Observation of giant dipole moments of interlayer excitons via layer engineering

Domain: physics
Published: 2025-11-27
Editorial outcome: major_revision

Abstract
Interlayer excitons in van der Waals (vdW) heterostructures (HSs) have garnered significant attention due to their unique properties, including prolonged lifetimes and long-range transport. While extensive studies have been conducted on interlayer excitons in HSs composed of different monolayers, research on HSs formed by multilayer constituents remains limited, particularly regarding dipole moments, which play a crucial role in light-matter interactions. In this study, we investigate the dipole moments of interlayer excitons in multilayer WS₂ and InSe HSs using the quantum-confined Stark effect. Our findings reveal that the dipole moment increases monotonically with the number of layers in InSe or WS₂, reaching a maximum of 3.18 e nm, which is the largest value reported to date. Consequently, the dipole-dipole interaction is enhanced with the increasing layer number, as demonstrated by excitation power-dependent measurements. Ab initio calculations further support our experimental results, indicating the delocalization of the excitonic wavefunction with increasing layer thickness. Our findings introduce a novel layer-engineered mechanism for tuning the dipole moments of interlayer excitons in vdW heterostructures, paving the way for manipulating many-body interactions in low-dimensional quantum systems.

Introduction
Heterostructures (HSs), formed by vertically stacking two different types of two-dimensional (2D) materials, exhibit exotic optoelectronic and quantum properties that are unattainable in their individual constituents1–3. Unlike their intralayer counterparts, interlayer excitons (IXs) are generated when electrons and holes are spatially separated across different layers, resulting in fundamentally distinct behaviors4–6. For example, these spatially indirect excitons demonstrate prolonged lifetimes—an order of magnitude longer than those of intralayer excitons—and possess long-range transport properties5. This leads to intriguing phenomena such as Bose–Einstein condensation at elevated temperatures and low-threshold lasing7. Moreover, the out-of-plane dipole moment characteristic of IXs allows for significant tunability (over 100 meV) in their spectra through the application of external fields, a phenomenon known as the quantum-confined Stark effect8.

Recently, IXs trapped in a Moiré potential created by a precise “magic” twist of the constituent layers have given rise to a multitude of quantum phenomena, including superconductivity and fractional quantum anomalous Hall states9. HSs provide a versatile platform for various fields, including nanoelectronics, condensed matter physics, and quantum optics, with properties that can be tailored through multiple degrees of freedom, such as material selection and stacking configurations.

In previous studies, the quantum behavior of IXs formed within hetero-bilayers has been extensively investigated, where electrons and holes are confined within their respective constituent monolayers, typically exhibiting type-II band alignment3. Recent research has expanded the focus from bilayer HSs to trilayer (or above) systems, unveiling new types of IXs. For instance, spatially trapped IXs have been observed by sandwiching a bilayer hBN between MoSe₂ and WSe₂ monolayers10,11. Additionally, quadrupolar excitons—such as those with one hole located in the central layer and two electrons residing in the top and bottom layers, respectively—have been identified in trilayers like WSe₂/WS₂/WSe₂ HS (as well as WSe₂/WS₂/WSe₂ and WS₂/WSe₂/WSe₂ HSs)12–16. These quadrupolar excitons exhibit a field-dependent dipole moment and reduced dipole-dipole interaction. In these multilayer systems, the carriers (either electrons or holes) that form the IXs remain confined within their specific monolayers, meaning that the dipole moment of these IXs is constrained by the interlayer spacing between the constituent monolayers.

Recently, pioneering works have shown that by extending one constituent material from monolayer to multilayer, the photoluminescence properties of IXs—such as resonance energy and valley lifetime—can be modified due to the renormalized band structures that arise with increasing layer number17,18. However, the layer-dependent behavior of the dipole moment of IXs in multilayer HSs has yet to be explored.

In this study, we systematically investigate the variation of interlayer dipole moments in multilayer HSs using the quantum-confined Stark effect. We observe an unusually large interlayer dipole moment in multilayer WS₂/InSe system with the recorded value up to 3.18 e nm, in strikingly contrast to the general believes that IXs are confined between adjacent layers. Through continuously varying the layer number of InSe from 3 layers (3L) to 6L, a monolithic increase of dipole moment of IX is observed, which is evidently manifested with the increased energy shift under the same applied field (Stark effects). Similar trend is also found when the layer number of WS₂ changed from 2L to 3L. The repulsive dipole-dipole interaction is enhanced with the larger dipole moment, which is unambiguously manifested in the power-dependent measurements. The ab-initio calculation results support our measured results, reveals the delocalization of carriers with the layer number which underpins the enhanced dipole moment of IXs. Our findings shed light on the layer-engineered dipole moment of IXs in multilayer HSs, showing the new paradigm for the tunable photoelectronic and quantum devices at low-dimension19–26.

Results
Variation of dipole moment of IXs with different layer number of InSe

A representative dual-gate device is schematically illustrated in Fig. 1a, featuring a bottom gate (Au film) and a top gate that independently control the voltage applied to each, effectively eliminating the influence of static doping (see details in Supplementary Note S1). The HSs are formed using WS₂ and InSe, both protected by top and bottom hexagonal boron nitride (h-BN) layers. Following the strategy in previous work27, we select 2L-WS₂ and multilayer (from 3L to 6L) InSe to achieve type-II band alignment at the Γ point (Fig. 1b). This alignment circumvents the momentum mismatch issues typically encountered by IXs at the K point, which require precise lattice matching of the constituent materials. Consequently, IX transitions in the multilayer WS₂/InSe system are insensitive to the twisted angle between the van der Waals layers, providing a viable platform for studying the dipole behavior of multilayer HSs. To directly assess the influence of layer number on the photoluminescence properties of IXs, we carefully select monolithic InSe layers of varying thicknesses (specifically, 4L and 5L) to combine with 2L-WS₂ (as shown schematically in Fig. 1a, with the inset in Fig. 1c showing a microscopic image). This approach ensures nearly identical experimental conditions for the device, aside from InSe thickness. For clarity, we denote the HS as mL/nL, where m represents the layer number of WS₂ and n represents the layer number of InSe.

Figure 1c presents the photoluminescence (PL) spectra for the two HS regions, i.e., 2L/4L and 2L/5L combinations. In addition to the PL signatures from pristine WS₂ and InSe layers (with a direct comparison of IXs to intralayer excitons from the constituent materials shown in Supplementary Fig. S2), IXs from these two HS regions are observed in the lower energy range of 850 nm to 900 nm, consistent with previously reported results27. The resonant energy of IXs exhibits a pronounced redshift as the thickness of the InSe layer increases, which is attributed to band structure renormalization.

IXs in vdW HSs exhibit a static out-of-plane dipole moment due to the spatial separation of electrons and holes across different layers. With the external vertical field applied, the energy shift of dipolar IX would be induced, i.e., ΔU = |p|E_HS, where p = ed represents the dipole moment (with e being the electron charge and d the displacement between the electron and the hole which is also known as dipole size). Utilizing this well-known Stark effects, the dipole moment of IX can thus be extracted through field-dependent PL spectra. For the 2L/4L HS region (Fig. 1d), the IX exhibits a blue shift of around 86 meV from 1.404 eV to 1.490 eV with the electric field increased from 0 to ~45 mV/nm. In contrast, for the 2L/5L HS region (Fig. 1e), the IX exhibits a blue shift of around 106 meV with the energy shift from 1.373 eV to 1.479 eV under almost the same variation of the electric field. The difference is more evident in Fig. 1f where the evolution of peak position of IXs are extracted from Fig. 1d and Fig. 1e, respectively. The distinct slopes represent different dipole moments (|p| = ΔU/|E_HS|), which are calculated as |p| ≈ 1.87 e nm (2L/4L) and |p| ≈ 2.35 e nm (2L/5L) separately. These extracted dipole moments significantly exceed the previously reported values (0.5–0.8 e nm)28 for HSs composed of vdW monolayers, suggesting that the dipole size of the multilayer HS systems remarkably surpasses the interlayer spacing between constituent vdW layers.

Layer-engineered out-of-plane dipole moment

To further investigate the dependence of increasing dipole moments with the layer number of InSe, we fabricated additional 2L/3L and 2L/6L HSs (Fig. 2a). The layer numbers of InSe flakes were identified via PL spectroscopy (see Supplementary Fig. S3). The IX shows an unambiguous and continuous redshift (Fig. 2c) with the increasing layer number of InSe due to the band structure renormalization, which is consistent with the previous work.

The evolution of IXs, with PL spectra normalized for each field strength, is presented in Fig. 2b for different layer combinations. For all HSs, the corresponding IX exhibits a nearly linear blue shift with increasing vertical electric field. The rate of blue shift with field strength (i.e., ΔU/|E_HS|) unambiguously increased with the number of InSe layers, as indicated by the extracted peak positions obtained through Lorentzian fitting (see Supplementary Figs. S9–S13) shown in the bottom image of Fig. 2b. The calculated dipole moments of IXs show a notable increase, ranging from ~1.35 e nm for the 2L/3L combination to around 2.68 e nm for the 2L/6L combination. In addition to the HSs presented in the main text, we also fabricated a series of similar HSs, which were fabricated using the same method to ensure consistency and reliability of the results. (see Supplementary Figs. S14–16) Additionally, Supplementary Figs. S18 and S19 illustrates the IX evolution under negative fields and larger positive fields. Under negative fields, the PL of IX demonstrates a clear near-linear redshift, while its intensity decreases dramatically, attributed to reduced electron-hole wavefunction overlap due to Coulomb forces (in contrast, PL intensity increases with positive fields). As the negative field strength further increases, the IX energy remains constant, likely due to a charging effect also noted in previous studies28. On the other hand, as the positive field continues to increase, the blue shift of IX begins to saturate. Band structure analyses suggest that at larger positive fields, the IX transition shifts from type-II band alignment at the Γ point to the InSe intralayer exciton transition, resulting in an unchanged peak position in the measured PL with further increases in positive field (Supplementary Fig. S17). Nevertheless, the linear Stark shift for all HSs is around 100 meV (Supplementary Fig. S19), ensuring the accuracy of the extracted dipole moments for the corresponding HSs. Through both the electric and layer engineering, the energy of IX can be continuously tuned across a broad range, as indicated in Fig. 2e and Supplementary Fig. S27.

It is anticipated that as the dipole size increases, the overlap of the electron-hole wavefunction is correspondingly reduced, leading to a prolonged lifetime for interlayer recombination. The lifetime measurements for different layer combinations, shown in Fig. 2f, unambiguously confirm this trend, with the lifetime increasing from 459 ps for the 2L/3L to 1069 ps for the 2L/6L HS. This significant increase in lifetime further supports the relationship between dipole size and recombination dynamics in these systems.

First-principle calculation

To further elucidate the behavior of IXs in multilayer WS₂/InSe HSs, we employed the GW-BSE (GW-Bethe-Salpeter Equation) method29,30 to investigate their electronic structure and excitonic properties in detail (for the computational details, refer to Supplementary Note S2). However, due to the significant lattice mismatch between WS₂ and InSe, an especially large supercell composed of these two layers would be required for the full computation of the whole system. Instead, without loss generality, a simplified model is proposed to give the qualitative illustration of our observation in our experiment.

In this model, the hole is fixed at the bottom selenium (Se) atom of the InSe layer (as indicated by blue stars in the bottom panels of Fig. 3a–c) to simulate hole confinement within the WS₂ layer. This approach mimics the experimental scenario where holes remain localized in WS₂, allowing us to study the electron behavior in InSe. In Supplementary Fig. S23, we systematically compare the influence of fixing the electron (Supplementary Fig. S23a) versus the hole (Supplementary Fig. S23b) on the dipole moment calculation for WS₂/WSe₂, where their lattices exhibit a close match. The resulting dipole sizes from these two configurations are nearly identical. Furthermore, we calculated the hole wave function distributions by fully considering both 1L-WS₂/1L-WSe₂ and 1L-WS₂/2L-WSe₂ configurations, as well as by only considering the 1L-WSe₂ and 2L-WSe₂ configurations with the electron fixed at the edge of the WSe₂ layer (which aligns closely with our simplified model). The results show that the calculated hole wave function distributions are similar (as depicted in Supplementary Fig. S24). The primary difference lies in the dipole moment calculated when only considering WSe₂, which is significantly smaller than that derived from the full configurations due to the absence of interlayer spacing. However, the increase in dipole moment associated with the increasing layer number of WSe₂ remains consistent across both configurations. These analyses validate that, although the model simplifies the system by eliminating one of the constituent materials in the HS, the carrier wave function distributions and the layer-engineered dipole moment increase can still be accurately reflected by our simplified model.

Figure 3a–c present the top views (top panels) and side views (bottom panels) of the wave function distribution of electrons, with the hole fixed, for 1L-, 2L-, and 3L-InSe. Due to Coulomb attraction, the electron distribution is centered in the x-y plane (as observed in the top views). Moreover, there is a pronounced reduction in the probabilities of electron distribution as the layer number of InSe increases, attributed to Coulomb screening. The side view of the wave function distribution reflects the trend observed in our experiments. As shown in Fig. 3a–c, while the electron remains confined within the InSe layers where the hole is fixed at the bottom Se atom, its spatial extension systematically shifts toward upper layers with increasing InSe thickness.

By integrating the probability density (|ψ|²) over the x-y plane, we quantitatively characterize the z-direction distribution (represented by the red curves adjacent to each side view), revealing that the excitonic wavefunction in 2L-InSe is strongly localized in the bottom layer nearest to the hole position, whereas in 3L-InSe it becomes nearly uniform across all layers, a difference likely originating from fundamental symmetry distinctions between even- and odd-layered InSe systems. The effective Bohr radius is calculated by r_B = φ*rφ where r is the relative distance between electron and fixed hole. The resultant calculated radius r_B is 2.54 Å for 1L-InSe, 5.78 Å for 2L-InSe, and 10.99 Å for 3L-InSe, whose value is lower than the measured results in Fig. 2c (e.g., 13.5 Å for 2L/3L system) owing to the elimination of WS₂ lattice in the calculation.

Due to the limitations of our computational capabilities, we considered up to 3 layers of InSe. However, the trends observed in these calculations align closely with our experimental findings. The theoretical interlayer spacing increases by 3.24 Å from 1L to 2L and by 5.21 Å from 2L to 3L, which closely parallels the experimental increments of 5.2 Å (from 3L to 4L), 4.7 Å (from 4L to 5L), and 3.3 Å (from 5L to 6L). Additionally, the delocalization of electrons—indicated by the reduction of electron-hole wave function overlap with increasing layer number of InSe—supports the observed increase in dipole moment and is consistent with our lifetime measurement results. This coherence between theoretical predictions and experimental data underscores the robustness of our model and its relevance in understanding the behavior of excitons in multilayer InSe systems.

Evolution of dipole moment with the layer number of WS₂

In addition to varying the layer number of InSe, we also explored the impact of WS₂ thickness on the dipole moment. Two HSs—2L-WS₂/6L-InSe and 3L-WS₂/6L-InSe—were fabricated, all encapsulated in h-BN layers (as shown in the microscopic image in Fig. 2a). Electric field-dependent PL measurements (ranging from 0 to 34.9 mV/nm) demonstrate characteristic Stark shifts. The 2L/6L configuration exhibits a 93.6 meV blue shift (from ~1.3219 to 1.4155 eV, as shown in Fig. 4a), while the 3L/6L structure shows a larger 110.3 meV shift (from around 1.2876 to 1.3979 eV, depicted in Fig. 4b) under nearly identical electric fields. Linear regression analysis of these shifts (illustrated in Fig. 4c) yields dipole moments of 2.68 e nm (2L/6L) and 3.18 e nm (3L/6L), respectively. Notably, the latter value represents, to our knowledge, the largest IX dipole moment ever reported in vdW HSs.

Employing a similar methodology as in our previous calculations (Fig. 3), where we fixed the electron position at the edge of WS₂ layer to model 6L InSe while varying WS₂ thickness, generate excitonic wave functions whose spatial distributions (Fig. 4d, e) provide microscopic insight into the enhanced dipole moments observed in thicker WS₂ configurations. The side-view depiction reveals that, the wave function of holes in WS₂ exhibits relatively uniform interlayer delocalization. Specifically, in 2L-WS₂, the hole wave function shows slight concentration in the layer proximal to the electron, while in 3L-WS₂, it becomes more evenly distributed across all layers. Z-direction distribution shows the effective center of the hole wave function (red dashed line) shifts away from the fixed electron position (black dashed line), with the effective Bohr radius of 4.24 Å (2L-WS₂) and 7.7145 Å (3L-WS₂) — qualitatively consistent with our experimental observation of a 5 Å increment in the 2L/6L to 3L/6L HSs.

This variation aligns qualitatively with the experimentally observed changes in the electric dipole moment, yet exhibits slight discrepancies in magnitude. Models that fix hole locations may not fully account for dynamic behavior. For instance, in the actual heterostructure, the holes are not completely fixed in the WS₂ layer but can migrate within and between layers. Additionally, the interfacial effects of the heterostructure, such as defects or doping at the contact surfaces, are often neglected. These interfacial effects can lead to non-radiative recombination and enhance the dielectric screening effect, thereby reducing the exciton binding energy.

Our study of IXs in multilayer HSs reveal that these systems exhibit exceptional electrical tunability due to giant Stark effects. The interlayer excitonic transitions in multilayer HSs cover a broad spectral range from ~1.25 eV to ~1.55 eV (Supplementary Fig. S27), offering promising opportunities for developing advanced photonic, nonlinear optical, and quantum devices. Importantly, the excitonic dipole moment can be precisely tuned by varying the thickness of constituent materials, enabling controlled manipulation of dipole-dipole interactions.

Enhanced dipole-dipole interaction with the increasing layer number

The existence of an out-of-plane dipole moment of IX leads to mutual interactions, which manifest as a blue shift with increasing IX density. As the dipole moment increases, these mutual interactions are expected to be enhanced. Figure 5a–d show a clear blue shift with increasing excitation power (the excited exciton density is linearly proportional to the excitation power) across different layer combinations. Previous work26 indicates that the energy shift can be estimated using the formula:

ΔE_XX = n_0 e² d / (ε_0 ε_HS) (1)

where ΔE_XX represents the energy shift due to the dipole-dipole interaction, n_0 is the exciton density, ε_0 is the vacuum permittivity, ε_HS is the relative permittivity of the heterostructure, e is the electron charge, and d is the dipole size of the IX.

Figure 5e illustrates the IX position as a function of excitation power for different layer combinations, indicating that the energy shift rate (m = ΔE_XX/P where P represents excitation power) increases with the layer number of WS₂ or InSe. The inset in Fig. 5e compares the corresponding dipole moments with the energy shift rate, revealing a strong correlation. These results clearly demonstrate that the dipole-dipole repulsion interaction is significantly enhanced due to the increased dipole moment engineered by the layer number.

Last but not least, while the layer configuration up to the 3L/6L combination exhibits the largest dipole moment observed in our experiments, it is clear that the upper limits have not yet been reached (see Supplementary Fig. S25). Two factors could lead to the disappearance of IXs with increasing layer number. First, band structure alignment plays a crucial role. As the layer number increases, the type-II band structures (illustrated in Fig. 1b) may become invalid, resulting in interlayer-intralayer exciton transitions. Second, binding energy is another critical factor. As the dipole size increases, the binding energy correspondingly decreases due to reduced Coulomb attraction. When the binding energy falls below the thermal energy of the environment, IXs can no longer be observed. Detailed analyses can be found in Supplementary Note S3, which provides upper limits for the dipole moment: ~6.28 e nm due to the limitations by band structure alignment and about 3.85 e nm due to the limitations by binding energy at 77 K. The latter estimation can be increased with the decreased temperature.

Methods
Device fabrications

Gold (50 nm) and titanium (5 nm, adhesion layer) films were sequentially deposited on a silicon substrate by electron-beam evaporation at a deposition rate of 1 Å/s. Few-layer graphene, bilayer WS₂, multilayer InSe, and hexagonal boron nitride (h-BN) flakes were mechanically exfoliated onto polydimethylsiloxane (PDMS) stamps. The HSs were assembled using a polypropylene carbonate (PPC)-assisted dry transfer method with precise alignment, followed by dissolution of the PPC stamp in acetone. The h-BN thickness was characterized by atomic force microscopy (Bruker Dimension Icon).

Optical measurements

All optical measurements were performed using a bright-field/dark-field confocal microscope. The photoluminescence (PL) spectrum was measured using a HR550 Horiba Jobin Yvon spectrometer. PL spectra were measured in an optical cryostat (Linkam) with a 532 nm laser excitation. A 50× objective lens with a numerical aperture of 0.5 was used. For time-resolved photoluminescence (TRPL) measurements, a second harmonic 1064-nm (532 nm) Ti:sapphire femtosecond laser beam (Coherent Chameleon Ultra II) was used to illuminate the sample. The laser had a repetition rate of 80 MHz. The signal was collected using a 50× objective lens (LCPLANN, NA = 0.65, OLYMPUS, JAPAN). The final signal was sent to a single-photon detector (MPD PDM Series), and the output was recorded using a Picoharp 300 for time-correlated single-photon counting (TCSPC) measurements.

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Zhu et al. investigate interlayer excitons (IXs) in van der Waals heterostructures (HSs) composed of multilayer WS₂ and\nInSe. Using photoluminescence (PL) spectroscopy under applied electric fields, the authors demonstrate that the dipole\nmoment of IXs increases monotonically with the layer number of either InSe or WS₂, reaching a record value of 3.18 e·nm.\nThis behavior is attributed to the delocalization of electron wavefunctions in thicker layers, supported by GW-BSE\ncalculations. The topic is of interest for light-matter interaction however the result is presented in a rather confusing way and,\nin my opinion, does not justify enough improvement over previous IX or hIX papers. I cannot suggest publishing in high\nimpact journal like nat comms, a revised version will be more suitable for more specialized journal like npj 2d mater appl,\nComm Phys or PRB.\n1. The layer dependent Gamma transition was previous studied systematically (ref. 25). The authors claim their main finding\non top of that is the electric field dependence, i.e. very large dipole moment of over previous works. However, I find this a\nhard sell. The point of pursuing large dipole moment is: 1) enabling large spectra tunability in Stark shift 2) introducing large\ndipolar repulsive/attractive interaction to realize large IX diffusion or collective behavior like quadrupolar excitons,\nrespectively. Authors fail to introduce advancement in these two crucial fields, for 1) their Stark shift saturate after 0.03 V/nm,\nresulting in similar spectra tunability over previous papers. From the way the authors present their data I cannot get clear\npicture at higher field, as Fig4 reaches the conventional field strength but present very few line cuts at high field. For 2) I do\nnot see any exciton density dependent characterization or many-body effect.\n2. Following previous comment, despite the claim of having ‘record high’ dipole moment to meet the eye, all the main\ncharacterizations like dipole extraction are confined within 0.03 V/nm. This does not make fair comparison with other system\nshowing continuous linear Stark shift towards the 0.3 V/nm or larger field range. In other words, this system limits the useful\nfield range one order of magnitude lower than conventional vdW devices. The reason could be due to the intrinsic Gamma\ntransition for this largely layer-engineered structure. As the effective e-h separation increases the intrinsic dipolar moment, it\nalways risk reducing exciton oscillator strength or binding energy, which results in shift saturation at very low field. Some PL\nlinecuts in Supp info also show quite dim emission which suggest weak oscillator strength. In comparison the hIX or every-\nother-layer IX e.g. (ref. 11) may show a better balance with both enhanced dipole moment as well as sufficient oscillator\nstrength due to interlayer tunneling, which stabilize the field dependence of dipole. In this work when it goes to few layer-few\nlayer structure the interlayer tunneling is simply not strong enough, hence the very limited range of Stark shift. In a word the\nrepresented data does not show enough scientific merits over previous IX system, thus I cannot agree with the technical and\napplication potential claimed by the authors.\n3. Some typos are found in line 49 it should be ‘every-other-layer exciton’ rather than every-other exciton.", "reviewer_2": "The submitted manuscript, \"Observation of Giant Dipole Moment of Interlayer Excitons in Multilayer Heterostructure\", reports\na systematic study on interlayer excitons in multilayer WS₂/InSe heterostructures. By varying the thickness of constituent\nlayers, the authors demonstrate a prominent increase in exciton dipole moment, reaching up to 3.18 e·nm — the largest\nvalue reported to date in van der Waals heterostructures. These findings are substantiated by quantum-confined Stark effect\nmeasurements and supported by ab initio simulations. The manuscript offers valuable insight into dipole engineering via\nlayer number control, thus extending the design toolkit for next-generation infrared and excitonic optoelectronic devices.\nNotably, the authors reveal that the interlayer excitonic wavefunction becomes increasingly delocalized as the thickness of\nInSe or WS₂ increases. This delocalization underlies the enhancement of the vertical dipole length beyond the conventional\nvdW gap distance. The study combines careful device design, spectroscopic analysis, and theoretical calculations to\nprovide a comprehensive picture of dipole evolution in such multilayer systems.\nGiven the novelty and potential impact of the results, I find this manuscript to be of strong interest to readers of Nature\nCommunications. However, I recommend the authors address the following concerns before it is suitable for publication:\nMajor Concerns:\n1. Lack of Reversed Field Data:\nWhile the manuscript provides compelling evidence of linear Stark shifts under positive gate bias, it lacks data under\nreversed (negative) field direction. Since a hallmark of dipolar excitons is a symmetric energy response to field reversal, this\nomission weakens the claim. The authors should either present reversed-field data or clearly explain why it is not available,\nand whether any asymmetry arises from built-in fields or device structure.\n2. WS₂ Emission Behavior in Heterostructures (Fig. 1d):\nIn Figure 1d, the WS₂ exciton peak within the heterostructure region exhibits a shift in both position and lineshape compared\nto pristine WS₂. This suggests possible charge transfer or interface interactions. The authors should clarify whether these\neffects influence the interpretation of interlayer exciton resonance and whether they affect the extraction of Stark shifts.\n3. Color Similarity in Figure 1d:\nThe PL spectra of 4L-InSe and 5L-InSe in Figure 1d are rendered in colors that are difficult to distinguish (cyan vs aqua\ngreen). This reduces the figure's clarity and accessibility. The authors are encouraged to choose more distinguishable colors\nor adopt different line styles to improve visual clarity.\n4. Clarify Theoretical Assumptions on Carrier Fixation\nThe theoretical modeling assumes either the electron or the hole is fixed at a certain atomic layer (e.g., bottom Se in InSe) to\nsimplify exciton wavefunction calculations. However, the justification for this approximation is not well explained in the main\ntext. Given the importance of wavefunction asymmetry in determining the dipole moment, the authors should clarify why this\nassumption is valid, what physical behavior it aims to reproduce, and how it affects the accuracy of the extracted dipole\nmoments.\n5. Clarify Treatment of Interlayer Coupling in Simulations:\nThe exciton dipole enhancement is attributed to wavefunction delocalization across layers, but the manuscript does not\nclearly explain how interlayer coupling is treated in the simulations. The authors should briefly clarify whether and how\ninterlayer hybridization is included when calculating the electron wavefunction distribution, as this directly impacts the\nextracted dipole trend.\n6. Discuss the Upper Limit of Dipole Moment\nWhile the authors report record-high excitonic dipole moments, the manuscript lacks a discussion on the theoretical and\nexperimental upper bounds of dipole length in such multilayer heterostructures. It would be valuable to briefly address what\nlimits the maximum achievable dipole moment—e.g., exciton binding energy, dielectric screening, or wavefunction\ndelocalization saturation—and whether further increases in layer number are expected to continue enlarging the dipole\nmoment or lead to diminishing returns.\nOverall Assessment:\nThis manuscript reports a compelling study of tunable interlayer excitons with giant dipole moments in multilayer WS₂/InSe\nheterostructures. The results are novel, experimentally robust, and supported by theory. Clarifying the modeling\nassumptions, addressing dipole symmetry under reversed fields, and discussing the upper bound of dipole strength would\nfurther improve the work. With minor revisions, the paper is suitable for publication in Nature communications.", "reviewer_3": "The manuscript titled “Observation of Giant Dipole Moment of Interlayer Excitons in Multilayer Heterostructure” presents a\nsystematic investigation of dipole moments in WS₂/InSe heterostructures with varying layer numbers.\nThe study demonstrates that the dipole moment increases monotonically with the number of InSe or WS₂ layers, reaching a\nmaximum value of 3.18 e·nm in the 3L WS₂/6L InSe configuration.\nThe experimental data are well-presented, detailed, and informative, though the findings are not entirely unexpected.\nWhile the work is solid, I recommend acceptance after revisions to address the following points:\n1. The manuscript examines 2L WS₂/nL InSe (n=3–6), but 1L- and 2L-InSe cases are absent. What is the rationale for\nomitting these configurations?\nAdditionally, the WS₂ thickness is fixed at 2L in most cases. What would be the expected behavior for 1L WS₂/nL InSe\nheterostructures? A brief discussion and experiment data on this would strengthen the study’s comprehensiveness.\n2. The results suggest that thicker heterostructures yield larger dipole moments, with the maximum observed in 3L WS₂/6L\nInSe. Does this trend continue beyond 6L InSe or 3L WS2? Is there a theoretical or experimental upper limit to the dipole\nmoment in such systems? A discussion on this would provide deeper insight.\n3. While PL spectroscopy effectively probes interlayer exciton energies, sometime reflectance measurements could offer\nadditional insights—particularly in distinguishing intralayer exciton contributions and hybrid interlayer exciton states.\nIncluding such data would allow direct comparison with prior studies and enhance the manuscript’s robustness.\n4. The manuscript contains numerous spelling errors (e.g., References [5, 9, 13, 14, 19, 30, 31…]), suggesting insufficient\nattention to detail. Journal name formatting is inconsistent (e.g., “Nature Communications”, “Nat Commun”, “Nat Photonics”).\nThe references should follow a uniform style (preferably abbreviated journal names, e.g., Nat. Commun., Nat. Photon.).\nBest regards,"}, "author_response": "Response letter for the manuscript (NCOMMS-25-35571) entitled “Observation of Giant Dipole\nMoments of Interlayer Excitons via Layer Engineering”\nReviewer 1\nZhu et al. investigate interlayer excitons (IXs) in van der Waals heterostructures (HSs) composed of\nmultilayer WS₂ and InSe. Using photoluminescence (PL) spectroscopy under applied electric fields, the\nauthors demonstrate that the dipole moment of IXs increases monotonically with the layer number of either\nInSe or WS₂, reaching a record value of 3.18 e·nm. This behavior is attributed to the delocalization of electron\nwavefunctions in thicker layers, supported by GW-BSE calculations. The topic is of interest for light-matter\ninteraction however the result is presented in a rather confusing way and, in my opinion, does not justify\nenough improvement over previous IX or hIX papers. I cannot suggest publishing in high impact journal like\nnat comms, a revised version will be more suitable for more specialized journal like npj 2d mater appl, Comm\nPhys or PRB.\nResponse: We thank reviewer for the feedback and appreciate the time took to review our work. The major\ncontributions of our work to the fields of IXs can be summarized in the following:\nUnveiling the Layer-Engineered Dipole Moment of IXs in Heterostructures: Our study is, to the best of our\nknowledge, the first systematic investigation of the layer-dependent behavior of the dipole moment of IXs in\nheterostructures. We find that the dipole moment of IXs can be monotonically tuned with the increasing number\nof layers, achieving a record-high dipole moment of approximately 3.18 enm. In previous studies, either the\ndipole moment of IXs in heterostructures or the excitons in every other layer of homotrilayers remained fixed.\nOur work paves the way for exploring tunable low-dimensional devices.\nRevealing the Delocalization of Carrier Wavefunctions via Ab Initio Methods: The mechanism of\ndelocalization of electron or hole wavefunctions increases with the number of layers, as demonstrated by our\nab initio calculations. This finding aligns perfectly with the observed increase in dipole moment and prolonged\nlifetime as the layer number increases.\nObserving Enhanced Dipole-Dipole Interactions with Increasing Layer Number: Following the reviewers'\nsuggestions, our power-dependent measurements indicate that dipole-dipole interactions are significantly\nenhanced with the increasing dipole moment. This enhancement may have important implications for the fields\nof Bose–Einstein condensation and high-temperature superconductivity [1, 2].\nOur work provides substantial experimental and theoretical evidence to support these findings. In response to\nthe reviewers' questions, we have provided detailed point-to-point responses below.\nComment 1. The layer dependent Gamma transition was previous studied systematically (ref. 25). The\nauthors claim their main finding on top of that is the electric field dependence, i.e. very large dipole moment\nof over previous works. However, I find this a hard sell. The point of pursuing large dipole moment is: 1)\nenabling large spectra tunability in Stark shift 2) introducing large dipolar repulsive/attractive interaction to\nrealize large IX diffusion or collective behavior like quadrupolar excitons, respectively. Authors fail to\nintroduce advancement in these two crucial fields, for 1) their Stark shift saturate after 0.03 V/nm, resulting\nin similar spectra tunability over previous papers. From the way the authors present their data I cannot get\nclear picture at higher field, as Fig. 4 reaches the conventional field strength but present very few line cuts at\nhigh field. For 2). I do not see any exciton density dependent characterization or many-body effect.\nOur response: We thank the reviewer for this insightful comment. The major contribution of our work is the\nunveiling of the layer-engineered dipole moment of interlayer excitons (IXs) in heterostructures, which enables\nthe observation of a giant dipole moment (~3.18 enm) in the experiments. While previous study [3] has explored\nlayer-dependent behaviors of IXs (PL peak position) at the Γ point, which is attributed to the renormalized band\nstructure as the number of layers increases, our findings present distinct advancements: (1) We are the first to\nreveal the layer-engineered dipole moment of IXs in heterostructure experimentally. (2) We achieve a record-\nhigh dipole moment in heterostructures. (3) We realize enhanced dipole-dipole interactions through layer\nengineering (following the reviewr’s suggestions).\nFor the reviewer’s first concern on spectra tunability by Stark effect:\nAccording to the dipole model, i.e., Δ𝐸 = −𝒑∙𝑬 where 𝒑 is the dipole moment and 𝑬 is the external\nelectric field, the Stark shift (ΔE) will be larger for a larger dipole moment under the same applied electric field.\nThis relationship is unambiguously confirmed in our experiment. However, a larger dipole moment does not\nnecessarily lead to a broader spectral range that can be tuned by the electric field. As we analyze in the following,\nwe find that the extent of energy shift induced by the external field is actually determined by the band alignment\nof the constituent materials, rather than the dipole moment.\nAs shown in Figure R1a, the multilayer InSe and WS form a type-II band alignment, with the IX transition\n2\noccurring between the conduction band minimum (CBM) of InSe at the Γ point and the valence band maximum\n(VBM) of WS , also at the Γ point. Figure R1b presents a simplified band structure that corresponds to state 2\n2\nshown in Figure R2.\nFigure R1. (a) Band structures of InSe and WS showing type-II band alignment. (b) Simplified band alignment\n2\nfor IX transition.\nWith a positive external field applied (transitioning from state 2 to state 3 in Figure R2), the CBM of InSe\nand the VBM of WS move further apart in the energy domain, resulting in a blue shift of the IX energy. As the\n2\npositive field is further increased (transitioning to state 4), an interlayer-to-intralayer exciton transition occurs,\nwhere the VBM of WS becomes lower than the VBM of InSe. In this scenario (state 4), the type-II band\n2\nalignment for the IX transition is no longer valid. With an even greater increase in the field (state 5), the\nintralayer exciton emission from InSe, which cannot be tuned by the electric field, dominates, resulting in a\nconstant PL energy. Conversely, under a negative (reversed) electric field (i.e., transitioning from state 2 to state\n1 in Figure R2), the energy experiences a corresponding red shift.\nThe band structure analyses align perfectly with the experimental results when the electric field extends\nbeyond the region of linear Stark effects. As shown in Figure R3a, for the 2L/3L heterostructure, the significant\nenergy difference between the IX and the InSe intralayer exciton allows for continuous tuning of the energy\n(blue shift) as the field increases beyond 80 mV/nm. However, a higher field cannot be applied due to limitations\nin the voltage that the device can withstand. In contrast, for the 2L/4L, 2L/6L, and 3L/6L heterostructures\n(Figures R3b-d), the energy blue shift saturates as the IX energy approaches the energy of the InSe intralayer\nexciton (indicated by the green arrows). To achieve a larger tuning range for the IX, alternative material\ncombinations with a greater band contrast could be explored.\nNevertheless, since the primary focus of our work is to investigate the layer-dependent behavior of the\ndipole moment of IXs, we adopted Stark effect measurements as our characterization method. The linear Stark\neffect, resulting in an energy shift of around 100 meV, is sufficient for extracting the dipole moment of the\ncorresponding IX.\nFigure R2. Schematic illustration of the evoluation of band structures of multilayer InSe/WS heterostructure\n2\nwith external field.\nFigure R3. Evolution of IX emission with electric field for different combinations of heterostructures: 2L/3L\n(e), 2L/4L (f), 2L/6L (g), and 3L/6L (h). (a-d) Corresponding PL spectra at zero electric field.\nRevision: Figure R2 and Figuer R3 were added as Supplementary Figure 17 and Figure S19 in the revised\nsupplementary materials.\nThe discussion of the saturation of blue shift with increasing electric field was added on the revised\nmanuscript:\n“On the other hand, as the positive field continues to increase, the blue shift of IX begins to saturate. Band\nstructure analyses suggest that at larger positive fields, the IX transition shifts from type-II band alignment at\nthe Γ point to the InSe intralayer exciton transition, resulting in an unchanged peak position in the measured PL\nwith further increases in positive field (Supplementary Figure S17). Nevertheless, the linear Stark shift for all\nheterostructures is around 100 meV (Supplementary Figure S19), ensuring the accuracy of the extracted dipole\nmoments for the corresponding HSs.”\nFor the reviewer’s second concern regarding enhanced many-body interactions with increasing dipole\nmoments:\nWe have supplemented our analysis with power-dependent measurements across various heterostructures. As\nshown in Figures R4a-d, the IX PL peak clearly exhibits a blue shift with increasing excitation power, which\nwe attribute to enhanced dipole-dipole repulsion [4]. Moreover, these interactions strengthen with the increasing\ndipole moment. Figure R4e illustrates the extracted blue shift (∆E) relative to excitation power for different\nheterostructure combinations, each displaying distinct rates of increase (defined as m = ∆E/P where P represents\nthe excitation power). Accroding to previous work [5], m is proportional to the dipole momen of IXs. The inset\nprovides a direct comparison of the corresponding dipole moments and m, revealing a significant consistency.\nFigure R4. Power-dependent PL spectra for 2L/4L (a), 2L/5L (b), 2L/6L (c), and 3L/6L (d) heterostructures.\nThe increasing excitation powers (from bottom to top) for (a-d) are 0.13 mW, 0.2 mW, 0.325 mW, and 0.5 mW,\nrespectively. (e) Energy shift with the increasing excitation power for 2L/4L (red), 2L/6L (green), and 3L/6L\n(blue) hestrostructures. Inset: comparison of blue shifts (with respect to the power) and dipole moment for\ndifferen layer combinations.\nRevision: Figure R4 was added as the Figure 5 in the revised manuscript. The related power-dependent\nanalyses is attached:\n“Figure 5e illustrates the IX position as a function of excitation power for different layer combinations,\nindicating that the energy shift rates (m= Δ𝐸 /𝑃 where P represents excitation power) increase with the\n𝑋𝑋\nlayer number of WS₂ or InSe. The inset in Figure 5e compares the corresponding dipole moments with the\nenergy shift rate mmm, revealing a strong correlation. These results clearly demonstrate that the dipole-dipole\nrepulsion interaction is significantly enhanced due to the increased dipole moment engineered by the layer\nnumber.”\nComment 2. Following previous comment, despite the claim of having ‘record high’ dipole moment to meet\nthe eye, all the main characterizations like dipole extraction are confined within 0.03 V/nm. This does not\nmake fair comparison with other system showing continuous linear Stark shift towards the 0.3 V/nm or larger\nfield range. In other words, this system limits the useful field range one order of magnitude lower than\nconventional vdW devices. The reason could be due to the intrinsic Gamma transition for this largely layer-\nengineered structure. As the effective e-h separation increases the intrinsic dipolar moment, it always risk\nreducing exciton oscillator strength or binding energy, which results in shift saturation at very low field. Some\nPL linecuts in Supp info also show quite dim emission which suggest weak oscillator strength. In comparison\nthe hIX or every-other-layer IX e.g. (ref. 11) may show a better balance with both enhanced dipole moment\nas well as sufficient oscillator strength due to interlayer tunneling, which stabilize the field dependence of\ndipole. In this work when it goes to few layer-few layer structure the interlayer tunneling is simply not strong\nenough, hence the very limited range of Stark shift. In a word the represented data does not show enough\nscientific merits over previous IX system, thus I cannot agree with the technical and application potential\nclaimed by the authors.\nResponse: We thank the reviewer for raising this question. As mentioned in our response to the previous\ncomment, the limits of the Stark shift are due to the band alignment of the constituent materials and the\nmaximum field that the heterostructure can withstand. We achieved a energy shift range of approximately 100\nmeV for each heterostructure configuration (Figure 2e in the main text). Furthermore, by combining electric\nand layer engineering, we can achieve continuous broad band tunability for a large spectral range (from ~1.25\neV to ~1.55 eV, as shown in Figure 2e in the revised manuscript and Supplementary Figure S27 in the revised\nSupplementary materials).\nFollowings are the specific points to reviewer’s questions:\n1. Decrease of the PL intensity with the electric field.\nThe reduction in PL under electric field (as shown in Figure R5a where the 2L/3L heterostructure is adopted\nfor an representative example) is attributed to the Coulomb force exerted by the external field. As schematically\ndepicted in Figure R5c, a positive field exerts an attractive Coulomb force on the IX dipole, enhancing the\noverlap of the wavefunctions of the electron and hole, leading to the increased IX PL. Conversely, a negative\nfield results in a significant reduction in PL at relatively large negative values. This phenomenon occurs not\nonly for at-Γ IXs but also for at-K IXs. For instance, the field-dependent PL of the WSe /WS heterostructure\n2 2\n[4] exhibits a close results to ours, as shown in Figure R5b.\nFigure R5. (a) Same image as Figure 3e. (b) Cited image from the Figure 2a in the main text of ref [3]. (c)\nSchematic illustration of PL variation with the field.\n2. Comparison of IXs Formed in Heterostructures and Homostructures\nThe formation of IXs in heterostructures and homostructures is fundamentally different. In heterostructures, the\nelectron-hole separation results in an inherently negligible oscillator strength (approximately 10-3 to 10-4 smaller\nthan that of intralayer excitons) [6]. Consequently, only PL measurements are used for IX characterization in\nheterostructures. Despite the small oscillator strength, carriers from different layers can tunnel to the VBM and\nCBM for the IX transition. Although an increased layer number generally reduces the binding energy and\nelectron-hole wavefunction overlap, the pronounced electric-field-dependent PL observed due to Stark effects\n(Figures R3 and R4) evidences the existence of IXs in all heterostructure configurations presented in our\nmanuscript.\nIn contrast, IXs in homostructures (e.g., IXs in MoS homobilayers [7] or every-other-layer excitons in\n2\ntrilayer or >3L WSe [8]) arise from the admixture of intralayer excitons and thus possess a much larger\n2\noscillator strength, allowing for measurement via reflection or absorption. However, the results from these\nstudies have the following constraints compared to our work:\n1. The bilayer or trilayer (or thicker) homostructures are indirect bandgap semiconductors, where IX\ntransitions are of low efficiency, leading to negligible PL emission (Figure R6c). This limitation\nimpacts potential applications, including exciton condensation and lasing.\n2. Although a larger dipole moment (~1.4 enm) is observed for every-other-layer IXs, protected by lattice\nsymmetry, increasing the layer number does not yield further enhancements in the dipole moment. That\nis, unlike layer-engineered IXs in our work, the every-other-layer IXs are of the fixed dipoe moment.\nFigure R6. Evolution of the differential reflectance spectra (a, cited from the Figure 2a in the ref [6]) and\nphotoluminescence (c, cited from the extended data Figure 2 in the ref [6]) of the every-other-layer exciton\nwith the electric field. (b) Schematic illustration of IXs in heterostructure (left) and homostructure (right).\nRevision: Figure R5 was added as Supplementary Figure S20 in the revised supplementary materials. The\ncomparison of our work with every-other-layer IXs in homostructures was added in the discussion in the revised\nmanuscript. The related sentences are attached for reference:\n“It is well known that, compared to the negligible oscillator strength (ranging from 10−3 to 10−4 of that of\nintralayer excitons) in heterostructures, IXs in homostructures, such as bilayer MoS₂, exhibit finite oscillator\nstrength, which can be detected in reflection or absorption measurements. Recently, the every-other-layer\nexciton observed in trilayer WSe₂ has demonstrated a large dipole moment of approximately 1.4 enm. However,\nthese multilayer homostructures are indirect bandgap semiconductors, resulting in relatively low quantum\nefficiency for IX transitions, which limits their applications in exciton condensation or lasing. Moreover,\nalthough a larger dipole moment is observed for every-other-layer IXs, protected by lattice symmetry,\nincreasing the layer number does not lead to further enhancements in the dipole moment.”\nComment 3. Some typos are found in line 49 it should be ‘every-other-layer exciton’ rather than every-other\nexciton.\nResponse: We thank reviewer for pointing out the typos and we fixed all of them in the revised manuscript.\nReviewer 2\nThe submitted manuscript, \"Observation of Giant Dipole Moment of Interlayer Excitons in Multilayer\nHeterostructure\", reports a systematic study on interlayer excitons in multilayer WS₂/InSe heterostructures.\nBy varying the thickness of constituent layers, the authors demonstrate a prominent increase in exciton dipole\nmoment, reaching up to 3.18 e·nm — the largest value reported to date in van der Waals heterostructures.\nThese findings are substantiated by quantum-confined Stark effect measurements and supported by ab initio\nsimulations. The manuscript offers valuable insight into dipole engineering via layer number control, thus\nextending the design tlkit for next-generation infrared and excitonic optoelectronic devices.\nNotably, the authors reveal that the interlayer excitonic wavefunction becomes increasingly delocalized as\nthe thickness of InSe or WS₂ increases. This delocalization underlies the enhancement of the vertical dipole\nlength beyond the conventional vdW gap distance. The study combines careful device design, spectroscopic\nanalysis, and theoretical calculations to provide a comprehensive picture of dipole evolution in such\nmultilayer systems.\nGiven the novelty and potential impact of the results, I find this manuscript to be of strong interest to\nreaders of Nature Communications. However, I recommend the authors address the following concerns before\nit is suitable for publication:\nResponse: We thank the reviewer for the recogniation and high evaluation of our work. The point-to-point\nresponse is detailed in the following.\nComment 1. Lack of Reversed Field Data:\nWhile the manuscript provides compelling evidence of linear Stark shifts under positive gate bias, it lacks\ndata under reversed (negative) field direction. Since a hallmark of dipolar excitons is a symmetric energy\nresponse to field reversal, this omission weakens the claim. The authors should either present reversed-field\ndata or clearly explain why it is not available, and whether any asymmetry arises from built-in fields or device\nstructure.\nResponse: We thank the reviewer for this meaningful suggestion. Following the reviewer’s recommendations,\nwe measured the Stark shifts under both positive and negative fields, which are presented in Figure R7.\nFigure R7a-d shows the evolution of PL with positive and negative fields for different heterostructure\ncombinations, while Figure R7e-h presents the corresponding peak positions for field-dependent IXs. For all\nheterostructures shown in Figure R7a-d, the intensity of the IX PL decreases due to reduced electron-hole\nwavefunction overlap caused by the Coulomb force, as schematically illustrated in Figure R5c.\nSpecifically, for the 2L/3L combination, the PL peak positions exhibit an (almost) linear relationship with\nthe negative field, displaying the same slope as observed under positive fields. A slight deviation from linearity\nis noted when the negative field strength exceeds 20 mV/nm. For the other combinations (2L/4L, 2L/6L, and\n3L/6L), the linear Stark shift is initially observed at low field strengths (less than 20 mV/nm), after which the\nPL peak positions saturate (i.e., remain unchanged) with increasing negative field strength. For the 3L/6L\ncombination, the PL intensity becomes too weak under larger negative fields (>20 mV/nm), making it difficult\nto extract the corresponding peak positions. This deviation from linear Stark shifts under large negative fields\nhas been reported in other studies (e.g., in Ref [9]) which is attributed to charging effects. Despite the\nobservation of energy shift saturation at negative fields, the linear Stark shift exceeding 100 meV across the\n(small) negative to positive field range provides a sufficient region to extract the dipole moments of IXs for the\nvarious heterostructure combinations.\nFigure R7. Evolution of IX PL with the electric field for 2L/3L (a), 2L/4L (b), 2L/6L (c), and 3L/6L (d)\nheterostructures where mL/nL represents that heterostructure is composed of mL-WS and nL-InSe.\n2\n(e-h)\nCorresponding IX peak positions extracted from (a-d). Red line is the guide for the eye for the linear dispersion\nof IX with electric field.\nRevisions: Figure R7 was added as Supplementary Figure S18 in the revised supplementary materials.\nThe analyses on negative field was added in the revised manuscript with the following sentences:\n“Additionally, Supplementary Figure S18 and S19 illustrates the IX evolution under negative fields and\nlarger positive fields. Under negative fields, the PL of IX demonstrates a clear near-linear redshift, while its\nintensity decreases dramatically, attributed to reduced electron-hole wave function overlap due to Coulomb\nforces (in contrast, PL intensity increases with positive fields). As the negative field strength further increases,\nthe IX energy remains constant, likely due to a charging effect also noted in previous studies. On the other hand,\nas the positive field continues to increase, the blue shift of IX begins to saturate. Band structure analyses suggest\nthat at larger positive fields, the IX transition shifts from type-II band alignment at the Γ point to the InSe\nintralayer exciton transition, resulting in an unchanged peak position in the measured PL with further increases\nin positive field. Nevertheless, the linear Stark shift for all heterostructures is around 100 meV (Supplementary\nFigure S19), ensuring the accuracy of the extracted dipole moments for the corresponding HSs.”\nComment 2. WS₂ Emission Behavior in Heterostructures (Fig. 1d):\nIn Figure 1d, the WS₂ exciton peak within the heterostructure region exhibits a shift in both position and\nlineshape compared to pristine WS₂. This suggests possible charge transfer or interface interactions. The\nauthors should clarify whether these effects influence the interpretation of interlayer exciton resonance and\nwhether they affect the extraction of Stark shifts.\nResponse: We thank the reviewer for highlighting this question. The energy shift of the WS exciton between\n2\npristine 2L WS and the heterostructure is attributed to the different temperatures during measurements (300 K\n2\nfor pristine 2L WS and 80 K for the heterostructure). We apologize for the misleading information conveyed\n2\nby this image. Additionally, we noticed that the lineshape of the PL spectrum near the WS exciton in the original\ninstrument setup, we have mitigated these artifacts.\nFigure R8b-c shows the remeasured PL spectra from the 2L/4L and 2L/5L heterostructures, along with the\ncorresponding PL spectra from their constituent WS and InSe layers. As illustrated in Figure R8b, the 2L-WS\n2 2\nexhibits an A exciton emission (X , ~620 nm) and an indirect bandgap emission (X , ~720 nm), while the\nA indirect\n4L-InSe shows an intralayer exciton emission around 800 nm (Figure R8a depicts their respective transition\nprocesses). After the formation of the heterostructure, the PL of both WS and InSe is quenched due to charge\n2\ntransfer. For the 2L/4L heterostructure, the characteristic peaks from the constituent layers remain, with only\nslight energy shifts relative to their original positions. This minor shift can be attributed to changes in the\ndielectric environment or small strains during the transfer process, as observed in other studies [10]. In the case\nof the 2L/5L heterostructure (Figure R8c), similar conditions apply, but the X emission is completely\nindirect\nquenched or obscured by the background of the IX spectrum.\nFigure R8. (a) Band structure of InSe/WS heterostructure. (b) Comparison of the PL spectra from 2L/4L heterostructure\n2\n(blue curve), 2L-WS (orange curve), and 4L-InSe (yellow curve). (c) Comparison of the PL spectra from 2L/5L\n2\nheterostructure (purple curve), 2L-WS (orange curve), and 5L-InSe (yellow curve).\naddition, in the revised manuscript the PL spectra of heterostructures (Figure 1c in the revised manuscript) were\nreplaced by the remeasured PL shown in Figure R8.\nComment 3. Color Similarity in Figure 1d:\nThe PL spectra of 4L-InSe and 5L-InSe in Figure 1d are rendered in colors that are difficult to distinguish\n(cyan vs aqua green). This reduces the figure's clarity and accessibility. The authors are encouraged to choose\nmore distinguishable colors or adopt different line styles to improve visual clarity.\nResponse: We appreciate the valuable suggestion from the reviewer. We have carefully adjusted the\ncorresponding colors (Figure 1c in the revised manuscript).\nComment 4. Clarify Theoretical Assumptions on Carrier Fixation\nThe theoretical modeling assumes either the electron or the hole is fixed at a certain atomic layer (e.g., bottom\nSe in InSe) to simplify exciton wavefunction calculations. However, the justification for this approximation is\nnot well explained in the main text. Given the importance of wavefunction asymmetry in determining the dipole\nmoment, the authors should clarify why this assumption is valid, what physical behavior it aims to reproduce,\nand how it affects the accuracy of the extracted dipole moments.\nResponse: We thank the reviewer for this insightful question for about the simplified model we adopted in the\ncalculations.\nFirst, we clarify the rationale for fixing either the electron or the hole to a specific atomic layer. The exciton\nwavefunction is intrinsically six-dimensional, and directly visualizing such a function in real space is extremely\ndifficult, if not impossible. Fixing the position of the hole (or the electron) effectively selects a particular two-\ndimensional slice of this six-dimensional space. This slice represents the spatial probability distribution of the\nelectron (or the hole) when the hole (or the electron) is “pinned” at a specific position R . The result is a three-\n0\ndimensional function that can be directly visualized in real space. This approach provides the most\nstraightforward and practical means of understanding the spatial distribution of excitons, their degree of\nlocalization, and the relative motion between electrons and holes. Such methodology is well established in the\nliterature (see, e.g., [11-15]). Here, the 1L-WS /1L-WSe is used as a representative example. By fixing the\n2 2\nelectron (hole) in 1L-WS (WSe ), we can calculate the hole wavefunction distribution in 1L-WSe (1L-WS )\n2 2 2 2\ncorrespondingly, as indicated in Figure R9a (Figure R9b). These two independent calculations yield nearly\nequivalent dipole sizes, with d=4.53 Å for the case in Figure R9a and d=4.6 Å for the case in Figure R9b.\nNext, we discuss the implications and validity of this simplified model, and demonstrate that it can\naccurately capture the experimental observations. Due to the large lattice mismatch between InSe and WS ,\n2\ndirectly visualizing the exciton wave function of their heterostructure while fully accounting for the lattice\nmismatch is computationally intractable. Therefore, we adopt a simplified model in which either the electron or\nthe hole in one material is fixed, and the spatial distribution of the other carrier within the same material is\ncalculated (i.e., Figure 3 and Figure 4d, e in the main text).\nTo validate the effectiveness of this approach, we consider multilayer WSe /WS heterostructures, where\n2 2\nthe lattice constants are very similar, making it feasible to model the full heterostructure explicitly. Figure R10a\nand R10b compare the hole wave function distribution in monolayer WSe obtained from the complete 1L-\n2 2\nR10b). The two results are strikingly similar, thereby supporting the validity of our simplified model. Moreover,\nthe effective dipole size using 𝑟 = ∫𝜑∗𝑟𝜑 (r is the displacement with respect to the fixed electron) can be\n𝐵\ncalculated as 4.6 Å (which is very close to the value reported in the previous results [9, 16]) for Figure R10a\nand 1.73 Å for Figure R10b. Because in a real case, the electron only resides within the WS layer, the\n2\nconsideration in Figure R10a is thus close to real results while the simplified model in Figure R10b results in\na large deviation.\nWe further calculate the 2L-WSe /1L-WS configuration with fully considering the 2L-WSe /1L-WS\n2 2 2 2\nheterostructure (Figure R10c) and without considering 1L-WS2 (Figure R10d). For both cases, the hole\nwavefunction distrubtions distributions within 2L-WSe are close, with the wavefunction distributed in both\n2\nlayers of WSe . The dipole size is thus calculated for these cases, giving the value of 7.66 Å (Figure R10c)and\n2\n4.37 Å (Figure R10d). Though a similar offset of calculated dipole size for these two cases is found, the\nincreased dipole size with the increasing layer are is found to be similar. That is, for Figure R10a and Figure\nR10c where the fully heterostructure configuration is considered, the dipole size is increased by 3.06 Å (7.66 Å\n- 4.74 6 Å), which is very close to the dipole size change 2.64 Å (4.37 – 1.73 Å) for Figure R10b and Figure\nR10d.\nAs a result, through the above analysis, we can summarize the applicability and limitations of the simplified\nmodel for calculation in heterostructure:\n1. Fixing either the electron or hole in the calculation of IXs in heterostructures gives a close value of dipole\nmoments.\n2. The electron and hole wavefunction distrubtions distributions by this simplified method provides provide a\ndecent agreement with the those calculated by the full heterostructure configuration, reflecting the\ndelocation of electrons or holes with the increasing layer number of constituent material.\n3. The calculated dipole size for this simplified method shows the deviation from the results calculated by the\nfull configuration, owing to the direct placement of electron or hole at the edge atom of one a certain material.\n4. Though the deviation of dipole size is found, the increased dipole size with the layer number shows a decent\nconsistence consistency with the results by considering the full configuration. As a result, the simifield\nmodel can convincingly reflect the trend of the increasing dipoe dipole moment with the increasing layer\nnumber, which is the major finding for our work.\nFigure R9. (a) Hole wavefunction distrubtion within 1L-WS for 1L-WS /1L-WSe heterostructure. The\n2 2 2\nelectron is fixed at the WSe layer. (b) Electron wavefunction distrubtion within 1L-WSe for 1L-WS /1L-WSe\n2 2 2 2\nheterostructure. The hole is fixed at the WS layer.\n2\n1L-WS (a equvvalent electron is fixed at the edge of WS . (b) The same as (a) but there is no 1L-WS and the\n2 2) 2\nfixed electron is at the edge Se atom of WSe . (c-d) Same as (a-b) but for the 2L-WSe system.\n2 2\nRevisions: Figure R9 and R10 were added as Supplementary Figure S23 and Figure S24 in the revised\nsupplementary materials.\nThe discussion on validity and limitations was added in the revised manuscript with the following related\nsentences:\n“In Supplementary Figure S23, we systematically compare the influence of fixing the electron\n(Supplementary Figure S23a) versus the hole (Supplementary Figure S23b) on the dipole moment\ncalculation for WS₂/WSe₂, where their lattices exhibit a strong match. The resulting dipole sizes from these two\nconfigurations are nearly identical. Furthermore, we calculated the hole wave function distributions by fully\nconsidering both 1L-WS₂/1L-WSe₂ and 1L-WS₂/2L-WSe₂ configurations, as well as by only considering the\n1L-WSe₂ and 2L-WSe₂ configurations with the electron fixed at the edge of the WSe₂ layer (which aligns closely\nwith our simplified model). The results show that the calculated hole wave function distributions are similar (as\ndepicted in Supplementary Figure S24). The primary difference lies in the dipole moment calculated when only\nconsidering WSe₂, which is significantly smaller than that derived from the full configurations due to the\nabsence of interlayer spacing. However, the increase in dipole moment associated with the increasing layer\nnumber of WSe₂ remains consistent across both configurations. These analyses validate that, although the\nmodel simplifies the system by eliminating one of the constituent materials in the HS, the carrier wave function\ndistributions and the layer-engineered dipole moment increase can still be accurately reflected by our simplified\nmodel.”\nComment 5. Clarify Treatment of Interlayer Coupling in Simulations:\nThe exciton dipole enhancement is attributed to wavefunction delocalization across layers, but the manuscript\ndoes not clearly explain how interlayer coupling is treated in the simulations. The authors should briefly clarify\nwhether and how interlayer hybridization is included when calculating the electron wavefunction distribution,\nas this directly impacts the extracted dipole trend.\nResponse: We thank the reviewer for this insightful and critical comment. We agree that a clearer explanation\nof how interlayer coupling is treated in our simulations is essential and should be added to the manuscript.\nIn our first-principles calculations (DFT and GW-BSE), interlayer coupling and hybridization are physical\nresults intrinsically embedded within the computational framework, rather than manually introduced parameters.\nWhen calculating the exciton wavefunctions in multilayer InSe (or WS₂), the Hamiltonian inherently\nincludes all intra-layer and inter-layer hopping terms. Therefore, the distribution of the electron (hole)\nwavefunction is a result of interlayer hybridization and Coulomb attraction. Consequently, the distribution of\nthe electron (hole) wavefunction is a result of the combined effects of interlayer hybridization and Coulomb\nattraction. In other words, the delocalized wavefunction features we obtained (as shown in the Fig. 3 and Fig.\n4d-e of the revised manuscript) are direct evidence of the existence of interlayer coupling.\nSpecifically:\n1. DFT calculation self-consistently determines the electronic ground state of the system by solving the Kohn-\nSham equations, which incorporate the potential from all atomic nuclei and the Coulomb and exchange-\ncorrelation potentials from all electrons. The resulting wavefunctions, if delocalized across layers, are a\ndirect manifestation of interlayer coupling and hybridization. The use of Grimme's D3 correction ([cite: J.\nChem. Phys. 2010, 132, 154104]) ensured the physical accuracy of the interlayer distances, providing a\nreliable foundation for this calculation.\n2. The subsequent GW calculation performs quasiparticle corrections based on the wavefunctions and\nelectron density provided by the DFT step. It fully inherits the interlayer coupling and hybridization\ninformation from the DFT wavefunctions, modifying the energy levels without altering the spatial\ndelocalization characteristics of the wavefunctions.\n3. Finally, the BSE calculation uses the delocalized single-particle states from GW as a basis and solves the\nelectron-hole interaction. The resulting exciton wavefunction naturally spans multiple layers, successfully\ncapturing the trend of increasing dipole moment with layer number, which aligns qualitatively with our\nexperimental results.\nRevision: We added the related discussion on first-principle calculations in the revised supplementary materials:\n\"In our first-principle calculations (DFT and GW-BSE), interlayer coupling and hybridization are physical\nresults intrinsically embedded within the computational framework, rather than manually introduced parameters.\nWhen calculating the exciton wavefunctions in multilayer InSe/WS₂, the Hamiltonian inherently includes all\nintra-layer and inter-layer hopping terms. Therefore, the distribution of the electron/hole wavefunction is a result\nof interlayer hybridization and Coulomb attraction. Furthermore, we employed the D3 correction ([cite: J. Chem.\nPhys. 2010, 132, 154104]) to ensure the physical accuracy of the interlayer distances, providing a reliable\nfoundation for the calculation.\"\nComment 6. Discuss the Upper Limit of Dipole Moment\nWhile the authors report record-high excitonic dipole moments, the manuscript lacks a discussion on the\ntheoretical and experimental upper bounds of dipole length in such multilayer heterostructures. It would be\nvaluable to briefly address what limits the maximum achievable dipole moment—e.g., exciton binding energy,\ndielectric screening, or wavefunction delocalization saturation—and whether further increases in layer\nnumber are expected to continue enlarging the dipole moment or lead to diminishing returns.\nResponse: We sincerely appreciate the reviewer for this insightful suggestion, which has facilitated a deeper\ndiscussion on interlayer excitons in multilayer heterostructures. As shown in Figure R11, the increase in dipole\nmoment with the rising number of InSe or WS layers is not saturated. There are primarily two factors that will\n2\nlimit the maximum dipole moment we can achieve:\n1. Disruption of Type-II Alignment with Increasing InSe and WS Layers\n2\n0.39 eV to 0.18 eV as the number of InSe layers increases from 2L to 5L (according to Ref. [3]). Experimental\ndata (Figure R12b, directly cited from Figure 3a in the reference [npj 2D Mater Appl 8, 12 (2024)]) indicates\nthat this energy difference approaches zero as the number of InSe layers approaches 18, rendering the type-II\nalignment invalid. Consequently, we can roughly estimate the upper limit of the dipole moment at 18L InSe as\n𝑝 =(2.68 enm)+(0.3 enm×12)=6.28 enm. Here, 2.68 enm is the dipole moment for the 2L/6L\n𝑙𝑎𝑟𝑔𝑒𝑠𝑡\nheterostructure, and we estimate that each additional layer increases the total dipole moment by 0.3 enm (based\non the increase from 2L/5L to 2L/6L).\nA similar analysis can be applied to WS . As indicated in Figure R12c, the CBM of InSe and WS\n2 2\napproaches each other with an increasing number of WS layers. However, the variation in the CBM of WS2\n2\nwith layer number is smaller (as seen in Peak I of Figure R12d, which is directly cited from Figure 3c in [Sci\nRep 3, 1608 (2013)]) compared to the trend observed in InSe. Increasing the WS layers to bulk would result in\n2\na CBM of WS2 that is very close to that of InSe, rather than surpassing it, which would compete with interlayer\nexciton transitions. However, due to the lack of further band structure data for various layers of WS , the\n2\nestimation of the upper limits of the dipole moment with increasing WS layers remains uncertain.\n2\n2. Binding energy:\nThe interaction between the electron and hole can be described by the Coulomb potential, which is proportional\n1\nto where 𝜀 is the relative permittivity of heterostructure (approximately treated as constant across\n𝑟\n𝜀𝑟𝑑\ndifferent layer combinations) and d is the dipole size. Consequently, a larger dipole size results in weaker\nCoulomb attraction, thereby reducing the binding energy of the exciton.\nIn a previous report (supplementary materials in Ref. [3]), the binding energy for the 2L/3L heterostructure\n1\nwas estimated to be less than 20 meV. Given that the binding energyis proportional to 𝐸 ∝ and that d=1.35\n𝑏\n𝑑\nnm for the 2L/3L combination, and considering that the binding energy must exceed the thermal energy of the\nenvironment (i.e., k T≈7 meV for T=77 K), we estimate the maximum dipole size to be around 3.85 enm.\nB\nHowever, the limits set by binding energy can increase with a decrease in temperature, as this leads to a reduction\nin the thermal energy from the environment.\nFigure R11. The evolution of dipole moment with different layer combinations.\nFigure R12. (a) Evolution of band structures of 2L-WS /NL-InSe heterostructure with the increasing layer\n2\nnumber of InSe. (b) Measured PL spectra for InSe of various layer number (directly cited from Figure 3a in [npj\n2D Mater Appl 8, 12 (2024).]). (c) Evolution of band structures of NL-WS /2L-InSe heterostructure with the\n2\nincreasing layer number of WS . (d) The PL peak positions for WS of various layer number (directly cited from\n2 2\nFiguer 3c in [Sci Rep 3, 1608 (2013).]).\nRevisions: The related discussion on the upper limits of the dipole moment by layer-engineering in the revised\nmanuscript is attached:\n“Last but not least, while the layer configuration up to the 3L/6L combination exhibits the largest dipole\nmoment observed in our experiments, it is clear that the upper limits have not yet been reached (see\nSupplementary Figure S25). Two factors could lead to the disappearance of interlayer excitons (IXs) with\nincreasing layer number. First, band structure alignment plays a crucial role. As the layer number increases, the\ntype-II band structures (illustrated in Figure 1b) may become invalid, resulting in interlayer-intralayer exciton\ntransitions. Second, binding energy is another critical factor. As the dipole size increases, the binding energy\ncorrespondingly decreases due to reduced Coulomb attraction. When the binding energy falls below the thermal\nenergy of the environment, IXs can no longer be observed. Detailed analyses can be found in Supplementary\nNote S3, which provides upper limits for the dipole moment: approximately 6.28 enm due to the limitations by\nband structure alignment and about 3.85 enm due to the limitations by binding energy at 77 K. The latter\nestimation can be increased with the decreased temperature.”\nOverall Assessment:\nThis manuscript reports a compelling study of tunable interlayer excitons with giant dipole moments in multilayer WS₂/InSe\nheterostructures. The results are novel, experimentally robust, and supported by theory. Clarifying the modeling\nassumptions, addressing dipole symmetry under reversed fields, and discussing the upper bound of dipole strength would\nfurther improve the work. With minor revisions, the paper is suitable for publication in Nature communications.\nResponse: We thank reviewer again for the recognination of our work. Following the suggestions by the reviewr,\nthe supplement of the reversed field and discussion on the upper bound of the dipole moment were added in the\nrevised version of this work.\nReviewer #3 (Remarks to the Author):\nThe manuscript titled “Observation of Giant Dipole Moment of Interlayer Excitons in Multilayer\nHeterostructure” presents a systematic investigation of dipole moments in WS₂/InSe heterostructures with\nvarying layer numbers. The study demonstrates that the dipole moment increases monotonically with the\nnumber of InSe or WS₂ layers, reaching a maximum value of 3.18 e·nm in the 3L WS₂/6L InSe configuration.\nThe experimental data are well-presented, detailed, and informative, though the findings are not entirely\nunexpected. While the work is solid, I recommend acceptance after revisions to address the following points:\nResponse: We sincerely thank reviewer for the recognition of our work. We give the point-to-point reponse in\nthe following.\nComment 1. The manuscript examines 2L WS₂/nL InSe (n=3–6), but 1L- and 2L-InSe cases are absent. What\nis the rationale for omitting these configurations?\nAdditionally, the WS₂ thickness is fixed at 2L in most cases. What would be the expected behavior for 1L\nWS₂/nL InSe heterostructures? A brief discussion and experiment data on this would strengthen the study’s\ncomprehensiveness.\nResponse: We thank reviewer for this question on the layer number slection for the formation of the\nheterostructures. We follow the strategy in Ref [3] to form the type-II band alignment that supports interlayer\ntransition at k=0 (i.e., at Γ point) in the Brillouin zone, and thus avoids momentum mismatch required, for\ninstance, by the interlayer transition at K point in other heterostructure systems (such as 1L-MoS /1L-WSe\n2 2\nheterostructure shown in Ref [9]). For this purpose, the bilayer and thicker multilayer of WS with the its VBM\n2\nat the Γ point, and multilayer InSe with its conduction-band minimum (CBM) also at Γ point are selected.\nThis is schematically illustrated in the band structure alignment in Figure R13a.\nIndeed, 2L-InSe also matches this goal (as indicated in Figure R13b, whose CBM is lower than CBM of\n2L-WS by aournd 0.13 eV, as indicated in Ref [3]), which is expected to show a smaller dipole moment than\n2\nthat of the heterostructure formed by 3L-InSe. However, during our experiment, we unfortunately failed to find\nthe 2L-InSe (also, the InSe layer with very thin thickness is not as detectable as WS in the experiment [17])\n2\nwith large enough area to form the heterostructure. Although the 2L-InSe sample is absent, the heterostructures\ncomposed of InSe, with layer numbers ranging from 3L to 6L, sufficiently demonstrate a trend of the increasing\ndipole moment with the increasing layer number.\nCompared with the 2L InSe, monolayer (1L) InSe shows a dramatic increase (> 0.5 eV, according to the\ncalculated results in ref [18, 19]) in the bandgap. CBM of 1L-InSe would be higher than that of 2L-WS (Figure\nFigure R13. Schematic band structuers for heterostructure composed of multilayer InSe and WS (a).\n2\n1L WS is the direct bandgap semiconductor with VBM resides at K point (as indicated in Figure R14a)\n2\ninstead of Γ point, which consequently doesn’t align with our purpose. In comparison, 2L-(>2L) WS meets\n2\nthis requirement with its VBM resides at Γ point (Figure R14b).\nFigure R14. Band structures for 1L-WS (a) and 2L-WS (b) with images cited from Figure 3 and Figure 4 in\n2 2\nRef [20] respectively.\nComment 2. The results suggest that thicker heterostructures yield larger dipole moments, with the maximum\nobserved in 3L WS₂/6L InSe. Does this trend continue beyond 6L InSe or 3L WS ? Is there a theoretical or\n2\nexperimental upper limit to the dipole moment in such systems? A discussion on this would provide deeper\ninsight.\nResponse: We sincerely appreciate the reviewer for this insightful suggestion, which has facilitated a deeper\ndiscussion on interlayer excitons in multilayer heterostructures. As shown in Figure R15 (the same as Figure\nR11), the increase in dipole moment with the rising number of InSe or WS layers is not saturated. There are\n2\nprimarily two factors that will limit the maximum dipole moment we can achieve:\n1. Disruption of Type-II Alignment with Increasing InSe and WS2 Layers\nAs shown in Figure R16a, the energy difference between the VBM of InSe and that of WS decreases from\n2\n0.39 eV to 0.18 eV as the number of InSe layers increases from 2L to 5L (according to Ref. [3]). Experimental\ndata (Figure R16b, directly cited from Figure 3a in the reference [npj 2D Mater Appl 8, 12 (2024)]) indicates\nthat this energy difference approaches zero as the number of InSe layers approaches 18, rendering the type-II\nalignment invalid. Consequently, we can roughly estimate the upper limit of the dipole moment at 18L InSe as\n𝑝 =(2.68 enm)+(0.3 enm×12)=6.28 enm. Here, 2.68 enm is the dipole moment for the 2L/6L\n𝑙𝑎𝑟𝑔𝑒𝑠𝑡\nheterostructure, and we estimate that each additional layer increases the total dipole moment by 0.3 enm (based\non the increase from 2L/5L to 2L/6L).\nA similar analysis can be applied to WS . As indicated in Figure R16c, the CBM of InSe and WS\n2 2\napproaches each other with an increasing number of WS layers. However, the variation in the CBM of WS2\n2\nwith layer number is smaller (as seen in Peak I of Figure R16d, which is directly cited from Figure 3c in [Sci\nRep 3, 1608 (2013)]) compared to the trend observed in InSe. Increasing the WS layers to bulk would result in\n2\na CBM of WS2 that is very close to that of InSe, rather than surpassing it, which would compete with interlayer\nexciton transitions. However, due to the lack of further band structure data for various layers of WS , the\n2\nestimation of the upper limits of the dipole moment with increasing WS layers remains uncertain.\n2\n2. Binding energy:\nThe interaction between the electron and hole can be described by the Coulomb potential, which is proportional\n1\nto where 𝜀 is the relative permittivity of heterostructure (approximately treated as constant across\n𝑟\n𝜀𝑟𝑑\ndifferent layer combinations) and d is the dipole size. Consequently, a larger dipole size results in weaker\nCoulomb attraction, thereby reducing the binding energy of the exciton.\nIn a previous report (supplementary materials in Ref. [3]), the binding energy for the 2L/3L heterostructure\n1\nwas estimated to be less than 20 meV. Given that the binding energyis proportional to 𝐸 ∝ and that d=1.35\n𝑏\n𝑑\nnm for the 2L/3L combination, and considering that the binding energy must exceed the thermal energy of the\nenvironment (i.e., k T≈7 meV for T=77 K), we estimate the maximum dipole size to be around 3.85 enm.\nB\nHowever, the limits set by binding energy can increase with a decrease in temperature, as this leads to a reduction\nin the thermal energy from the environment.\nRevisions: The related discussion on the upper limits of the dipole moment by layer-engineering in the revised\nmanuscript is attached:\n“Last but not least, while the layer configuration up to the 3L/6L combination exhibits the largest dipole\nmoment observed in our experiments, it is clear that the upper limits have not yet been reached (see\nSupplementary Figure S25). Two factors could lead to the disappearance of interlayer excitons (IXs) with\nincreasing layer number. First, band structure alignment plays a crucial role. As the layer number increases, the\ntype-II band structures (illustrated in Figure 1b) may become invalid, resulting in interlayer-intralayer exciton\ntransitions. Second, binding energy is another critical factor. As the dipole size increases, the binding energy\ncorrespondingly decreases due to reduced Coulomb attraction. When the binding energy falls below the thermal\nenergy of the environment, IXs can no longer be observed. Detailed analyses can be found in Supplementary\nNote S3, which provides upper limits for the dipole moment: approximately 6.28 enm due to the limitations by\nband structure alignment and about 3.85 enm due to the limitations by binding energy at 77 K. The latter\nestimation can be increased with the decreased temperature.”\nFigure R15. The evolution of dipole moment with different layer combinations.\nFigure R16. (a) Evolution of band structures of 2L-WS /NL-InSe heterostructure with the increasing layer\n2\nnumber of InSe. (b) Measured PL spectra for InSe of various layer number (directly cited from Figure 3a in [npj\n2D Mater Appl 8, 12 (2024).]). (c) Evolution of band structures of NL-WS /2L-InSe heterostructure with the\n2\nincreasing layer number of WS . (d) The PL peak positions for WS of various layer number (directly cited from\n2 2\nFiguer 3c in [Sci Rep 3, 1608 (2013).]).\nComments 3. While PL spectroscopy effectively probes interlayer exciton energies, sometime reflectance\nmeasurements could offer additional insights—particularly in distinguishing intralayer exciton contributions\nand hybrid interlayer exciton states.\nIncluding such data would allow direct comparison with prior studies and enhance the manuscript’s robustness.\nResponse: We thank reviwer for this question and we agree on that that reflection (or transmission/absorption)\nmeasurements would offer additional insights. People did found the interlayer excitons and their hybridization\nwith intralayer excitons in homostructure through reflection measurements, such as bilayer MoS or trilayer\n2\nwhole layers (Figure R17b), the electron and hole of IXs in heterostructures are separated in different layers\n(Figure R17a), leading to the small oscillator strength (which is estimated of 10-3 to 10-4 smaller than that of\nintralyer exciton, according to Ref [6]) owing to the reduced electron-hole wave function overlap.\nAs a\nconsequence, for IXs in heterostructure people (including us) majorly adopted PL measurements for the\ncharacterization.\nWe measured the reflection spectrum for an representative sample with the 2L/5L configuration. As\nindicated in Figure R18, the reflection spectrum doesn’t show the visible signals at around IX resonance (which\nis reflected in corresponding PL spectrum). In fact, only the intralayer A exciton of WS has shown the\n2\npronounced dip in the reflection spectrum (the intralyer exciton in InSe has a out-of-plane dipole moment [12]\nwhich is thus not detectable under normal reflection measurement).\nRevisons: Figure R18 was added as Supplementary Figure S28 in the revised supplementary materials.\nFigure R17. Schematic comparison of the formation of IXs in heterostructures and homostructures.\nFigure R18. Measured reflection (orange curve) and PL (green curve) spectra of a representative 2L/5L heterostructure.\nComment 4. The manuscript contains numerous spelling errors (e.g., References [5, 9, 13, 14, 19, 30, 31…]),\nsuggesting insufficient attention to detail. Journal name formatting is inconsistent (e.g., “Nature\nCommunications”, “Nat Commun”, “Nat Photonics”). The references should follow a uniform style\n(preferably abbreviated journal names, e.g., Nat. Commun., Nat. Photon.).\nResponse: We thank the reviewer for pointing out these issues. We carefully checked the manuscript and\ncorrected all typos we can find in the revied manuscript, including the spelling erros and inconsistent formatting.\nReferences:\n[1] Sun, Z., Ciarrocchi, A., Tagarelli, F. et al. Excitonic transport driven by repulsive dipolar interaction in a\nvan der Waals heterostructure. Nat. Photon. 16, 79–85 (2022).\n[2] Wietek E, Florian M, Göser J, et al. Nonlinear and negative effective diffusivity of interlayer excitons in\nmoiré-free heterobilayers. Phys. Rev. Lett., 132, 016202 (2024).\n[3] Ubrig, N. et al. Design of van der Waals interfaces for broad-spectrum optoelectronics. Nat Mater 19, 299-\n304, (2020).\n[4] Yu, L., Pistunova, K., Hu, J. et al. Observation of quadrupolar and dipolar excitons in a semiconductor\nheterotrilayer. Nat. Mater. 22, 1485–1491 (2023).\n[5] Sun, Z., Ciarrocchi, A., Tagarelli, F. et al. Excitonic transport driven by repulsive dipolar interaction in a\nvan der Waals heterostructure. Nat. Photon. 16, 79–85 (2022).\n[6] Barré, E. et al. Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures.\nScience 376, 406-410 (2022).\n[7] Leisgang, N., Shree, S., Paradisanos, I. et al. Giant Stark splitting of an exciton in bilayer MoS . Nat.\n[8] Zhang, Y., Xiao, C., Ovchinnikov, D. et al. Every-other-layer dipolar excitons in a spin-valley locked\nsuperlattice. Nat. Nanotechnol. 18, 501–506 (2023).\n[9] Karni O, Barré E, Lau S C, et al. Infrared interlayer exciton emission in MoS /WSe heterostructures. Phys.\n2 2\nRev. Lett. 123, 247402 (2019).\n[10] Tan Q, Rasmita A, Li S, et al. Layer-engineered interlayer excitons. Science Advances, 7(30): eabh0863\n(2021).\n[11] Lau K W, Cocchi C, Draxl C. Electronic and optical excitations of two-dimensional ZrS 2 and HfS 2 and\ntheir heterostructure. Physical Review Materials, 3 074001 (2019).\n[12] Brotons-Gisbert, M., Proux, R., Picard, R. et al. Out-of-plane orientation of luminescent excitons in two-\ndimensional indium selenide. Nat Commun 10, 3913 (2019).\n[13] Molina-Sánchez A, Sangalli D, Hummer K, et al. Effect of spin-orbit interaction on the optical spectra of\nsingle-layer, double-layer, and bulk MoS . Phy. Rev. B, 88, 045412 (2013).\n2\n[14] Torun E, Miranda H P C, Molina-Sánchez A, et al. Interlayer and intralayer excitons in MoS /WS and\n2 2\nMoSe /WSe heterobilayers. Phy. Rev. B, 97, 245427 (2018).\n2 2\n[15] Wu K, Zhong H, Guo Q, et al. Identification of twist-angle-dependent excitons in WS /WSe heterobilayers.\n2 2\nNational Science Review, 9, nwab135 (2022).\n[16] Ciarrocchi, A., Unuchek, D., Avsar, A. et al. Polarization switching and electrical control of interlayer\nexcitons in two-dimensional van der Waals heterostructures. Nature Photon 13, 131–136 (2019).\n[17] Yi-Ying Lu et al, Optical determination of layered-materials InSe thickness via RGB contrast method\nand regression analysis. Nanotechnology 33 485702 (2022).\n[18] Paylaga N T, Chou C T, Lin C C, et al. Monolayer indium selenide: an indirect bandgap material exhibits\nefficient brightening of dark excitons. npj 2D Materials and Applications, 8, 12 (2024).\n[19] Sang D K, Wang H, Qiu M, et al. Two dimensional β-InSe with layer-dependent properties: band\nalignment, work function and optical properties. Nanomaterials, 9, 82 (2019).\n[20] Roy S, Bermel P. Electronic and optical properties of ultra-thin 2D tungsten disulfide for photovoltaic\napplications. Solar energy materials and solar cells, 174, 370-379 (2018).\nResponse letter for the manuscript (NCOMMS-25-35571) entitled “Observation of Giant Dipole\nMoments of Interlayer Excitons via Layer Engineering”\nReviewer #1\nComment 1: I thank the authors for the reply. I appreciate that the authors clarify the interlayer to\nintralayer character transition of this specific heterostructure. This does not remove my concern\nabout the impact of achieving large dipole but only within very small field, i.e. only limited deltaE.\nNevertheless I acknowledge the novelty of this feature in its own context compared to K valley\nexciton in MX2. The added power dependent PL makes sense but not unexpected. The authors stated\nthat their 2L/3L device can not stand a field beyond 0.08 V/nm. which seems like a very low\nthreshold. A second device or some clarification would be encouraged.\nOur response: We thank the Reviewer for this question. The maximum electric field that can be\napplied to the device is determined by the limits of the electric field that h-BN can withstand. These\nlimits can be attributed to defects, such as vacancies or impurities, which create localized states within\nthe bandgap that facilitate tunneling and conduction. Figure R1b illustrates the evolution of leakage\ncurrent with the applied electric field for the 2L-WS /3L-InSe device (Figure R1a). When the electric\n2\nfield exceeds 70 mV/nm, the leakage current across the device increases dramatically. Consequently,\nwe refrain from further increasing the field to avoid damaging our devices.\nThe limits of the applied field vary slightly among different devices, ranging from approximately 80\nmV/nm to 120 mV/nm, due to the device variations (please check the Figure S19 in the Supplementary\nMaterial). In comparison to previous studies on interlayer excitons (see Figure R2, refs. [1-3]), the\nelectric field ranges applicable to our heterostructures are similar, albeit slightly smaller. This range\nprovides a sufficient linear Stark shift for extracting dipole moments across various layer combinations.\nFigure R1. (a) Schematic illustration of experimental setup of 2L-WS /3L-InSe heterostructure\n2\nencapsuled between two hBN layers. The leakage current (orange arrow) is detected when the vertical\nelectric field is increased. (b) The current versus the applied electric field.\nFigure R2. Cited images from the previous publishes. (a-c) from ref. [1], [2], and [3] separately.\nComment 2: Note that the authors reply that they layer engineered the IX dipole in heterostructure\nfor the first time, but I disagree with such claim. Fig 6c in supp info of Nat. Mater. 19, 630–636\n(2020) showed clear dipole tuning of K valley IX with various component thickness. Similarly see\nalso Fig S7 and S8 in Ref.19 indicating similar effect on K valley IX. Various papers with\nheterobilayer separated by BN spacer in principle is also a type of dipole-layer engineering.\nOur response: We appreciate the Reviewer for bringing this issue to our attention. The primary\ncontribution of our work is a systematic study of the layer-engineered dipole moment of interlayer\nexcitons, as demonstrated by the linear Stark effects. Additionally, the dipole-dipole interaction is\nenhanced with the increasing dipole moment, and the underlying mechanism is revealed through\nfirst-principles calculations. We modified our expressions in the revised manuscript with the related\nsentences listed below:\n“In this study, we systematically investigate the variation of interlayer dipole moments in multilayer\nheterostructures using the quantum-confined Stark effect.”\nComment 3: Overall in my opinion the authors did not provide exceptional critical new results in\ntheir revision, but I acknowledge the findings provide new insight for dipole engineering and\ninterlayer-intralayer transition in the context of Γ-related excitons. Authors reply to all the technical\nquestions from other referees in details. I can suggest acceptance of the paper after addressing the\ncomments above.\nOur response: As Reviewer mentioned, the major contributions of our work are providing the new\ninsight of the layer-engineering dipole moment and observation of the giant dipole moment in the\nexperiment. We thank Reviewer for the recognition of our work and appreciate the suggestions and\ncomments by the Reviewer.\nReviewer #2\nThe authors have successfully addressed my concerns. The paper is in good shape now and can be\naccepted.\nOur response: We thank Reviewer for the insightful suggestions and recognition of our work.\nReviewer #3\nThe authors addressed all of my questions thoroughly. I recommend that this manuscript be\npublished in Nature Communications.\nOur response: We appreciate the comments and suggestions by the Reviewer, and thank for the\nrecognition of our work.\nReferences:\n[1] Ciarrocchi, A., Unuchek, D., Avsar, A. et al. Polarization switching and electrical control of\ninterlayer excitons in two-dimensional van der Waals heterostructures. Nature Photon 13, 131–136\n(2019).\n[2] Meng, Y., Ma, L., Yan, L. et al. Strong-interaction-driven quadrupolar-to-dipolar exciton transitions\nin a trilayer moiré superlattice. Nat. Photon. (2025).\n[3] Yu, L., Pistunova, K., Hu, J. et al. Observation of quadrupolar and dipolar excitons in a\nsemiconductor heterotrilayer. Nat. Mater. 22, 1485–1491 (2023)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I thank the authors for the reply. I appreciate that the authors clarify the interlayer to intralayer character transition of this\nspecific heterostructure. This does not remove my concern about the impact of achieving large dipole but only within very\nsmall field, i.e. only limited deltaE. Nevertheless I acknowledge the novelty of this feature in its own context compared to K\nvalley exciton in MX2. The added power dependent PL makes sense but not unexpected. The authors stated that their 2L/3L\ndevice can not stand a field beyond 0.08 V/nm. which seems like a very low threshold. A second device or some clarification\nwould be encourgaed.\nNote that the authors reply that they layer engineered the IX dipole in heterostructure for the first time, but I disagree with\nsuch claim. Fig 6c in supp info of Nat. Mater. 19, 630–636 (2020) showed clear dipole tuning of K valley IX with various\ncomponent thickness. Similarly see also Fig S7 and S8 in Ref.19 indicating similar effect on K valley IX. Various papers with\nheterobilayer separated by BN spacer in principle is also a type of dipole-layer engineering.\nOverall in my opinion the authors did not provide exceptional critical new results in their revision, but I acknowledge the\nfindings provide new insight for dipole engineering and interlayer-intralayer transition in the context of Γ-related excitons.\nAuthors reply to all the technical questions from other referees in details. I can suggest acceptance of the paper after\naddressing the comments above.", "reviewer_2": "The authors have successfully adressed my concerns. The paper is in good shape now and can be accpeted.", "reviewer_3": "The authors addressed all of my questions thoroughly. I recommend that this manuscript be published in Nature\nCommunications."}, "author_response": "Response letter for the manuscript (NCOMMS-25-35571) entitled “Observation of Giant Dipole\nMoments of Interlayer Excitons via Layer Engineering”\nReviewer #1\nComment 1: I thank the authors for the reply. I appreciate that the authors clarify the interlayer to\nintralayer character transition of this specific heterostructure. This does not remove my concern\nabout the impact of achieving large dipole but only within very small field, i.e. only limited deltaE.\nNevertheless I acknowledge the novelty of this feature in its own context compared to K valley\nexciton in MX2. The added power dependent PL makes sense but not unexpected. The authors stated\nthat their 2L/3L device can not stand a field beyond 0.08 V/nm. which seems like a very low\nthreshold. A second device or some clarification would be encouraged.\nOur response: We thank the Reviewer for this question. The maximum electric field that can be\napplied to the device is determined by the limits of the electric field that h-BN can withstand. These\nlimits can be attributed to defects, such as vacancies or impurities, which create localized states within\nthe bandgap that facilitate tunneling and conduction. Figure R1b illustrates the evolution of leakage\ncurrent with the applied electric field for the 2L-WS /3L-InSe device (Figure R1a). When the electric\n2\nfield exceeds 70 mV/nm, the leakage current across the device increases dramatically. Consequently,\nwe refrain from further increasing the field to avoid damaging our devices.\nThe limits of the applied field vary slightly among different devices, ranging from approximately 80\nmV/nm to 120 mV/nm, due to the device variations (please check the Figure S19 in the Supplementary\nMaterial). In comparison to previous studies on interlayer excitons (see Figure R2, refs. [1-3]), the\nelectric field ranges applicable to our heterostructures are similar, albeit slightly smaller. This range\nprovides a sufficient linear Stark shift for extracting dipole moments across various layer combinations.\nFigure R1. (a) Schematic illustration of experimental setup of 2L-WS /3L-InSe heterostructure\n2\nencapsuled between two hBN layers. The leakage current (orange arrow) is detected when the vertical\nelectric field is increased. (b) The current versus the applied electric field.\nFigure R2. Cited images from the previous publishes. (a-c) from ref. [1], [2], and [3] separately.\nComment 2: Note that the authors reply that they layer engineered the IX dipole in heterostructure\nfor the first time, but I disagree with such claim. Fig 6c in supp info of Nat. Mater. 19, 630–636\n(2020) showed clear dipole tuning of K valley IX with various component thickness. Similarly see\nalso Fig S7 and S8 in Ref.19 indicating similar effect on K valley IX. Various papers with\nheterobilayer separated by BN spacer in principle is also a type of dipole-layer engineering.\nOur response: We appreciate the Reviewer for bringing this issue to our attention. The primary\ncontribution of our work is a systematic study of the layer-engineered dipole moment of interlayer\nexcitons, as demonstrated by the linear Stark effects. Additionally, the dipole-dipole interaction is\nenhanced with the increasing dipole moment, and the underlying mechanism is revealed through\nfirst-principles calculations. We modified our expressions in the revised manuscript with the related\nsentences listed below:\n“In this study, we systematically investigate the variation of interlayer dipole moments in multilayer\nheterostructures using the quantum-confined Stark effect.”\nComment 3: Overall in my opinion the authors did not provide exceptional critical new results in\ntheir revision, but I acknowledge the findings provide new insight for dipole engineering and\ninterlayer-intralayer transition in the context of Γ-related excitons. Authors reply to all the technical\nquestions from other referees in details. I can suggest acceptance of the paper after\naddressing the comments above.\nOur response: As Reviewer mentioned, the major contributions of our work are providing the new\ninsight of the layer-engineering dipole moment and observation of the giant dipole moment in the\nexperiment. We thank Reviewer for the recognition of our work and appreciate the suggestions and\ncomments by the Reviewer.\nReviewer #2\nThe authors have successfully addressed my concerns. The paper is in good shape now and can be\naccepted.\nOur response: We thank Reviewer for the insightful suggestions and recognition of our work.\nReviewer #3\nThe authors addressed all of my questions thoroughly. I recommend that this manuscript be\npublished in Nature Communications.\nOur response: We appreciate the comments and suggestions by the Reviewer, and thank for the\nrecognition of our work.\nReferences:\n[1] Ciarrocchi, A., Unuchek, D., Avsar, A. et al. Polarization switching and electrical control of\ninterlayer excitons in two-dimensional van der Waals heterostructures. Nature Photon 13, 131–136\n(2019).\n[2] Meng, Y., Ma, L., Yan, L. et al. Strong-interaction-driven quadrupolar-to-dipolar exciton transitions\nin a trilayer moiré superlattice. Nat. Photon. (2025).\n[3] Yu, L., Pistunova, K., Hu, J. et al. Observation of quadrupolar and dipolar excitons in a\nsemiconductor heterotrilayer. Nat. Mater. 22, 1485–1491 (2023)."}]

Decision letter