Tuning moiré excitons and correlated electronic states through layer degree of freedom

Moiré coupling in transition metal dichalcogenides (TMDCs) superlattices introduces flat minibands that enable strong electronic correlation and fascinating correlated states, and it also modifies the strong Coulomb-interaction-driven excitons and gives rise to moiré excitons. Here, we introduce the layer degree of freedom to the WSe2/WS2 moiré superlattice by changing WSe2 from monolayer to bilayer and trilayer. We observe systematic changes of optical spectra of the moiré excitons, which directly confirm the highly interfacial nature of moiré coupling at the WSe2/WS2 interface. In addition, the energy resonances of moiré excitons are strongly modified, with their separation significantly increased in multilayer WSe2/monolayer WS2 moiré superlattice. The additional WSe2 layers also modulate the strong electronic correlation strength, evidenced by the reduced Mott transition temperature with added WSe2 layer(s). The layer dependence of both moiré excitons and correlated electronic states can be well described by our theoretical model. Our study presents a new method to tune the strong electronic correlation and moiré exciton bands in the TMDCs moiré superlattices, ushering in an exciting platform to engineer quantum phenomena stemming from strong correlation and Coulomb interaction.

In summary, this is a well designed study and the manuscript is well written. The conclusion is interesting and would indeed introduce a new control knob to the Moire superlattice studies. However, before I can recommend acceptance, I wish the authors could consider improving their manuscript along the lines listed above.
Reviewer #3 (Remarks to the Author): Dongxue Chen et al. report experimental study of moire excitions and correlated electronic states in multilayer WSe2 / 1L WS2 heterostructure. The authors perform combined optical spectroscopy and microwave impedance measurement and show the systematic layer number dependence (1L to 3L) of intralayer exciton spectrum including moire effect and correlated electronic states. As far as I know this is the first systematic study of layer number dependence of moire excitons and correlated electronic states in WSe2/WS2 moire system and the experimental effort is impactful for the 2D material research community.
However, I have a major concern about the microscopic mechanism of intralayer exciton and moire exciton hybridization which the authors discuss extensively in the first half of the manuscript.
In line 59 -64 in Supplementary Note 2, the authors state that moire potential folds the energy bands and compensates the large momentum separation of K -K' valley. However, the momentum difference which moire potential can compensate is only the order of moire reciprocal vector which is much smaller than K -K' momentum difference. I cannot completely deny the possibility, but back-of-the-envelope calculation tells that assuming that the moire lattice constant is ~ 8nm, and intrinsic lattice constant is ~ 0.32nm, order of N = 8nm/0.32nm = 25 times of perturbation process is required to compensate the momentum difference, which would be unlikely to happen coherently. I tried but failed to come up with different scenario. It is worth to mention that the exchange interaction, which the authors did not discuss explicitly but shown in the last term of the exciton Hamiltonian H_A in Supplementary Note 1, mixes K -K' valley excitons at non-zero momentum. (There is an experimental report regarding the mixing of K -K' valley states of moire exciton, PRX 11, 021027 (2021).) Another thing I want to mention is that even though interlayer tunneling is forbidden for conduction band electrons due to symmetry as the authors mention, it is allowed for nonzero momentum electrons. Therefore, moire potential would enable the hybridization of intravalley conduction band electrons off resonantly between two layers.
We sincerely thank the reviewers for their time and efforts. We also greatly appreciate the reviewers' recognition of our work and their constructive feedback. Here we provide a point-topoint reply to their comments in the following (blue colored). We have also revised our manuscript accordingly, with the revision highlighted in the main text and SI for the reviewers' convenience.
Here we list the major revisions we have made in the main text and SI. 1. We have developed the microscopic mechanism of exciton hybridization and added the corresponding discussion in the main text and Supplementary Note 2. 2. We have included an extensive discussion of layer characterization of WSe2 in Supplementary Note 4. 3. We have included extensive data from other devices in Supplementary Note 5.
With these revisions, we believe that our manuscript is ready for publication in Nature Communications. We thank all three reviewers for helping us improve our manuscript.

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): In this work, the authors studied the properties of the moiré excitons and the correlated insulating states in the WSe2/WS2 moiré superlattice with additional WSe2 layers. Based on the optical spectrum of the exciton excitations, they demonstrated the interfacial nature of the moiré couplings. And the influence of additional layers to the correlated insulating states has been addressed by the MIM measurements. The authors propose this multilayer system as a new platform to study the correlation physics.
Although, the experimental results are quite reasonable, the novelty of the manuscript is questionable. Thus, I would not recommend its publication in Nature Communications due to the following comments: Response: We thank the reviewer for the efforts in reviewing our manuscript. Here, we take this opportunity to elaborate on the novelty of our work. We have also revised our manuscript accordingly to emphasize some of the discussions below. We thank the reviewer for helping us improve our manuscript.
To the best of our knowledge, our work is the first study of TMDC heterojunction moiré superlattices with a layer degree of freedom.
In this work, we find that the added layer(s) significantly modulate moiré excitons' resonance energies. We have also developed the microscopic mechanism of the moiré exciton modulation: hybridization of moiré excitons and intralayer excitons from the added layer(s). Both experimental tuning and theoretical understanding of the moiré exciton are critical for future investigation of excitonic physics in TMDC moiré superlattices.
We also find that the added layer(s) reduce the correlation strength in the moiré superlattices. We have theoretically calculated the bandwidth of the moiré miniband, which is consistent with the experimental observations. We emphasize that, even the reduced correlation strength in 3L/1L WSe2/WS2 moiré superlattice is still much stronger than that in graphene moiré systems, evidenced by the Mott transition temperature. Considering the valley-spin-layer locking, the multilayer TMDC moiré superlattices provide an exciting platform to engineer new correlated physics, especially considering the valley contrasting excitons.
Finally, our study reveals the highly interfacial nature of the moiré interaction, which provides critical guidance for future studies and applications of moiré physics.
In summary, we believe that our results provide stimulating results for researchers working on excitons, moiré superlattices, and correlated physics in 2D, and the multilayer TMDC moiré superlattices will provide a new exciting platform for excitonic physics and correlated states.
Below we provide a point-to-point reply to the reviewer's comments: 1. The main result of the article is the modulation of the moiré excitons due to intralayer A excitons in the nearby WSe2 layers. Experimentally, they found nearby A excitons would induce energy shift of the moiré excitons as shown in Figure 1(b) of the main text. As clarified in this article, the moiré excitons are originated from splitting of the A excitons by the moiré coupling. Thus, the energy shift of moiré excitons in 2L and 3L WSe2 cases could be expected from level repulsion and the interfacial nature of the moiré coupling. Since WSe2 layers coupled with each other by the van-der Waals force, the energy shift in 3L is comparable with 2L case is obvious.
Response: As we mentioned above, the modulation of the moiré excitons is one of our major results.
The large moiré exciton modulation, especially when the WSe2 is changed from 1L to 2L, is significant. Such large tunability of the moiré excitons will be important for applications, and the understanding will also provide critical insight on moiré excitons. We have developed a hybridization mechanism for the moiré exciton with the intralayer A exciton, which well describes our observation. To the best of our knowledge, this is the first observation of such hybridization. It can also be seen from our reply to reviewer 3's comments that the mechanism is nontrivial and highly intriguing.
In addition, the optical spectra of the new exciton resonance close to the intralayer exciton A exciton is a direct consequence of the interfacial nature of moiré coupling, and we believe our work is the first report of that. The interfacial nature of the moiré coupling is critical for designing future systems to study and utilize moiré excitons.
Finally, the exact nature of the moiré exciton in WS2/WSe2 superlattice is of great interest and under active investigation. Our experimental observations of the moiré exciton modulation could stimulate and help further theoretical efforts in understanding the moiré excitons.
2. The modulated moiré exciton resonances at certain fillings were attributed to the change of dielectric constant due to the formation of the Mott insulators. Although the excitons are sensitive to the surrounding dielectric environments, the Hubbard bands from fractional filled moiré valance bands would also influence the exciton resonances. It's unclear which one dominates the experimental results.
We wonder if the reviewer is referring to Hubbard bands at the half-filled valence bands. If so, we agree with the reviewer that the gap opening due to Hubbard band formation can potentially affect the moiré excitons as well, which is stated in the main text "The modulation of the moiré excitons at the n=±1 is likely due to the dielectric constant change and gap opening associated with the Mott insulator states." The exact mechanism of how the formation of correlated states affects the moiré exciton is intriguing but it is not the focus of our manuscript. In fact, the mechanism remains unclear, despite that it has been used to investigate the correlated states in quite a few recent works [2,3]. Although the exact mechanism is out of the scope of this manuscript, our work provides a clear layer dependence of the electron correlation through temperature-dependent MIM measurements. The corresponding moiré exciton spectra shown in this work, therefore, will be helpful for further investigation of the mechanism.
3. Also, the weakened Mott insulating states were explained by the increased dielectric constant and band widths with additional WSe2 layers. Since the band widths have been calculated by the effective model. It would be important to estimate how does the Coulomb energy change with additional layers.
Estimating the Coulomb interaction and how it affects the correlated states is challenging, as the effective dielectric constant of the structure is difficult to calculate, considering the 2D nature of the added layers. But that is exactly the beauty of our work, as we experimentally provide high quality data that clearly show the layer dependence. Our results, therefore, provide critical information for this new flatform and will stimulate future theoretical exploration.
We also emphasize that, although one might expect the reduced Mott transition temperature with added layers, it is not clear how much reduction there will be. Even more critically, it is not clear whether the correlated states will survive with the added layers. Our work is the first to show that the correlated states persist with the added layers. Even in the 3L/1L WSe2/WS2 region, where the correlation strength is much reduced compared with the 1L/1L WSe2/WS2, the electron correlation is still much more robust than that of graphene moiré superlattices, with the Mott transition temperature of ~60 K compared with the ~4 K [4] in the graphene moiré superlattices. This is exciting because one can envision controlling correlated electrons' distribution in different layers to engineer new quantum states, and it is not feasible in the 1L/1L WSe2/WS2, in which the large band offset between WSe2/WS2 strictly restrains electrons to reside in the WS2 layer and holes in the WSe2 layer. We have revised manuscript accordingly to reflect this discussion.
Reviewer #2 (Remarks to the Author): The authors reported an interesting study on Moiré excitons in monolayer-few layer TMDC heterostructures. A 1L WS2 flake is covered by a flake of WSe2 containing regions of 1L, 2L, and 3L. The two flakes, with near 0 twist angle, form a Moiré lattice with an 8-nm period, due to their lattice mismatch. The heterostructure is encapsulated by hBN flakes and is subject to a back gate for doping, through a few-layer graphene flake serving as electrode. The device structure is similar to previously reported ones to study Moiré excitons. The key new element is the inclusion of the 2L and 3L regions. Gate dependent low-temperature reflectance spectroscopy and microwave impedance microscopy were performed to probe the electronic and excitonic states of the device.
The key findings include the additional exciton peaks in thicker samples, with increased energy differences. Along with theoretical calculations, the authors concluded that the Moiré potential is localized at the interface, and the layer thickness can be used to tune the electronic correlation and Moiré exciton bands.
I found the topic timely and results interesting. The data reported are of high quality. However, I feel that there are several missing key elements that I wish the authors could consider: Response: We greatly appreciate the reviewer's recognition of our work, and we provide a pointto-point reply to all the questions by the reviewer in the following.
1. It appears that only one device was studied. Although having all three heterostructurers on a same sample is definitely an advantage and facilitates their direct comparison, ideally, repeating the study on another independent device appears necessary to solidify the conclusions.

Response:
Although we only presented the data from one device in the main text, the observations are robust. We have studied the moiré excitons behavior of 9 different samples (not necessary all include 1L/1L, 2L/1L, and 3L/1L WSe2/WS2 regions as it is more difficult to fabricate), and all the data are consistent with the one presented in the main text. We have summarized the results in Table R1 and included it in the revised Supplementary Information (Supplementary Table 1). We also include it for the reviewer's convenience. Table R1. Exciton resonances from different samples.
In addition, we have added the optical spectra of device D2 in the revised Supplementary Information. Device D2 is similar to the device D1 (data presented in the main text) and has welldefined 1L/1L, 2L/1L and 3L/1L WSe2/WS2 regions, with the optical image shown in Supplementary Figure 3b. The optical spectra from D2 are similar to what we present in the main text, which we include in the revised Supplementary Figure 7. For the reviewer's convenience, we also include the data here as Fig. R1, which show consistent results compared with the device shown in the main text (D1, Fig. 1). Figure R1. (a), (b) and (c) are the differential reflectance spectra as a function of the gate voltage in the regions of 1L/1L, 2L/1L, and 3L/1L WSe2/WS2, respectively. All data were taken at 10 K. 2. There is a lack of sample characterization information. For example, how did the author determine the thickness of the samples? Are there AFM or Raman characterization? Since the authors converted gate voltage to carrier density ( Figure 1) and used it in the discussions, do they know the background doping density of the samples?

Response:
Over the past few years, we have developed a systematic method to determine the layer number of WSe2 in the few-layer regime. The optical reflectance from a thin flake of 2D materials is related to its absorption [5,6] and thus a powerful method to determine the thickness of the 2D materials such as WSe2. The microscope image of three WSe2 flakes (including a standard WSe2 flake, device D1, and device D2) are shown in Fig. R2. We can apply optical contrast analysis method [5,6] to identify the thickness by numerically analyzing the RGB optical images of the samples.
The microscope images of the standard WSe2 flake, the WSe2 flake used in D1, and D2 are shown in Figure R4a-c. The reflectance contrast (R contrast, defined as (Rsubstrate -Rsample)/Rsubstrate) for these three pieces of WSe2 flake is also calculated (the red channel), and the values for different layer regions are plotted in Fig. R2d. It is evident that WSe2 regions with a certain layer number share similar R contrast, while the increase of one single layer will increase the R contrast by one "step". Thus, by comparing with the R contrasts of standard WSe2 flake and the WSe2 flakes used in D1 and D2, we can accurately confirm the number of layers of WSe2. We further confirm the layer thickness through AFM measurements (Fig. R3). For the standard WSe2 sample, we overlay the AFM topography measurements with the microscope image. It is evident that each layer adds to about 0.74± 0.03 nm in height, consistent with previous reports [7]. Finally, the layer assignment is consistent with the Raman measurements. Fig. R4 shows the Raman spectra taken from the different regions on the standard sample using 532 nm laser excitation. A Raman peak is observed at 308.0 cm -1 on the 2L WSe2 region and at 307.7 cm -1 on the 3L WSe2 region, yet it is absent on the monolayer WSe2 region, as shown in Fig. R4c. We also observe a splitting between the A1g mode and the 2 1 mode on the 2L WSe2 region and the 3L WSe2 region, shown in Fig. R4a. All these observations are consistent with the Raman spectra reported in Ref. [8]. The initial doping of the samples is close to zero, which can be shown by the device behavior at zero gate voltage (MIM data in Fig. 4 and optical reflection spectra in Fig. 1 of the main text).
3. Although reflectance measurement can probe the exciton energies, some complementary photoluminescence experiments would offer a more complete picture of these excitons. Such data are routinely included in most studies on Moiré excitons. Hence, if the authors could include such data, it would allow a benchmark comparison with literatures.

Response:
We thank the reviewer for the suggestion. Here we include the gate-dependent PL spectra of the interlayer excitons for the device shown in the main text (device D1) in Fig. R5. The data from the 1L/1L WSe2/WS2 clearly show the emergence of the correlated insulating states at fractional fillings (see Fig. R5a). The n=1 (-1) is the Mott insulator state for the half-filling corresponding to one electron (hole) per moiré superlattice. The fillings at 1/3, 2/3, 1/4, and 1/2 correspond to correlated insulating states we reported earlier [9,10], and the capability of revealing them directly in the PL spectra demonstrates the high quality of the data.
The PL of interlayer excitons is weaker in 2L/1L and 3L/1L WSe2/WS2 regions, as shown in Fig.  R5b, c. The exact mechanism is still under investigation. Although PL spectra are of high sensitivity, it is also incoherent in nature, and the mechanism could be complicated. Unlike reflectance spectroscopy, which is directly linked to absorption, both absorption and emission processes are important for PL emission. For the 1L/1L WSe2/WS2 superlattice system, since moiré modulation of the intralayer excitons is robust and reasonably well understood [11], we focus on using reflectance spectroscopy to understand the modulation due to layer numbers in the main text.
We also include the PL spectra in Fig. R5 in the revised Supplementary Information as Supplementary Figure 9. Figure R5. Gate-dependent PL spectra from 1L/1L, 2L/1L, and 3L/1L WSe2/WS2 region of device D1. All data were taken at 4.5 K.
4. When calculating carrier density from gate voltage, it appears that the authors didn't consider the different thicknesses of the three regions. Maybe this is valid, but given the broader readership of this journal, it would be helpful if the authors can provide better justification or a reference.

Response:
We thank the reviewer for the suggestion. The AFM measurements of device D1 show a uniform thickness of 52 nm, much larger than the thickness difference between 1L/2L/3L (one layer is about 0.74 nm, see reply to comment 2). For a geometry capacitance model, = / , where n is the density of carrier, is the dielectric constant, V is the voltage effectively applied to the sample, e is the elementary charge of the electron, and d is the thickness of the dielectric. In this case, d is approximately 52 nm, with the difference between different layers having negligible effects.
In summary, this is a well designed study and the manuscript is well written. The conclusion is interesting and would indeed introduce a new control knob to the Moiré superlattice studies. However, before I can recommend acceptance, I wish the authors could consider improving their manuscript along the lines listed above.
Response: Again, we greatly appreciate the reviewer's recognition of our work. We also thank the reviewer for the comments and suggestions that help us to improve our manuscript.
Reviewer #3 (Remarks to the Author): Dongxue Chen et al. report experimental study of Moiré excitions and correlated electronic states in multilayer WSe2 / 1L WS2 heterostructure. The authors perform combined optical spectroscopy and microwave impedance measurement and show the systematic layer number dependence (1L to 3L) of intralayer exciton spectrum including Moiré effect and correlated electronic states. As far as I know this is the first systematic study of layer number dependence of Moiré excitons and correlated electronic states in WSe2/WS2 Moiré system and the experimental effort is impactful for the 2D material research community.

Response:
We thank the reviewer for the positive evaluation of our work.
However, I have a major concern about the microscopic mechanism of intralayer exciton and Moiré exciton hybridization which the authors discuss extensively in the first half of the manuscript.
In line 59 -64 in Supplementary Note 2, the authors state that Moiré potential folds the energy bands and compensates the large momentum separation of K -K' valley. However, the momentum difference which Moiré potential can compensate is only the order of Moiré reciprocal vector which is much smaller than K -K' momentum difference. I cannot completely deny the possibility, but back-of-the-envelope calculation tells that assuming that the Moiré lattice constant is ~ 8nm, and intrinsic lattice constant is ~ 0.32nm, order of N = 8nm/0.32nm = 25 times of perturbation process is required to compensate the momentum difference, which would be unlikely to happen coherently. I tried but failed to come up with different scenario. It is worth to mention that the exchange interaction, which the authors did not discuss explicitly but shown in the last term of the exciton Hamiltonian H_A in Supplementary Note 1, mixes K -K' valley excitons at non-zero momentum. (There is an experimental report regarding the mixing of K -K' valley states of Moiré exciton, PRX 11, 021027 (2021).)

Response:
We thank the reviewer for the critical comment, which helps us to reconsider and figure out the microscopic mechanism of interlayer hybridization between moiré and intralayer A excitons. We find that the hybridization is enabled by the combination of moiré-potential-induced Umklapp scattering and intervalley exchange interaction. To show this explicitly, let us first examine the nature of moiré excitons. In 1L/1L WSe2/WS2, the moiré potential can hybridize two exciton states if their momenta are differed by the moiré reciprocal lattice vectors , as displayed in Fig. R1a. Here we show that the WSe2 bright intralayer A exciton with zero center-of-mass momentum couples to the six Umklapp exciton states in the first shell. These Umklapp states are originally momentum dark, and the intervalley exchange interaction hybridizes the K and K' valley excitons at nonzero momentum that splits the exciton dispersion into two branches [12][13][14], as mentioned by the reviewer. In Fig. R1b, we show the exciton minibands at the moiré potential = 0 meV such that the bare WSe2 intralayer A exciton bands (which are represented by the red dashed curves) are trivially folded into the mini Brillouin zone (MBZ). The bright A exciton and the six degenerate Umklapp states from the lower branch of the bare dispersion are coincident at the point of MBZ and are highlighted in Fig. R1b. Now we turn on a weak = 5 meV and the hybridization between and Umklapp states splits the six-fold degenerate point into two double degenerate points and two nondegenerate points, as shown in Fig. R1c. As the moiré potential increases further to = 25 meV, the well-separated lowest three double degenerate points give rise to the moiré excitons , , and , which are highlighted in Fig. R1d. The moiré excitons inherit the component of through the Umklapp scattering and are bright. To show this, we plot the valley pseudospin vectors of the moiré exciton states , , and in Fig.  R1e-g, respectively. The north and south poles of the Bloch sphere are the valley polarized bright A exciton states | , ⟩ and | , ′ ⟩. Each moiré exciton is formed by two degenerate Kramers pairs with opposite valley pseudospins. Apparently, the pseudospin vectors have finite components along the direction of | , ⟩ or | , ′ ⟩ . On the other hand, the exciton states from the two nondegenerate points are orthogonal to and therefore dark. Because the hybridization between and Umklapp states from the upper branch of the bare dispersion is suppressed by the larger energy gap, the higher-energy exciton states at are also dark. Now we have established that the moiré exciton is a mixture of the K and K' valley excitons. On the other hand, in 2L/1L and 3L/1L WSe2/WS2, the moiré coupling is highly localized at the WSe2/WS2 interface, and the valley remains approximately a good quantum number of the bright intralayer excitons in the added WSe2 layers away from the interface. As a result, the moiré excitons at the interface can always hybridize with the valley excitons in added WSe2 layers, whether they are in K or K' valley. The interlayer hybridization decreases exponentially with the interlayer distance. Another thing I want to mention is that even though interlayer tunneling is forbidden for conduction band electrons due to symmetry as the authors mention, it is allowed for nonzero momentum electrons. Therefore, Moiré potential would enable the hybridization of intravalley conduction band electrons off resonantly between two layers. Given that interlayer tunneling is unlikely to hybridize intervalley electron states as I discuss above, it only hybridizes intravalley A exciton and B exciton states with the assist of Moiré potential off resonantly. However, A and B excitons do not hybridize within a same layer, so cannot realize A exciton -A exciton hybridization between two layers in this manner.

Response:
We agree with the reviewer that A and B excitons do not hybridize within the same layer. Therefore, the A exciton -A exciton hybridization we observed cannot be mediated by the A exciton -B exciton hybridization, which is not considered in our analysis.
I agree that the 4x4 matrix model (Eq. #(2)) captures the experimental observation, but the microscopic physics is unlikely to happen. I recommend the authors to reconsider the microscopic model carefully.

Response:
We thank the reviewer for the suggestion. We hope our detailed explanation above can convince the reviewer that the moiré-potential-induced Umklapp scattering and intervalley exchange interaction can hybridize the moiré exciton and intralayer A exciton which can be captured by the 4×4 model.
The layer number dependence of correlated electrons is well discussed and the results are convincingly presented.

Response:
We greatly appreciate the reviewer's positive comments on our work, and we particularly thank the reviewer for the constructive advice that help us to improve our manuscript.

Minor comments
1. What is the spatial resolution of MIM measurement?

Response:
The spatial resolution of MIM measurement is about 100 nm, limited by the AFM tip size.
2. For the case of 3L/1L WSe2/WS2, n=±1 gate voltage condition is different from the other cases (2L/1L or 1L/1L). Is this attributed to the existence of other bands (non-interfacial layer of WSe2) as shown in Fig. 3c? I did not find the discussion, but this is worth to be mentioned explicitly.

Response:
We are not exactly sure about the mechanism causing the difference in the gate voltage. But since it is symmetric for n=+1 and n=-1, the most likely scenario is a small difference in the twist angle in 3L/1L region compared to other regions. From the gate voltage values of the n=+1 or n=-1 states, we have estimated the twist angles, which is ~1.3° for the 3L/1L region, and ~0.9° for the 1L/1L and 2L/1L regions. The small difference can be due to a small distortion or wrinkle between the 3L/1L and other regions. It is unlikely due to other bands since the doped electrons reside in the WS2 layer while the holes reside in the WSe2 layer, which would unlikely to be symmetric as there is only one layer of WS2. We will explore it in our future study. We have added a brief discussion in the revised manuscript.
3. Line 90-92: "exciton-exciton interaction" is bit misleading since this paper is discussing exciton coupling but not exciton-exciton interaction which is rather used for many body effect such as nonlinear effect or biexcitonic process. Tunnel coupling of electrons is not regarded as electronelectron interaction for example.
Response: we agree with the reviewer on this suggestion. We have revised manuscript accordingly to avoid possible confusion. 4. Line 286 (Fig.2 caption): "Supplementary Information Note 2" instead of "Supplementary Information Note 1"

Response:
We thank the reviewer for spotting the mistake. We have corrected it in the revised manuscript.
5. In Supplementary Note 1, the value of J used in Hamiltonian H_A is missing.

Response:
We thank the reviewer for pointing this out. = 0.04 eV·nm is specified in the revised version and is referred to that used in Nature 567, 76-80 (2019), which is cited as Ref. [6] in the Supplementary Information. 6. In Supplementary Note 1, how the authors quote electron-hole total mass M=0.75m_e from 2D Mater. 2 (2015) 022001? In Fig. 4 of that paper, they define K^(1)_cb (m^(1)_cb ~ 0.28m_e) and K^(1)_vb (m^(1)_cb ~ 0.36m_e) as the bright A exciton bands, and the total mass seems to be rather M ~ 0.64m_e. However, for the dark A exciton bands, K^(2)_cb (m^(2)_cb ~ 0.39m_e) and K^(1)_vb (m^(1)_cb ~ 0.36m_e), the total mass seems to be M ~ 0.75m_e, which agrees with what the authors quote. Probably the theoretical prediction and experimental measurement of the effective mass would not be precise enough to distinguish this difference, but it is nice to be quoted properly.

Response:
We agree with the reviewer that the electron-hole total mass should be M = 0.64m_e. The total mass has been corrected and the exciton spectra in Fig. 2 have been recalculated for M = 0.64m_e in the revised version. We thank the reviewer for the suggestion. 7. Line 88 in Supplementary Note 2: Why the authors chose t_III = -0.04i as an imaginary number? Whether t_III = -0.04 or -0.04i does not make difference in terms of the eigen values of the matrix (2).

Response:
We thank the reviewer for the question. (where = I, II, III) denotes the coupling between different exciton states and its value is determined by the overlap integral of exciton wavefunctions. In principle, is a complex number and its phase depends on the phase difference between exciton wavefunctions. In the phenomenological model Hamiltonian Eq. #(2), we chose these parameters to match the optical absorption spectra observed in the experiment and we found that III = −0.04 can better reproduce the experimental results. Although III = −0.04 does not change the eigenvalues of the Hamiltonian Eq. #(2), the eigenstates are changed that affects the resonant peak height, as shown in Fig. R7  8. Line 51 in Supplementary Note 2: "shown in Fig. S1" instead of "shown in Fig. S2" We thank the reviewer for catching the typo and we have corrected it in the revised manuscript.
We have also gone through the manuscript carefully to correct other typos and grammar mistakes. We thank the reviewer for reading our manuscript carefully and his/her constructive comments that helped to improve our manuscript significantly.

Response:
We thank the reviewer for the suggestion. We adopt 0 = 15 meV and = /4 from PRB 102, 201115 (2020), which is cited as Ref. [10] in the revised version. I trust the experimental results with considerable efforts and the paper is worth to be published. However, I afraid that this unclear discussion which would mislead the community in future. Compared to the experimental efforts which the authors made, solving this problem analytically is not a big deal and I hope that the authors convince the readers properly with bit more efforts.
We sincerely thank the reviewers for their time and efforts. Following the suggestion of Reviewer #3, we have performed analytical calculations to reveal the nature of moiré excitons which are detailed in our reply below. An extensive discussion about the possible mechanism for interlayer hybridization between different excitonic states are also provided in the reply. Our observation is well explained by a phenomenological model using the 4 by 4 matrix, while the proposed exciton hybridization provides one possible microscopic mechanism of the phenomenological model. We have also revised our manuscript accordingly. With these revisions, we believe that we have addressed the reviewer's question and our manuscript is now ready for the publication in Nature Communications.

REVIEWER COMMENTS
Reviewer #3 (Remarks to the Author): I appreciate the authors for their detailed reply.
I am confused with the double headed arrows in Bloch sphere in Supplementary Figure 2 e-f which are not well defined (usually pseudospin is represented as single headed arrow). Let me interpret these as pairs of eigenstates, which are energetically degenerate (otherwise there should be time reversal symmetry breaking due to the finite |X_A,K> population which has non-zero angular momentum). Since all pseudospin states in the Bloch sphere can be represented with the superposition of these paired eigenstates which are energetically degenerate, that means there is essentially no valley mixing (all pseudospin states are energetically degenerate). I imagine that the authors solved the problem numerically and obtained these pairs of eigenstates with random orientation in Supplementary Figure 2e-f. I suspect that the numerical approach which the authors took hinders the essential understanding of the problem. I rather recommend to solve the problem analytically with some approximation to clarify the symmetry of the problem (For example, what determines the axis of the pseudospin states in Supplementary Fig. 2e-f?) I trust the experimental results with considerable efforts and the paper is worth to be published. However, I afraid that this unclear discussion which would mislead the community in future. Compared to the experimental efforts which the authors made, solving this problem analytically is not a big deal and I hope that the authors convince the readers properly with bit more efforts.

Response:
We thank the reviewer for the critical question about the valley pseudospin vectors. We indeed used the doubled headed arrow to represent a pair of degenerate eigenstates which are time-reversal counterparts. We agree with the reviewer that all pseudospin states in the Bloch sphere are degenerate eigenstates and the pseudospin vectors in Fig. 2e-f were indeed randomly chosen in the numerical simulation. Therefore, there is essentially no valley mixing as pointed out by the reviewer. To address the issue, we follow the reviewer's suggestion to solve the moiré exciton states analytically by treating the moiré potential as a perturbation. Our analytical results reveal the nature of moiré excitons in 1L/1L WSe2/WS2. Furthermore, we consider the intralayer-like and interlayer-like hybrid excitons in 2L WSe2 due to the interlayer tunneling between valence bands. We show that the intralayer-like hybrid excitons coupled to the moiré potential can give rise to the moiré excitons in 2L/1L WSe2/WS2. To understand the energy shifts of moiré excitons in 2L/1L WSe2/WS2 compared with those in 1L/1L WSe2/WS2, we propose a possible mechanism by considering the hybridization between moiré excitons and interlayer-like hybrid excitons. The similar analysis can be extended to 3L/1L WSe2/WS2. The exciton hybridization picture provides a possible microscopic mechanism responsible for the phenomenological model (Eqn. R10) that well explains our experimental observations, while the exact mechanism warrants future exploration.
The detailed analytical calculation of moiré excitons and extensive discussion about hybrid excitons are provided in the reply below and updated in the Supplementary Information. The figures of pseudospin vectors are eliminated. The manuscript has also been revised accordingly.

Nature of moiré excitons in 1L/1L WSe 2 /WS 2
To reveal the nature of moiré excitons, we first consider the WSe2 intralayer A exciton described by the effective Hamiltonian , = + ℏ 2 + | | + | | cos 2 + sin 2 where and , are the identity matrix and Pauli matrices acting on the valley space [1,2]. is the exciton center-of-mass momentum whose polar angle is and = 0.64 is the total mass of an electron-hole pair in WSe2 [3]. The eigenstates and eigenvalues of are: ±, = √ ± , ±, = + ℏ + | | ± | | Note that the two eigenstates are degenerate at = and any superposition of ±, remains the eigenstate of , . Namely, there is an emergent valley pseudospin rotational symmetry, i.e., , is invariant under any pseudospin rotation operation. However, this emergent symmetry is merely induced by combining the two A exciton states from opposite valleys together in , even when they are not hybridized at = . Since valley is a good quantum number for the bright A exciton states, we should fix  R1a) [4]. = 0.04 eV·nm, = 25 meV and = 15° [5]. Then the moiré exciton can be described by the Hamiltonian = , + R1 The moiré potential can couple two excitonic states if their momenta are differed by a primitive moiré reciprocal lattice vector with ∈ 1, ⋯ ,6 . Therefore, the bright A exciton states | , ⟩ and I thank the authors for their efforts to figure out the microscopic physics behind their observations. To couple |iX_K,↑> with |ψ^2L_ξ,Gi>, the interlayer tunnel coupling of conduction band states is also required. Given that the interlayer tunneling of the conduction band state at K point is prohibited by rotational symmetry in 2H stacked bilayer TMDs, I am not sure this is plausible. However, I cannot deny the possibility that some Umklapp scattered conduction band state may carry proper angular momentum for the interlayer tunnel coupling. The origin of X_IV state is supported without this argument of this interlayer exciton coupling, so it may not be critical for the qualitative interpretation of the data. Again, I thank the authors for their efforts to deepen the discussion. I think the paper is ready for publication.