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Zhen Lian, Dongxue Chen, Yuze Meng, Xiaotong Chen, Ying Su, Rounak Banerjee, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Sefaattin Tongay, Chuanwei Zhang, Yong-Tao Cui, Su-Fei Shi

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[Exciton Superposition across Moiré States in a Semiconducting Moiré Superlattice](https://mdr.nims.go.jp/datasets/91c07e8b-d3a0-4dc9-bc81-8d50904bc20c)

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Exciton Superposition across Moiré States in a Semiconducting Moiré SuperlatticeArticle https://doi.org/10.1038/s41467-023-40783-zExciton Superposition across Moiré States ina Semiconducting Moiré SuperlatticeZhen Lian1,8, Dongxue Chen 1,8, Yuze Meng1, Xiaotong Chen1, Ying Su2,Rounak Banerjee3, Takashi Taniguchi 4, Kenji Watanabe 5,Sefaattin Tongay 3, Chuanwei Zhang 2, Yong-TaoCui 6 & Su-Fei Shi 1,7Moiré superlattices of semiconducting transition metal dichalcogenidesenable unprecedented spatial control of electron wavefunctions, leading toemerging quantum states. The breaking of translational symmetry furtherintroduces a new degree of freedom: high symmetry moiré sites of energyminima behaving as spatially separated quantum dots. We demonstrate thesuperposition between two moiré sites by constructing a trilayer WSe2/monolayer WS2 moiré heterojunction. The two moiré sites in the first layerWSe2 interfacing WS2 allow the formation of two different interlayer excitons,with the hole residing in either moiré site of the first layer WSe2 and theelectron in the third layer WSe2. An electric field can drive the hybridization ofeither of the interlayer excitons with the intralayer excitons in the third WSe2layer, realizing the continuous tuning of interlayer exciton hopping betweentwomoiré sites and a superposition of the two interlayer excitons, distinctivelydifferent from the natural trilayer WSe2.Design and control of symmetries can lead to symmetry-protectedstates that are promising to revolutionize the field of quantum mate-rials. For example, breaking the inversion symmetry or time-reversalsymmetry can lead to Weyl semimetals1. The inversion symmetrybreaking in transition metal dichalcogenides (TMDCs) gives rise to avalley degree of freedom that is promising for valleytronics andquantum information science based on valley-spin2, which can beaccessed through chiral light.The recent emergence of semiconducting TMDC moirésuperlattices3–9, which are constructed through twisted TMDCs with alattice mismatch or twist angle, enables spatial control of the excitonsin two-dimension (2D) with the tunable periodicity of 1–10 nm andushers in unprecedented opportunities in engineering electrons andexcitons, leading to intriguing correlated electronic states3,6,10–15, thearray of quantum emitters, and correlated exciton states resultingfrom flat excitonic band16–18.Translation symmetry breaking in TMDC moiré superlatticesintroduces a new degree of freedom: moiré sites, the high symmetrypoints in a moiré supercell, which can be local energy minima and actas quantum dots5,19,20 that can confine electrons and excitons, asschematically shown in Fig. 1c. In addition, these high symmetry pointsare protected by the three-fold rotation symmetry and possess theunique valley degree of freedom through the pseudo angularmomentum conservation4,19. As a result, coupling and hybridization ofthese high symmetry points will usher in new venues toward quantuminformation storage and processing. However, unlike the energydegeneracy of different valleys (K and K’), the energy barrier betweendifferentmoiré sites (on the order of 10 s’meV), alongwith their spatialseparation, greatly suppresses the direct coupling between thesemoiré sites.Here, we demonstrate the superposition between two differentmoiré sites by introducing a layer degree of freedom to the TMDCReceived: 15 March 2023Accepted: 10 August 2023Check for updates1Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 2Department of Physics, University of Texas,Dallas, TX 75083, USA. 3School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA. 4International Center forMaterials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5Research Center for Functional Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 6Department of Physics and Astronomy, University of California, Riverside,California 92521, USA. 7Department of Electrical, Computer & Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 8These authorscontributed equally: Zhen Lian, Dongxue Chen. e-mail: yongtao.cui@ucr.edu; shis2@rpi.eduNature Communications |         (2023) 14:5042 11234567890():,;1234567890():,;http://orcid.org/0000-0002-7440-4230http://orcid.org/0000-0002-7440-4230http://orcid.org/0000-0002-7440-4230http://orcid.org/0000-0002-7440-4230http://orcid.org/0000-0002-7440-4230http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0002-0344-6847http://orcid.org/0000-0002-0344-6847http://orcid.org/0000-0002-0344-6847http://orcid.org/0000-0002-0344-6847http://orcid.org/0000-0002-0344-6847http://orcid.org/0000-0002-8015-1049http://orcid.org/0000-0002-8015-1049http://orcid.org/0000-0002-8015-1049http://orcid.org/0000-0002-8015-1049http://orcid.org/0000-0002-8015-1049http://orcid.org/0000-0001-5158-805Xhttp://orcid.org/0000-0001-5158-805Xhttp://orcid.org/0000-0001-5158-805Xhttp://orcid.org/0000-0001-5158-805Xhttp://orcid.org/0000-0001-5158-805Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40783-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40783-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40783-z&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40783-z&domain=pdfmailto:yongtao.cui@ucr.edumailto:shis2@rpi.edumoiré superlattice. It is well known that the two neighboring layers of2-H TMDC flakes, due to the intralayer inversion symmetry breaking,possess a layer degree of freedom that acts as pseudospins alternatingin odd and even layers2,21. In an angle-aligned trilayer WSe2/monolayerWS2 heterojunction (3LWSe2/1LWS2), new types of interlayer excitonsemerge, with holes residing in the first WSe2 layer either trapped inmoiré A or B site (Fig. 1c)5, and electrons with the same pseudospinresiding in the third WSe2 layer. In particular, we find that these twointerlayer excitons can hybridize through coupling with the intralayerexcitons in the third WSe2 layer. The resulting hybridized excitoninherits both the large oscillator strength from the intralayer excitonsand the sensitive electric field dependence from the moiré interlayerexcitons7,22–24. More interestingly, by applying an electric field, we candrive the transition between the two interlayer moiré excitons’ hybri-dization with the intralayer exciton in the third WSe2 layer, enablingthe continuous tuning of hopping of the interlayer exciton from 100%at one moiré site to 100% at the other, which is otherwise suppressed.In between the transition points, we obtain an excitonic complex thatis the superimposition of the interlayer excitons that are otherwiselocalized at moiré A and B sites.Results and DiscussionsGate dependence of reflectance contrastThe schematic of the 3LWSe2/1LWS2moiré heterojunction is shown inFig. 1a, which is fabricated into a dual-gated device structure in whichthe doping and electric field can be independently controlled. We alsofabricated a device of a dual-gated 2-H phase trilayer WSe2 (3L WSe2)(schematically shown in Fig. 1b) for the control study.The doping-dependent optical reflectance contrast spectra of the3L WSe2/1L WS2 heterojunction device are shown in Fig. 2e, which isevidently different from that of the natural trilayer (3L) WSe2 device(Fig. 2f). Themost pronounced resonance for the natural trilayerWSe2(Fig. 2f) is the intralayer exciton resonance XA, which is at ~ 1.70 eV atzero doping, redshifted compared to the A exciton resonance inmonolayer WSe2 (~1.73 eV)25. XA is redshifted linearly for both n and pdoping in a symmetric fashion, with a slope of ~1.3meV/1012 cm−2. IX3Lare the interlayer excitons with the hole and electron separated in thefirst and third WSe2 layer, which have two degenerate modes asschematically shown in Fig. 2c and are named as IX+3L and IX�3L (“+” and“−” denote the direction of the dipole moment in the sample coordi-nate. The direction of the positive electric field or dipole moment isdefined as from the top gate to the back gate in 3 L WSe2, and fromWSe2 to WS2 in 3L WSe2/ 1 L WS2.). IX2s3L is the 2s state of the IX3L. Thenatures of IX3L and IX2s3L become obvious in our later discussion of theelectricfielddependent reflectance contrast spectra. Zoom-in of Fig. 2fwith enhanced contrast is plotted in Fig. S2 to show IX3L and IX2s3L moreclearly. Accompanying XA is a less pronounced resonance XA’ with alarger slope (2.7meV/1012 cm−2). XA’ is likely the exciton resonance ofthe middle (second) layer WSe2 and is not the focus of this work (seedetailed discussion in Supplementary Section 14).In the optical reflectance contrast spectra of 3L WSe2/1L WS2moiré heterojunction (Fig. 2e), there is an exciton resonance ðXIMÞlocated at the lower energy side of XA (~1.667 eV), which is onlyobservable in angle-aligned 3L WSe2/1L WS2 heterojunctions butabsent in heterojunctions with large twist angles (See supplementarysection 10 for detailed discussion). XIM is the previously discoveredmoiré intralayer exciton peak in the first layer WSe2 interfacing WS2,with the exciton trapped at the moiré A site. The doping dependenceof XIM clearly show the signature of the correlated insulating states atthe filling factor of 1 and −1, corresponding to one electron and onehole per moiré superlattice, which was discussed in our previouspublication26. On the p-doping side, the exciton resonances of XA andXA’ are labeled as such due to their similar behaviors compared withthat from the trilayer WSe2 (Fig. 2f), with a redshift slope of 1.0 and2.1meV/1012 cm−2, respectively. The n-doping side is differentbecause the electrostatically introduced electrons are in the WS2layer instead of the WSe2 layers due to the type II alignment, leavingthe WSe2 layers charge-neutral. We identify the XA and XA’ in then-doping side through their slopes as well, 1.0 and 2.1meV/1012cm−2,respectively, the same as those in the p-doping region. The abruptblueshift of the XA in the n-doping side (starts at n > 1 and resonantenergy around 1.725 eV) is likely due to the built-in electric field onWSe2 layers arising from the electron accumulation in WS2. We leavethe related discussion in Supplementary Information Section 15. Thefocus of our work here is on the interlayer excitons within the 3LWSe2 of the 3L WSe2/1L WS2 moiré heterojunction, with their sche-matics shown in Fig. 2a, b. The IX+3L branch is visible and pronouncedat the blue arrow in Fig. 2e, partially because it hybridizes withintralayer excitons and gains some oscillator strength but alsobecause it retains the extended nature of interlayer excitons, hencesensing dielectric environment change associated with the Mottinsulator transition at filling of one electron per moiré superlatticeVbgabcVtgVbgVtghh (A) hX (B)hhhM (C)WSe2WS2AuAu Auh-BNh-BNFLGFLGSiO  2  /SiAuAu AuFLGFLGSiO  2  /Sih-BNh-BNFig. 1 | Moiré site degree of freedom. a and b are schematics of 3 L WSe2/ 1 L WS2moiré heterojunction device and natural trilayer WSe2 devices, respectively. Bothdevices are in a dual-gate configuration. c is the schematic of the WSe2/WS2 moirésuperlattice, with three high symmetry points of C3 symmetry shown as hh, hX andhM. The naming convention of hh, hX and hM corresponds to aligning the hexagoncenter of the hole layer (WSe2)with the hexagoncenter (h), the chalcogen atom (X),and themetal atom (M) of the electron layer (WS2)20, whichwe also call asA, B andCmoiré sites for convenience. A and B sites are energy minima for holes and behaveas quantumdots that confine carriers and excitons.Weuse the holes for illustrationin c, but the trapping of electrons and excitons will be similar.Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 2(n = 1). The nature of both resonances are revealed in our later dis-cussion of the electric field dependence study.Interlayer hybridized excitons in 3L WSe2The electricfield-dependent reflectance contrast spectra of the trilayerWSe2 device is shown in Fig. 3a, which is symmetric about the electricfield due to its symmetric structure. Themost noticeable feature is the“cross” pattern originating from the electric field evolution frominterlayer exciton IX3L. The slope of eachbranchof the cross is roughlythe same. These are arising from the Stark shift of the interlayer exci-ton IX3L, with the two degenerate modes (IX�3L and IX+3L) shiftingoppositely under an electric field due to the dipole moment of oppo-site polarity. The Stark energy shift can be expressed as ΔE = � edF ,where F is the local electric field, e is the electron charge, and d is theelectron and hole separation. We extract the value of d to be about1.26 nm for both IX�3L and IX+3L, which is about twice that of interlayerexciton dipole moment in WSe2/WS2 (0.7 nm)7, confirming that theelectron and hole of interlayer exciton occupy the two outside WSe2layers in a natural trilayer WSe2.The level avoiding at the intralayer exciton A (~1.70 eV) in Fig. 3aarises from the hybridization of the interlayer exciton and intralayerexciton. In the 2H trilayer WSe2, there is significant tunneling of holesbetween the first and third layer WSe2 as they have the same valley-layer pseudo spin, allowing the hybridization of the interlayer excitonswith the intralayer excitons in either the first or third WSe2 layer27, asschematically shown in Fig. 3d. This hybridization canbewell capturedby a coupled two-level system, which is given by the followingHamiltonian in the basis of intralayer exciton and interlayer exciton:Xa ΔΔ XiðFÞ� �ð1Þwhere Xa is the energy of the intralayer exciton, XiðFÞ is the energy ofthe interlayer exciton at a given electric field F, Δ is the couplingstrength (see Supplementary Information Section 13 for details).Take the positive electric field (direction defined in Fig. 3d) sce-nario as an example (Fig. 3c): a linearly dispersed interlayer excitonIX+3L (white dotted line in Fig. 3c) and a non-dispersed intralayer exci-ton XA (black dotted line) can be used to well fit the observed hybri-dized spectra (red and blue dashed lines). From the fitting, we extractthe coupling strength to be 10.7 ± 0.3meV, larger than the linewidth ofthe hybridized exciton (~ 9.0 ±0.3meV). The scenario of the negativeelectric field is similar, where the other interlayer exciton mode, IX�3L,hybridizes with the intralayer exciton (XA) when the energy of the twoexcitons is tuned to resonance via the electric field. It is worth notingthat we ignore the conduction band hybridization of the first and thirdlayer WSe2, which is theoretically predicted to be nonzero but ordersof magnitude smaller than the holes27. The neglection of the conduc-tion band hybridization is also justified by the electric-field-dependentreflectance contrast spectra of 3 L WSe2/ 1 L WS2, which is asymmetricabout positive and negative electric fields (later discussion of Fig. 4).The additional level avoiding at the energy around 1.79 eV inFig. 3a is due to the hybridization of the interlayer exciton ðIX3LÞ withthe 2s state of intralayer A exciton (Fig. 3a and Fig. S4a, b). The secondlevel avoiding at higher energy (~1.80 eV) is due to the hybridization ofthe excited state of the interlayer exciton ðIX2s3LÞ and 2s of theA exciton,which we enhance the contrast and show in Fig. S4a, b. It is interestingto note that the energy difference between the ground state and 2s ofinterlayer exciton IX3L is about 51meV, smaller but at the same orderof magnitude compared with the energy difference between 2s and 1sof A exciton for trilayer WSe2 (~95meV, Fig. S4a, b), suggesting thestrongly bound nature of the interlayer exciton IX3L. All these hybri-dization features are absent in a dual-gated nature bilayer WSe2(Fig. S8), which is AB stacked with two layers of different layer pseu-dospin, further confirming our interpretation. The electric-field-dependent reflectance contrast spectra of a 4 L WSe2 device (Fig. S7)show similar hybridization features but with two “crosses” slightlyshifted in energy, about 10meV. According to the interpretation of the3 L WSe2 data, these two crosses are the two types of interlayer exci-tons from the 1st and 3rd layer WSe2 and the 2nd and 4th layer WSe2,which slightly shift in energy due to possible dielectric environmentdifferences28,29.Hybridized Excitons across Moiré States in 3 L WSe2/ 1 L WS2We now turn to the study of the electric field-dependent reflectancecontrast spectra of the 3 LWSe2/ 1 L WS2 moiré heterojunction, shownin Fig. 4c. The negative electricfield side has some similarity comparedwith that from trilayer WSe2, while the positive electric field side issignificantly different. More specifically, the hybridized spectrum onthe positive electric field side involves three exciton branches: two3L WSe2WS2eb c3L WSe2fn = 2n = 1n = 0n = -1XAXA’3L WSe2XA’XA’I   XAXA’eh eha3L WSe2/ 1L WS2eh ehId(n=1) XAFig. 2 | Doping-dependent reflectance contrast spectra of 3L WSe2/ 1L WS2 andnatural trilayerWSe2Devices. a,b and e are the schematic atomic structure, bandalignment, and the doping-dependent reflectance contrast spectra of 3L WSe2/ 1LWS2 measured from device D1. c, d and f are the schematic atomic structure, bandalignment, and the doping-dependent reflectance contrast spectra of natural tri-layer WSe2 measured from device D2. The blue arrow in e denotes the enhancedreflection signal of the hybridized exciton (interlayer exciton IX+3L hybridized withintralayer exciton) at the Mott insulator state at n = 1.Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 3dispersive (white dotted lines in Fig. 4e) and one non-dispersive (blackdotted line in Fig. 4e) branch. The necessity of involving three excitonbranches is also obvious from the derivative of Fig. 4e with respect tothe electricfield, as shown in Fig. S3d. The twodispersive excitons havea similar slope for the Stark shift, translating to electron and holeseparations of 1.313 ± 0.004nmand 1.609 ± 0.004 nm (fitting details inSupplementary Information Section 13). Therefore, they are theinterlayer excitons, similar to IX+3L in the natural trilayerWSe2, with thehole in the firstWSe2 layer interfacingWS2 and the electron in the thirdWSe2 layer away from the interface. The two different interlayer exci-tons stem from the moiré coupling modified valence band of the firstWSe2 layer. As schematically shown in Fig. 4a and b, the moiré mod-ulation folds the valence band of the first WSe2 layer into moiréminibands. The two interlayer excitons correspond to holes occupyingthe two moiré minibands located at different moiré sites20, whicheffectively behave as two spatially separated quantum dots. Each ofthem is located at an energyminimum at a high symmetry point withinthe moiré unit cell, which we call moiré A and B sites, respectively. Wethus label these two interlayer excitons as IX+ ðAÞ3L and IX+ ðBÞ3L . Since theWS2 and first WSe2 layer are aligned at 60 degrees (H stacked) asdetermined by the second harmonic generation (SHG) spectra(Fig. S5), themoiré A and B sites correspond to theHhh andHXh stackingconfigurations shown in Fig. 4b. The energy separation of the twointerlayer excitons at zero electric field, 69meV, represents the energydifference between the top two moiré minibands, if we ignore thedifference in exciton binding energy. This value is consistent with theenergy difference between the intralayer excitons trapped at moiré Aand B sites in the WSe2/WS2 moiré superlattice, ~53 meV26. Theremaining non-dispersive branch corresponds to the intralayer exci-ton, XA, with both hole and electron in the thirdWSe2 layer. Therefore,IX+ ðAÞ3L , IX+ ðBÞ3L , and XA hybridize by sharing the electron in the thirdWSe2 layer. The above picture of hybridization involving two moiréinterlayer excitons are confirmed by a control device (D4) of 3 LWSe2/1 LWS2 in the dual-gate configuration, with an intentionallymisalignedangle (20-degree) between WSe2 and WS2 layers. The electric-field-dependent reflectance contrast spectra (Fig. S11) indeed becomesymmetric about the electric field and similar to that of natural 3 LWSe2, and they show no signs of interlayer moiré excitons (IX+ ðAÞ3Land IX+ ðBÞ3L ).It is worth noting that direct tunneling between moiré A and Bsites is suppressed due to the energy barrier, their spatial separation,and different stacking symmetry. Therefore, a direct hybridizationbetween these two sites is difficult to achieve, unlike the degeneratevalley-spin bands in TMDCs. However, with the assistance from themobile intralayer exciton in the third WSe2 layer, hybridization ofmoiré A and B sites is realized, and we can controllably tune theinterlayer excitons IX+3L between moiré A and B sites. In fact, thehybridized exciton notated with the cyan dashed line is a mixture ofinterlayer excitons localized at the moiré A site and B site, with theprobability tunable from 100% at A to 100% at B site by controlling theelectric field (Fig. 4f).On the negative electric field side, the interlayer exciton involvedin the hybridization is IX�3L, with the hole in the third layer WSe2 notexperiencing the moiré modulation. Meanwhile, the intralayer excitonin the 1st WSe2 layer is modified by the moiré potential to have a lowerenergy of ~ 1.667 eV and is trapped at themoiré A site, which is labeledas XIM. As a result, hybridization occurs between IX�3L and XIM. Theircoupling strength is extracted to be 11.4 ± 0.1meV. The interlayerexciton IX�3L can also couple to the other moiré excitons from the 1stlayer WSe2, which contributes to the weak features in Fig. 4 and areshown with enhanced contrast in Fig. S4c, d.The asymmetry of Fig. 4c between the n- and p-doping sidesfurther justifies our neglection of conduction band hybridization: IX�3Lnearhybridization regiond inFig. 4c goes directly throughXA, and IX+3Lnear region e goes directly through XIM, with neither showing levelavoiding. If the conduction band hybridization is significant, we shouldbcabc3L WSe2dehhehh-E +EI+Ehe hheh-EFig. 3 | Interlayer and intralayer exciton hybridization in natural trilayerWSe2.a shows the electric field dependence of reflectance contrast spectra measuredfrom natural trilayer WSe2 device (D2) plotted in log scale. b is the zoom-in of a inthe region between 1.64 eV and 1.74 eV at negative electric fields plotted in linearscale. c is the zoom-in of a in the region between 1.64 eV and 1.74 eV at positiveelectric fields plotted in linear scale. The dashed red and blue lines show the fittingresult of the hybridized excitonic states obtained by fitting the peak positions witha two-level hybridization model. The white and black dotted lines are the energiesof unhybridized intralayer and interlayer excitons obtained from the fitting. dshows the schematics of the interlayer and intralayer excitons involved in thehybridization, both in real space and the band alignment configurations.Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 4observe the hybridization of two interlayer excitons (due to moirémodulated conduction bands) and XA. Similarly, the interlayer excitonfrom region e (IX+3L) in Fig. 4c should hybridize with XIM. We include adetailed discussion in Supplementary Information Section 16.In summary,wehavedemonstrateda strategy to realize continuoustuning of interlayer exciton hopping between differentmoiré sites in 3 LWSe2/ 1 LWS2moiré superlattices. These additional degrees of freedomenable the formation of a tunable honeycomb lattice of excitons withexciting opportunities for engineering new quantum states. For exam-ple, considering the large spin-orbit coupling in TMDCs, the continuoustuning of the hopping can be potentially exploited for constructingDirac andWeylmodes of excitons, aswell as the topologically protectededge states connecting these modes19. Our demonstration of thesuperposition of excitons across the different moiré sites also inspiresnew venues of quantum information processing and harnessing the newmoiré site degree of freedom for twistronics.MethodsSample FabricationWeused the samedrypick-upmethod30 as reported in our earlierworkto fabricate TMDC heterostructures17,26. The gold electrodes are pre-patterned on the Si/SiO2 substrate. The monolayer TMDC flakes, BNflakes, and few-layer graphene (FLG) flakes are exfoliated on siliconchips with 285 nm thermal oxide. The thickness of BN flakes wasdetermined by atomic force microscopy (AFM). The layer numbers ofWSe2 flakes were identified by optical contrast with the assistance ofsecond-harmonic generation (SHG). Top BN and bottom flakes withequal thicknesswere intentionally used for devices D1, D2, andD3. Thepolycarbonate (PC)/ polydimethylsiloxane (PDMS) stamp was used topick up TMDCmonolayer and other flakes sequentially. The alignmentof each layer is achieved under a home-builtmicroscope transfer stagewith the rotation controlled with an accuracy of 0.02 degrees. The PCis then removed in the chloroform/isopropanol sequence and driedwith nitrogen gas. The final constructed devices were annealed in avacuum (<10−6 torr) at 250 °C for 8 hours.Optical MeasurementsDuring the optical measurements, a home-built confocal imagingsystem was used to focus the laser onto the sample (with a beam spotdiameter ~ 2 µm) and collect the optical signal into a spectrometer(Princeton Instruments). The reflectance contrast measurement wasperformed using a supercontinuum laser source (YSL photonics). Arelative flat reflectance background R0 was obtained by fitting thereflectance spectrum at high hole-doping level with a polynomialfunction for each measured spot (see Supplementary Section 11 fordetails). The reflectance contrast is defined as dRR = R�R0R0. The reflec-tance contrast from device D1 and D2 are added by 0.3 and −0.3 forbetter presentation in the log scale. All optical spectroscopy mea-surements were performed at the temperature of 10 K with a Montanacryostat. The polarized SHG measurements were performed with ade 3L WSe2/1L WS2aec-E +Eehhbfd+Ehe hheh-EH0 20 40 60 80 100020406080100Probability (%)Electric field (mV/nm)XA IX+(A)3L IX+(B)3LhehFig. 4 | Interlayer and intralayer exciton hybridization in the angle-aligned 3LWSe2/1L WS2 heterostructure. a and b show the schematic band alignment andthe real-space distribution of the hybridized excitons in 3L WSe2/1L WS2 moiréheterojunction. c shows the electric field dependence of reflectance contrastspectra measured from 3 L WSe2/1L WS2 device (D1). d is the zoom-in of a in theregionbetween 1.62 eV and 1.72 eV at negative electricfields. e is the zoom-in of a inthe region between 1.64 eV and 1.74 eV at positive electric fields. The dashed linesshow the hybridized excitonic states obtained by fitting the peak positions. Thedotted lines are the energies of unhybridized intralayer and interlayer excitonsobtained from the fitting. A two-level hybridization model using one intralayerexciton and one interlayer exciton as bases is used to fit the peak positions ind, while a three-level hybridization model with one intralayer exciton and twodifferent interlayer excitons is used to fit the peak positions in e. f shows thefractional composition of the hybridized exciton corresponding to the cyan line asa function of the electric field, expressed as the probability of each interlayer orintralayer exciton.Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 5pulsed laser excitation centered at 900nm (Ti: Sapphire; CoherentChameleon) with a repetition rate of 80MHz and a power of 80mW.The crystal axes of the sample were fixed. A half-waveplate was placedbetween the beam splitter and the objective andwas rotated to changethe polarization angles of both the excitation laser and the SHG signal.Doping and Electric Field CalculationsThe density of carriers introduced by the electrostatic gating is givenby neðnpÞ=Ctg ðVtg � V0tg Þ+Cbg ðVbg � V0bg Þ, where Ctg ðCbg Þ are thegeometry capacitance of the top gate (back gate) and Vtg ðVbg Þ are thetop gate (back gate) voltage. V0tg and V0bg are the onset gate voltages ofthe top gate and the back gate, determined experimentally from theregions where the 2s peaks remain visible. The electrical field in theTMDC is given by F = εBN=εTMDCðVtg=2d1 � Vbg=2d2Þ, where d1ðd2Þ isthe thickness of the top (bottom) BN determined by atomic forcemicroscopy, εBN =3:5 and εTMDC = 7:2 are the relative dielectric con-stants of h-BN and TMDC, respectively31,32.Data availabilityThe data in Figs. 1–4 areprovided in the sourcedata files. All other datathat support the plots within this paper and other findings of this studyare available from the corresponding author upon reasonablerequest. Source data are provided with this paper.References1. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semi-metals in three-dimensional solids. Rev. Mod. Phys. 90,15001 (2018).2. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins inlayered transition metal dichalcogenides. Nat. Phys. 10,343–350 (2014).3. Regan, E. C. et al. Mott and generalized Wigner crystal states inWSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).4. Jin, C. et al. Identification of spin, valley and moiré quasi-angularmomentum of interlayer excitons. Nat. Phys. 15, 1140–1144 (2019).5. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 hetero-structure superlattices. Nature 567, 76–80 (2019).6. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2moiré superlattices. Nature 579, 353–358 (2020).7. Tang, Y. et al. 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The optical spectroscopy measurementswere supported by a DURIP awards through Grant FA9550-20-1-0179and FA9550-23-1- 0084. S.T. acknowledges DMR-2111812 for materialsdevelopment, DMR-2206987 for structural characterization and mag-netic impurity tests, DMR-2052527 for electronic tests, CMMI-2129412for structure-performance-property relations, and DOE SC-SC0020653 for initial excitonic characterization. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grant Numbers 19H05790,20H00354, and 21H05233). Y.S. and C.Z. acknowledge support fromNSF PHY-2110212, PHY-1806227, ARO (W911NF17-1-0128), and AFOSR(FA9550-20-1-0220).Author contributionsS.-F.S. conceived the project. Z.L., D.C. and Y.M. fabricated devices. Z.L.performed measurements. M.B. and S.T. grew the TMDC crystals. T.T.and K.W. grew the BNcrystals. S.-F. S., Y.-T.C., Z.L. andD.C. analyzed thedata. S.-F. S. supervised the project. S.-F. S. and Y.-T. C. wrote themanuscript with input from all authors.Competing interestsThe authors declare no competing interest.Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 6https://doi.org/10.48550/ARXIV.2212.14338https://doi.org/10.48550/ARXIV.2212.14338Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-40783-z.Correspondence and requests for materials should be addressed toYong-Tao Cui or Su-Fei Shi.Peer review information Nature Communications thanks Nadine Leis-gang, and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-40783-zNature Communications |         (2023) 14:5042 7https://doi.org/10.1038/s41467-023-40783-zhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Exciton Superposition across Moiré States in a Semiconducting Moiré Superlattice Results and Discussions Gate dependence of reflectance contrast Interlayer hybridized excitons in 3L WSe2 Hybridized Excitons across Moiré States in 3 L WSe2/ 1 L WS2 Methods Sample Fabrication Optical Measurements Doping and Electric Field Calculations Data availability References Acknowledgements Author contributions Competing interests Additional information