with the AB/BA domain structure in our case.Upon electron doping, the two exciton peaks are replaced by two emergent peaks exhibiting a red-shifted spectral feature with increasing . Such doping dependence is known to arise from the layer-hybridized  valley in t-WSe2. When electrons are doped in t-WSe2, the electrons are distributed almost equally within each layer. [78,79] As a result,  and  excitons are dressed by the electron-hole pairs in the  valley FS, and the spectra are split into the low-energy charged excitons (attractive polarons), and . For the high-energy spectral feature,  repulsive polaron  is expected to have similar energy as  (see the first-derivative RC spectra shown in Fig. S3 [45], which clearly identify the  and ). Also, in the electron-doped regime,  repulsive polaron  is spectrally shifted with decreased oscillator strength, similar to the case of MoSe2/hBN/MoSe2 structures. [80] 2. Polarization-resolved photoluminescence spectroscopyTo further corroborate our findings, we inspect the optical response of monolayer WSe2 and t-WSe2 using PL spectroscopy. Figure 2 (a) displays the measured PL for monolayer WSe2 (red solid) and t-WSe2 (black solid). For the monolayer WSe2, we observed several peaks around 1.67 eV including excitons (), trions , dark excitons  and their phonon replicas. These are further distinguished by performing the -dependent PL measurements [Fig. S4 [45]]. In contrast, t-WSe2 exhibits the momentum-indirect  interlayer exciton peaks () with a photon energy at around 1.5 eV, and the two intralayer excitons  are observed at around 1.65 – 1.68 eV. [21,78] To explore the difference of valley polarization between WSe2 and t-WSe2, we have conducted the -dependent helicity-resolved PL [Fig. S5 [45]]. The DOCP intensity for monolayer WSe2 exhibits no significant dependence of  [Fig. S5 (a) [45]]. Excitons, trions, dark excitons and phonon replicas all remain relatively high DOCP values across the whole doping range. Similarly, the t-WSe2 counterpart [Fig. S5 (b) [45]] shows that intralayer excitons also exhibit relatively high DOCP values throughout the doping range, which is consistent with prior study. [78] To investigate the valley coherence of the two excitons in t-WSe2, we performed -dependent linear polarization-resolved PL. Because linearly polarized light is a superposition of left-circularly and right-circularly polarized light, emitted photons can be considered as a superposition of  and  valley excitons. Here, the valley coherence is characterized by defining DOLP as , where  and  are parallel and perpendicular emission intensities. Figures 2 (b), and 2 (c) present the -dependent DOLP for monolayer WSe2 and t-WSe2 counterpart, respectively. For monolayer WSe2 [Fig. 2 (b)], the neutral exciton at charge neutrality exhibits significant DOLP (), indicating robust valley coherence. However, in both electron- and hole-doped regimes where the exciton peak corresponds to repulsive polarons, DOLP decreases substantially (). Furthermore, the charged excitons (trions , ) and associated phonon replicas display almost quenched DOLP . For t-WSe2 [Fig. 2 (c)], the behavior is markedly different. Both negatively charged excitons,  and  exhibit significant DOLP  in the electron-doped regime. In contrast, the DOLP intensity decreases for  under hole doping (). Upon further gating toward hole-doped regimes, the DOLP intensity remains finite  and does not show the abrupt suppression as seen for  (). Notably, in the neutral regime, both neutral excitons  and  exhibit low DOLP (). Such doping-dependent DOLP reflects differences in valley coherence among the various excitonic species. [21]The observed strong doping dependence of DOLP can be explained by the effect of pure-dephasing rates  of intralayer excitons [Fig. 2 (c)], where  serves as a significant source of coherence loss without contributing to the population decay. Within the Maialle-Silva-Sham framework, the electron-hole exchange interactions are responsible for setting . [32] In conventional analysis methods using TMM,  is typically neglected, because its contribution is negligible in the charge neutral regime. [31] Under finite doping, however, this assumption becomes inadequate. In our analysis, we have used a modified TMM that explicitly incorporates , allowing us to capture the effect in the doped case. [35,81] The examples of fitted RC spectra using the TMM analysis are presented in Fig. S6 [45].The extracted  from the RC spectrum as a function of  are shown in the bottom panel of Figs. 2 (b) and (c) for monolayer WSe2 and t-WSe2, respectively. In the case of monolayer WSe2,  increases in both electron- (), and hole-doped regime () where the exciton behaves as a repulsive polaron. This is well reflected in the DOLP value of the exciton. The charged exciton  exhibits an increased  with increasing electron density, whereas  exhibits only a marginal increase with increasing the hole density. Recalling that DOLP in Eq. (5) is sensitive to the ratio between the sum of  and  to , nearly-quenched but finite DOCP (shown in Eq. (6)) suggests . This confirms that optical decoherence is dominated by  for trions (, ) in monolayer WSe2; whereas the neutral exciton is primarily limited by . [26,31,82,83] For t-WSe2 [Fig. 2 (c) bottom], the extracted  values explain the distinct DOLP behaviors of  and . Under hole doping (),  for  increases; it correlates well with the suppressed DOLP (<5%). Conversely,  for  shows negligible dependence on  in this regime, consistent with the retained finite DOLP . In the neutral regime, both  and  exhibit low DOLP (<5%). Given that DOLP remains finite, the condition for near-zero DOLP [Eq. (5)] suggests that  dominates over intervalley scattering even at charge neutrality. This contrasts with the monolayer case, where the lifetime is the limiting factor at the charge neutrality. Under electron doping, both  and  show relatively lower  than  under hole doping. This is in fact consistent with the experimentally observed higher DOLP for  and . To understand why  becomes more prominent in t-WSe2 especially in charge-neutral regime, we note that  originates from fluctuations in the local environment that perturb exciton energy levels without leading to recombination. These can arise from lossless interactions with charge carriers, phonons, disorder or coupling to other excitonic states. In monolayer TMDs, particularly for  neutral excitons, two-dimensional coherent spectroscopy studies showed that quantum coherence is limited by the radiative recombination rate, implying near zero pure-dephasing rate. [26,31] In contrast, t-WSe2 introduces additional sources of dephasing. First, the presence of long-wavelength moiré potential modulates the local electronic environment. This breaks translational and rotational symmetries present in the monolayer and introduce position- dependent excitonic species. This spatial inhomogeneity leads to the enhancement of pure-dephasing. Second, the bilayer hosts a more complex valley and layer pseudospin structure which opens additional scattering channels between excitonic states, especially in the presence of elastic electron-phonon scattering. [84] In fact, the above discussions are consistent with the previous study in bilayer 2H MoSe2 [33], where enhanced dephasing was attributed to the increased density of exciton-phonon interaction pathways, which is not present in the monolayer. Although the exact magnitude of exciton-phonon coupling in t-WSe2 is still under investigation, it is expected to be enhanced, compared to the monolayer due to the increased density of accessible phonon modes and additional degree of freedom.To further support this interpretation, we compare the extracted  from RC measurements. In monolayer WSe2, the fitted  is , whereas for the t-WSe2, the fitted values are approximately  for  and for  [Fig. S6 [45]]. This comparison provides that  is indeed more prominent in twisted bilayer. This substantial increase in  suggests that exciton coherence in twisted bilayer is more susceptible to environmental fluctuations and scattering, i.e. those arising from moiré potentials and additional phonon modes.Considering the qualitative mechanisms of enhanced exciton-phonon scattering pathways, we further compare the lifetimes of excitons in monolayer and t-WSe2, and relate lifetimes to the observed DOLP. DOLP is generally governed by the ratio of exciton population decay rate () to the sum of valley decoherence rate ( and pure-dephasing rate [Eq. (5)]. For monolayer WSe2,  and  at 10 K for the bright A exciton, as reported in previous study [32], and our fitting indicates . In t-WSe2, the RC spectra yields  for  and  for , values comparable to monolayer WSe2. Assuming that  remains of similar magnitude as in the monolayer, the increase in  becomes the dominant mechanism limiting valley coherence in t-WSe2. This assumption is supported by the fact that, although t-WSe2 allows both interlayer  and intralayer  scattering channels, the interlayer scattering is hindered due to the nonzero momentum mismatch arising from the inversion symmetry breaking. [85] Thus, the increased magnitude of  plays a key role in explaining the reduced DOLP observed in t-WSe₂.This distinct responses of  and  can be understood by considering the lattice reconstruction and resulting band alignment in t-WSe2 [Figs. 1 (d) and (e)]. Reconstruction creates AB and BA stacked domains. Theoretical predictions and experimental evidence suggest that injected holes preferentially accumulate in the bottom layer of AB (MX) stacking and the top layer of BA (XM) stacking. [21,86] Upon hole doping, the carriers preferentially occupy in alternating layers associated with the alternating stacking order, corresponding to the spatial localization of . Consequently, when  resides in these domains, it is strongly affected by the hole-induced exchange interactions, leading to the increased . In contrast, because  is localized in a different layer of the same stacking environment, it exhibits negligible responses in both RC and PL spectra; stable DOLP with negligible . [21] Taken together, our polarization-resolved PL measurements and RC analysis provide a consistent picture.B. Ultrafast optical measurements1. Fluence dependent pump-probe spectroscopyTo understand the origin and subsequent dynamics of the two distinct excitons observed in our t-WSe2 sample, we performed ultrafast pump-probe spectroscopy at a base temperature of 4 K under various pump fluence , with the gate voltage set to . The pump pulse energy was tuned to 1.79 eV (above the exciton resonances), while the probe  was kept constant at . For the details on the experiments, see Supplemental Material S5 [45]. Figure 3 (a) illustrates the differential reflection signal (), defined as  where  and  are the probe reflection with and without the pump, respectively. The data were measured near zero probe delay for six different pump ’s; the linear  dependence is to be discussed later. We first present brief outlines of our measurements in the following. We observed two dominant features in the  spectra at 1.680 eV and 1.695 eV, corresponding to the intralayer excitons denoted as  and , respectively. The decay dynamics of these excitons were analyzed by fitting the time-resolved  traces using a biexponential function (see details in Supplemental Material S6 [45]), yielding a fast () and slow () decay component. The results for  and  are presented in Figs. 3 (b) and 3 (c), respectively. Initially, the signal exhibits a rapid rise within , a timescale likely limited by our instrumental response. This rise reflects the rapid formation of excitons from the photoexcited continuum state () [87], then followed by intraband relaxation, and eventual recombination through radiative and nonradiative channels. [88–90] Consequently, we assume that the exciton population generated by the pump leads to an instantaneous change in  at zero pump-probe time delay.To quantify the relationship between the initial signal amplitude (representing the initial exciton density) and , we employed the nonlinear saturable absorber model [91,92], represents the -dependent absorption,  is the saturation fluence,  is the saturable absorption coefficient, and  is the non-saturable absorption coefficient. Assuming near-unity photon-to-exciton conversion, the initial total exciton density exciton density  can be expressed aswhere  and  are the saturation and non-saturation densities, respectively, and  is the pump photon energy. Our observation of  suggests that saturable absorption associated with above-gap excitation is the dominant photoexcitation mechanism. Fits to the peak  data [solid lines in Fig. 3 (a)] yield saturation densities  for  and  for , respectively. These densities correspond to an average inter-exciton distances of , well below the estimated Mott transition density () in t-WSe2 [79]. It implies that our experimental condition is in a regime where interparticle distance is around  (where  is the exciton Bohr radius). Furthermore, linear fits to the data, i.e. weak pump regime (, dashed lines), confirm a linear response regime, justifying the negligible contributions of higher-order effects, such as exciton-exciton interactions or bandgap renormalization. [87] Followed by the exciton formation, we discuss the fast decay dynamics. Inset of Fig. 3 (a) displays the -dependence of  for both  and . Notably,  remains relatively constant for fluences below , indicating that the fast decay mechanism is not significantly influenced by the density-dependent processes, such as photoinduced absorption from filled localized states. The sub-picosecond  arise from several mechanisms including thermalization and defect-assisted recombination. [93] While thermalization and relaxation in TMD monolayers typically occur within  [94], the involved carrier-carrier and carrier-phonon scattering are typically completed within few hundreds of femtoseconds [95]. The lack of -dependence of  in the linear regime suggests these density-dependent scattering processes are not the primary contributors to the observed fast decay. [96] As seen by comparing the decays in Figs. 3 (b) and 3 (c),  and  exhibit distinct fast decay dynamics, but they show negligible -dependence at low densities. Therefore, we attribute  to a combination of initial intraband thermalization and radiative recombination within the light cone via direct relaxation processes. [96] Based on these findings, we selected a pump fluence of  for subsequent experiments to keep in the linear regime.2. Resonant pump-probe spectroscopyGiven that the two excitons reside in different layers of AB/BA staked bilayer and exhibit a small energy splitting, we investigated the mutual interactions or coupling between them. As interlayer tunneling in the  valley is nominally forbidden at marginal twist angles [86], any observed coupling might be influenced by the layer-asymmetric effects. To probe this in the time domain, we performed resonant pump-probe spectroscopy at  (pump energy = 1.687 eV, spanning both of the exciton resonances) while the probe is tuned to monitor both  and  transients. Figure 3 (d) shows the fit results using bi-exponential function near the zero pump-probe delay. The deduced rise time () is faster for  than that for , suggesting more rapid formation dynamics for . Then,  decays radiatively (bright  excitons within the light cone [97]), potentially experiences tunneling between layers which is facilitated by layer asymmetric coupling, and then decay via the layer-hybridized  valleys which subsequently repopulate the  and  states. The fitted  values under these resonant conditions are  for  and  for . The shorter  for  compared to  might be attributed to an additional decay pathway involving interlayer electron tunneling, which depletes the  population. This tunneling would concurrently reduce the hole population available for . Although such interlayer transitions would exhibit the polarization to be oriented in the in-plane z-direction, the corresponding experimental proof falls outside the detection capabilities of our spectroscopic techniques. C. Influence of temperature and doping on exciton dynamics1. Temperature-dependent RC spectroscopyTo further elucidate the exciton dynamics and dephasing mechanisms, we have performed the temperature dependent measurements from 4 K to 125 K, and have compared the steady-state RC spectroscopy data [Fig. 4 (a)] to the normalized transient  data [Fig. 4 (b)]. Figure 4 (a) shows the temperature-dependent RC spectra at . With increasing the lattice temperature, both exciton resonances exhibit a redshift feature with a decreased peak amplitude, consistent with observations in other TMD layers. [35] The resonance energies extracted from RC and pump-probe spectra show similar temperature dependence (see Fig. S9 [45]). From the RC spectra, we have extracted the homogeneous linewidth (and resonance energy using a modified TMM analysis. The linewidth increases with temperature for both excitons [Fig. 4 (c) top panel], indicating significant phonon interaction effects. This behavior is modeled using a simple expression, where  is the intrinsic linewidth at 0 K,  quantifies the coupling strength to acoustic phonons, and the last term describes interaction with longitudinal optical (LO) phonons of energy . The solid line represents the fit using Eq. (19). At low temperatures, we observe that the homogeneous linewidth increases linearly with temperature, primarily due to interactions with long-range acoustic phonons. Fit results using Eq. (19) yield , , ,  for  (black solid line), and , , ,  for  (red solid line), respectively. We confirm that the intrinsic linewidths are comparable to that of monolayer WSe2  for both  and . [26] However, the acoustic phonon coupling strengths are notably smaller than the reported value for monolayer WSe2 ( [26] This decreased coupling strength might represent the two-dimensional characteristics of TMDs; in the context of quantum wells, as the well width  increases,  decreases, following the relationship . [98] The temperature dependence of the exciton resonance energy [Fig. 4 (c) bottom panel] was analyzed using a modified Varshni equation to capture the phonon effect to the bandgap  [68,98,99] The equation is given by,where  is the energy at 0 K,  is a dimensionless exciton-phonon coupling strength, and  is the average interacting phonon energy. From the fit we yield,  for , and  for , respectively. Comparing the exciton-phonon coupling strength and average phonon energy,  consistently exhibits stronger exciton-phonon interaction compared to . Thus, the steady-state optical analysis suggests that exciton-phonon interaction is not a major cause for exciton dephasing in the case of ; on the other hand, exciton-phonon interaction is a dominant dephasing process in the case of .2. Temperature-dependent pump-probe spectroscopyWe then turn our attention to the nonequilibrium data. As aforementioned, Figure 4 (b) show the normalized temperature dependence of the exciton dynamics, obtained through pump-probe spectroscopy with above-gap excitation (pump photon energy of 1.79 eV). For  [Fig. 4 (b) right panel and see also Fig. 4 (d)],  decreases significantly from  at 4 K to  at 125 K. This trend mirrors the behavior of the population decay time  extracted from the RC linewidth [Fig. 4 (e)], which decreases from  at 4 K to  at 125 K. In contrast, for  [Fig. 4 (c) left panel and see also Fig. 4 (d)], both  and the corresponding  remain nearly constant across the measured temperature range [Fig. 4 (e)]. However, we note that despite the similar temperature trends for  and , there is a noticeable difference in their absolute timescales. This discrepancy arises because the two techniques are intrinsically sensitive to different aspects of the exciton decay process. Steady-state RC spectroscopy primarily reflects the coherent dephasing time (), from which  is calculated by distinguishing the pure-dephasing from . Pump-probe spectroscopy, on the other hand, captures the evolution of the excited state population, which includes both coherent effects at very early times and subsequent incoherent population dynamics. [27,97,100] These incoherent contributions, influenced by factors like exciton relaxation from higher-lying states, repopulation dynamics, and transitions involving momentum-indirect or dark excitons, can serve as an effective population reservoir. This prolongs the decay measured by pump-probe compared to the purely coherent decay time. [27,65,101] Previous studies indicate that such incoherent processes contribute significantly within the first picosecond and also dominate longer dynamics on the scale of hundreds of picoseconds. [33,88] Thus, early-time pump-probe dynamics likely reflect a mixture of coherent dephasing and incoherent population decay, leading to apparently longer  compared to . Importantly, although these two spectroscopies are fundamentally different, both techniques consistently reveal negligible exciton-phonon coupling for the  fast dynamics, and strong exciton-phonon coupling for the  fast dynamics. For the slow decay component () observed in , both  and  exhibit decays on the order of several hundred picoseconds [Fig. 4 (f)]. At 4 K,  has  of , while  has a longer  of . When temperature increases to 125 K,  decreases for both excitons, reaching  for  and  for . The decrease is more pronounced for , causing the  values to become similar at an elevated temperature above 100 K. This long-lived signal reflects the timescale of final exciton recombination pathways including the phonon-assisted recombination processes. The observed decrease in  with increasing temperature is consistent with thermally activated non-radiative decay channels or increased scattering ones into the energy loss pathways.  [102] The stronger temperature dependence of  for  compared to  further corroborates the conclusion derived from the linewidth analysis and the  behavior, where we see that  experiences stronger exciton-phonon interactions. While lattice cooling via heat transfer to the substrate can also contribute to slow  dynamics, the distinct temperature dependencies observed for  and  suggest that exciton-specific decay mechanisms modulated by phonons are the primary factors for differentiating their  behavior.When comparing the values of  for  and , however,  exhibits a shorter timescale than . Interpreting this result is more complex than attributing it solely to the exciton-phonon interactions, because several factors contribute to this observation, including lattice disorder and interactions with dark excitons. Assuming equivalent lattice disorder effects for both  and  residing in similar environments, other factors like interactions with dark excitons and specific phonon-mediated scattering channels must be considered. [100] Bright excitons can relax to lower-energy dark states via intervalley scattering or spin-flip processes. Fast intervalley scattering contributes to , while slow processes such as phonon-assisted spin-conserving or spin-flipping intervalley scattering can contribute to . One possibility is that  has a more efficient relaxation pathway to dark states (located near 1.6 eV) or other non-radiative channels compared to , leading to a shorter . The specific phonon modes in t-WSe2 may also play a crucial role. The twist between two layers introduces folding of phonon bands by the moiré superlattice, creating characteristic low-energy folded acoustic phonon modes, including interlayer shear () and breathing () modes. [103–106] Raman spectroscopy studies on reconstructed t-WSe2 indicate that while both modes exist, the breathing mode often exhibits relatively higher intensity, suggesting it couples more effectively to electronic states in these structures compared to the shear mode.  [103–106] This sensitivity of dynamics to interlayer modes is highlighted by comparison between 3R and 2H MoS2, where different stacking and interlayer coupling in 3R leads to significantly longer slow decay times () compared to the 2H phase. [94] Given that  exhibits stronger acoustic phonon coupling () than , and that  reflects interactions with acoustic modes including shear and breathing phonons, the distinct  behaviors might stem from differing coupling efficiencies of  and  to these specific interlayer modes. Considering the stronger interaction associated with the breathing mode, we believe that the differences in  dynamics between  and  reflect their coupling strengths primarily to the interlayer breathing mode, in addition to the dark state scattering pathways.3. -dependent pump-probe spectroscopyNext, we discuss the influence of charge carrier doping on the exciton dynamics by performing -dependent pump-probe spectroscopy. We also compare these dynamics with steady-state RC spectroscopy performed under identical conditions [Fig. 1 (c) bottom panel]. Figure 5 (a) presents the time-resolved  traces for  [Fig. 5 (a) top panel] and  [Fig. 5 (a) bottom panel] at various . The extracted fast decay times , population decay times inferred from RC linewidths , and slow decay times  are plotted as a function of  in Figs. 5 (b), 5 (c) and 5 (d), respectively. Interestingly, the dynamics of  show strong dependence of the doping level. At  (lightly hole-doped regime), the pump-probe signal [Fig. 5 (a), top panel] reveals features characteristic of charged excitons (trions); a longer rise time  compared to the sub-picosecond rise time  associated with the neutral exciton response observed near .  [107] Furthermore, the signal becomes non-negative, indicating induced absorption or recovery dynamics of bleaching that differ from those of the neutral exciton. In fact, these are consistent with the formation of trions.  [66,108] Under strong hole doping, the charged exciton response becomes non-negative and displays faster decaying across all , including the weakly hole-doped, neutral, and electron-doped regimes.This behavior of  under hole doping can be interpreted within the framework of exciton-polaron interactions, involving attractive polarons (AP, or trions) and repulsive polarons (RP). [98] As hole doping density increases from the charge neutrality, both AP and RP branches emerge and redshift until a critical doping density is reached. In the lightly hole-doped regime, these branches coexist. Beyond the critical doping density, the RP branch undergoes a non-radiative transition into the AP branch. [109] Although we cannot rule out the effect of the phonons and charge fluctuations in this process, these factors affect both branches in similar manner, thus being unlikely for the observed dephasing. This interplay between RP and AP states in the coexistence regime explain the sign change and can explain the prolonged dynamics observed at around . In contrast, under stronger hole doping where the AP branch dominates,  becomes shorter than the charge neutrality [Fig. 5 (b)]. Considering the overall trend for ,  decreases progressively from the electron-doped regime, and reaches its minimum in the strongly hole-doped regime. This trend is well reflected by the  values extracted from the modified TMM analysis of the RC spectra [Fig. 5 (c)], which also shows a monotonic decrease from the electron doping to the hole doping. The long  observed for  at around  [Fig. 5 (d)] might also be linked to the complex dynamics arising from AP-RP competition at that particular doping level, reserving a room for future investigations. For the  dynamics, the data are analyzed in the neutral and hole-doped regimes where the signal is prominent [Fig. 5 (a) bottom panel].  exhibits a non-monotonic dependence on hole-doping, where it is shortest around  , increases slightly at neutrality , and becomes significantly longer in the strongly hole-doped regime [Fig. 5 (b)]. The  values derived from the modified TMM for  show a related, though not an identical trend. It decreases form neutral to lightly hole-doped, then increases slightly under strong hole doping [Fig. 5 (c)]. As discussed in the context of steady-state measurements, electrostatically injected carriers modify the excitonic properties. In the hole-doped regime (assuming BA stacking), holes primarily reside in the top layer, influencing  (same layer) more strongly than  (bottom layer). Conversely, under electron doping, excess electrons populate  valley, leading to hybridization between each layer, and thus fluence both excitons. The observed correlations between the doping trends of  and  for both excitons suggest they stem from common underlying physical mechanisms, namely the doping-dependent radiative  and non-radiative  decay processes. Carrier injection screens the Coulomb interaction, which can reduce the electron–hole wavefunction overlap and the oscillator strength, thereby decreasing . These effects are captured in both transient and steady-state measurements. Despite the consistency in the doping-dependent trends of  and , a quantitative discrepancy exists. is typically around , whereas  ranges from . This difference likely reflects the complex electronic landscape of t-WSe2 compared to the monolayer counterpart. The presence of multiple low-energy valleys and interlayer hybridization introduces momentum-indirect excitonic states (e.g., involving , , and  valleys) with low oscillator strengths. While nearly invisible in the RC spectra, these states are known to participate in the ultrafast intervalley scattering and thermalization pathways [33,110,111] [Fig. S9 [45]]. These scattering processes act as intermediate steps or population reservoirs, effectively slowing down  in the pump-probe measurement, compared to the population decay time  obtained from the linewidth of the  bright exciton using the modified TMM. Furthermore, the modified TMM analysis does not explicitly account for ultrafast thermalization process or scattering of dark excitons. Nevertheless, the similar doping dependence supports the conclusion that both  and  are governed by the same fundamental exciton decay mechanisms, modulated by carrier density and intervalley/interlayer interactions.Finally, we examine the -dependence of the slow decay component,  [Fig. 5 (d)], which reflects long recombination pathways sensitive to charge environment, electric fields, and phonon coupling. The extremely long  for  near   is attributed to the AP-RP dynamics in the hole doping, as discussed earlier.  dominates the response with  in the stronger hole doping. This relatively slower decay for  may occur because holes are localized primarily in the same layer where  reside, reducing the exciton-charge interaction as well as the associated phonon coupling (e.g., modulation of electronic states via interlayer breathing modes [86,112]) for  in the other layer. Typical values  in the neutral regime are  for  and  for , respectively. Under electron doping, signal merges toward -like behavior with . Here, electrons are delocalized in  valleys, promoting interlayer hybridization. This hybridization, coupled with interlayer phonon modes (modulation of interlayer distance and hybridization strength), facilitates efficient interlayer scatterings or relaxation pathways, leading to the relatively faster  and the dominant -like response. While the modified TMM provides valuable insights into dephasing from RC spectra, its accuracy in complex twisted bilayers is limited. It mainly captures the linear response associated with the bright  exciton, which may underestimate the impact of intervalley scattering pathways involving hybridized or dark states. The latter is more prominent in nonlinear time-resolved measurements. Unlike monolayer WSe₂, where  intervalley scattering is often the key dephasing mechanism, twisted structures present a richer landscape of scattering possibilities. More sophisticated theoretical approaches, combining BSE-GW calculations with TMD Maxwell-Bloch equations under electrical doping within TMM framework [101], would be required for accurate description of dephasing and comparison with the pump-probe data. Further studies are also warranted to disentangle the competing effects of the charge environment on exciton binding energy, radius, and oscillator strength in these complex moiré homostructures.V. ConclusionIn summary, we have studied the effects of phonon and electron interactions on the exciton dynamics in the rhombohedral-stacked t-WSe2 using a combination of steady-state optical spectroscopy (RC and PL) and ultrafast pump-probe spectroscopy. Unlike monolayer WSe2, the reconstructed moiré AB/BA domains in t-WSe2 give rise to two distinct intralayer excitons, originating from different local dielectric and electric environment in each layer. These exciton features are confirmed by the -dependent RC and -dependent polarization-resolved PL, demonstrating asymmetric interlayer coupling. Using polarization-resolved PL and a modified TMM grounded in Lindblad master equation, we have extracted exciton dephasing parameters. We have additionally found that pure-dephasing rate plays a dominant role in limiting the valley coherence, particularly under electrostatic doping. By investigating the exciton population dynamics as a function of temperature and , we have identified that the interplay between exciton-phonon and exciton-charge interactions is the key driver for the observed behaviors. We assign the fast exciton decay component  to the direct recombination process within the light cone combined with intervalley scattering effects, which exhibits consistent trends for the temperature and -dependence based on TMM  analysis. Furthermore, degenerate pump–probe spectroscopy confirms the presence of asymmetric interlayer coupling affecting the early dynamics of excitons. The fast component of  is shorter than that of , suggesting that the exciton dynamics in the top layer  are more affected by the interlayer coupling compared to the bottom layer for the case of BA stacking order. Moreover, we uncover the phonon-induced dephasing asymmetry between the two excitonic species, where  exhibits strong coupling to acoustic phonons, while  remains largely unaffected. Charge doping modifies the dephasing through hole localization and electron hybridization in the  valley between the two layers. The effect signifies the Coulombic screening and directly affects the radiative lifetime. Crucially, the biexponential decay extracted from the pump-probe spectroscopy reveals that  is governed by the phonon-mediated population relaxation. We find that interlayer breathing phonons, in combination with the charge doping, lead to significantly different decay behaviors for electron- and hole-doped regime. In the hole-doped case, the non-bonding nature of AB/BA domains is modified by interlayer hybridization, resulting in longer-lived exciton states. Supplemental MaterialSupplemental Notes and Supplemental Figures.AcknowledgementsThis research was supported by the National Research Foundation of Korea (NRF) through the government of Korea (Grant No. 2021R1A2C3005905, RS-2024-00413957, RS-2024-38600466612, RS-2024-00487645), Scalable Quantum Computer Technology Platform Center (Grant No. 2019R1A5A1027055), the Institute for Basic Science (IBS) in Korea (Grant No. IBS-R034-D1), Global Research Development Center (GRDC) Cooperative Hub Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT) (Grant No. RS-2023-00258359), and the core center program (2021R1A6C101B418) by the Ministry of Education.References[1] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically Thin MoS 2 : A New Direct-Gap Semiconductor, Phys. Rev. Lett. 105, 136805 (2010).[2] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. 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(c) -dependent RC spectra of monolayer WSe2 (top) and t-WSe2 (bottom). The dotted lines mark the charge neutral points. Regions  and  correspond to electron-doped and hole-doped regimes, respectively. (d) Illustration of the domain structure in t-WSe2 at a marginal twist angle. At near-zero twist angle, where the WSe2 layers are parallel-stacked, lattice reconstruction and atomic relaxation result in the formation of AB (cyan)/BA (magenta) stacking domains. Right: side view of AB (MX, M: metal (W) on top of X (Se) chalcogen atoms), and BA (XM) stacking orders. Red, W; blue, Se. (e) Schematic of the electronic band structure. Blue and orange lines represent the conduction and valence bands of the top and bottom layers, respectively in the AB(MX) stacking order. Dashed lines indicate the degenerate bands that are not affected by reconstruction effects.  valley is highlighted in purple to emphasize strong interlayer hybridization, resulting in a layer-mixed (degenerate) character. The bands on the left depict the band structure near the  valley in the neutral regime , where the conduction band minimum and valence band maximum are split due to level repulsion and local chemical environment difference, such that . Intralayer excitons in the top and bottom layer WSe2 are labeled  and , respectively, and the transitions are drawn as blue and orange arrows. The black dashed line denotes the Fermi level, which can be tuned via electrostatic gating (). Under hole doping , the top layer valence band is selectively populated with holes. In contrast, under electron doping , the electrons (purple gradient) are populated in the  valley, where carriers reside in the hybridized states.Figure 2. - degree of linear polarization. (a) PL measurements for t-WSe2 (black) monolayer WSe2 (red). (b) -dependent degree of linear polarization (DOLP) measurements for monolayer WSe2 are shown in the top panel. -dependent pure-dephasing linewidth extracted using TMM method is shown in the bottom panel: exciton (black), positive trion (red), and negative trion (blue) in monolayer WSe2, respectively. (c) -dependent degree of linear polarization (DOLP) measurements for t-WSe2 are shown in the top panel. -dependent pure-dephasing linewidth obtained from RC spectra is shown in the bottom panel:  (black),  (red), and  RP (blue), respectively. Blue dashed lines indicate peak positions.Figure 3. Fluence- and excitation energy-dependent decaying dynamics. (a) Pump fluence ()-dependent  at time delay of , for  (black) and  (red), with the gate voltage set to . The dashed line indicates linear -dependence in low  regime (), while the curved line represents the fit from a nonlinear saturable absorber model. [Inset: -dependent fast component () fitted from a biexponential convolution function.  is independent of , implying no absorption occurs from defect states.] (b) Ultrafast dynamics of  (probe photon energy of ) at various  (pump photon energy of ), fitted with a biexponential convolution function. [Inset: A schematic that illustrates the pump pulse (red) forming an excited state, which then undergoes decay, while the probe pulse (blue) selective probes .] (c) Ultrafast dynamics of  (probe photon energy fixed at ) at various  (pump photon energy fixed at ), fitted with a biexponential convolution function. [Inset: A schematic that presents the pump pulse (red) forming an excited state, which then undergoes decay, while the probe pulse (blue) selective probes .] (d) Ultrafast dynamics of  (black) and  (red) under pump photon energy spanning both exciton resonances. [Inset: A schematic that shows the pump pulse whose spectrum covers both exciton resonances (yellow), and the probe pulse (blue) selectively probes  and . The transition between conduction band of  and valence band of  is indicated by the dashed grey arrow.] Figure 4. Temperature-dependent decaying dynamics. (a) Temperature-dependent RC spectra at the charge neutral point, showing the redshift of the exciton resonance energy and the linewidth broadening. (b) Normalized ultrafast dynamics of  (left) and  (right) at various temperatures. Solid line is the result of fits using a biexponential convolution function. (c) Homogeneous linewidth (up), exciton resonance energy (bottom) of  (black) and  (red) under various temperatures. Solid line is the fit considering both effects from the acoustic phonon coupled to exciton and optical phonon coupled to the exciton dynamics of the linewidth analysis. For exciton resonance energy, the lines are the fits from the modified Varshni equation. (d) Temperature-dependent evolution of fast decay component () from the temporal dynamics of  (black) and  (red), respectively. (e) Temperature-dependent evolution of  derived from TMM for  (black) and  (red), respectively. (f) Temperature-dependent evolution of fast decay component () from the temporal dynamics of  (black) and  (red), respectively. Vertical error bars in (d), (f) are obtained from the fits. Figure 5. -dependent decaying dynamics. (a) denotes the ultrafast dynamics of  (top) and  (bottom) at various . Solid line is the fit using a biexponential convolution function. (b) -dependent evolution of fast decay component () from the temporal dynamics of  (black) and  (red), respectively. (c) -dependent evolution of  derived from TMM for  (black) and  (red), respectively. (d) -dependent evolution of fast decay component () from the temporal dynamics of  (black) and  (red), respectively. Vertical error bars in (b) and (d) are obtained from the fits.2image2.jpegimage3.jpegimage4.jpegimage5.jpegimage1.jpeg