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Zhen Lian, Dongxue Chen, Lei Ma, Yuze Meng, Ying Su, Li Yan, Xiong Huang, Qiran Wu, Xinyue Chen, Mark Blei, [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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[Quadrupolar excitons and hybridized interlayer Mott insulator in a trilayer moiré superlattice](https://mdr.nims.go.jp/datasets/ef6f285c-7bd1-4e22-a120-0292adfd4b14)

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Quadrupolar excitons and hybridized interlayer Mott insulator in a trilayer moiré superlatticeArticle https://doi.org/10.1038/s41467-023-40288-9Quadrupolar excitons and hybridizedinterlayer Mott insulator in a trilayer moirésuperlatticeZhen Lian1,9, Dongxue Chen 1,9, Lei Ma 1,9, Yuze Meng1,9, Ying Su2, Li Yan1,Xiong Huang 3,4, Qiran Wu3, Xinyue Chen1, Mark Blei5, Takashi Taniguchi 6,Kenji Watanabe 7, Sefaattin Tongay 5, Chuanwei Zhang 2,Yong-Tao Cui 3 & Su-Fei Shi 1,8Transition metal dichalcogenide (TMDC) moiré superlattices, owing to themoiré flatbands and strong correlation, can host periodic electron crystals andfascinating correlated physics. The TMDC heterojunctions in the type-IIalignment also enable long-lived interlayer excitons that are promising forcorrelatedbosonic states, while the interaction is dictatedby the asymmetry ofthe heterojunction. Here we demonstrate a new excitonic state, quadrupolarexciton, in a symmetric WSe2-WS2-WSe2 trilayer moiré superlattice. Thequadrupolar excitons exhibit a quadratic dependence on the electric field,distinctively different from the linear Stark shift of the dipolar excitons inheterobilayers. This quadrupolar exciton stems from the hybridization ofWSe2 valence moiré flatbands. The same mechanism also gives rise to aninterlayer Mott insulator state, in which the two WSe2 layers share one holelaterally confined in one moiré unit cell. In contrast, the hole occupationprobability in each layer can be continuously tuned via an out-of-plane electricfield, reaching 100% in the top or bottom WSe2 under a large electric field,accompanying the transition from quadrupolar excitons to dipolar excitons.Our work demonstrates a trilayer moiré system as a new exciting playgroundfor realizing novel correlated states and engineering quantum phasetransitions.Monolayer TMDCs, as atomically thin direct bandgap semiconductors,offer a unique playground to explore novel optoelectronicphenomena1,2, especially with the ability to form heterostructures thatenable a new range of control knobs. For example, TMDC hetero-junctions in a type-II alignment host long-lived interlayer excitons3–6,with electrons and holes residing in different layers3,4. These interlayerexcitons possess the valley degree of freedom, as well as a large Starkshift due to the permanent dipolemoment, rendering thempromisingcandidates as tunable quantum emitters6. Recently, angle-alignedTMDC moiré superlattices exhibit strong Coulomb interactions in theReceived: 10 March 2023Accepted: 21 July 2023Check for updates1Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 2Department of Physics, University of Texas atDallas, Dallas, TX 75083, USA. 3Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA. 4Department of Materials Scienceand Engineering, University of California, Riverside, CA 92521, USA. 5School for Engineering ofMatter, Transport and Energy, Arizona State University, Tempe,AZ 85287, USA. 6International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.7ResearchCenter for FunctionalMaterials, National Institute forMaterials Science, 1-1 Namiki, Tsukuba305-0044, Japan. 8Department of Electrical, Computer& Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 9These authors contributed equally: Zhen Lian, Dongxue Chen, Lei Ma, YuzeMeng. e-mail: yongtao.cui@ucr.edu; shis2@rpi.eduNature Communications |         (2023) 14:4604 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/0000-0003-3325-0287http://orcid.org/0000-0003-3325-0287http://orcid.org/0000-0003-3325-0287http://orcid.org/0000-0003-3325-0287http://orcid.org/0000-0003-3325-0287http://orcid.org/0000-0003-2035-8387http://orcid.org/0000-0003-2035-8387http://orcid.org/0000-0003-2035-8387http://orcid.org/0000-0003-2035-8387http://orcid.org/0000-0003-2035-8387http://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/s41467-023-40288-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40288-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40288-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-40288-9&domain=pdfmailto:yongtao.cui@ucr.edumailto:shis2@rpi.eduelectronic flatbands, leading to correlated states7–19 such as Mottinsulator and generalizedWigner crystal7,8,12,17. Themoiré coupling alsogives rise to flat excitonic bands20–23 that could potentially be utilizedto realize correlated bosonic states24, such as Bose-Einstein con-densation (BEC) and superfluidity25–27. The interaction between inter-layer excitons is dominated by the repulsive force between theirpermanent dipoles, whose alignment is dictated by the asymmetry ofthe heterostructure, with electrons and holes separated in two differ-ent layers.In this work, we report a new interlayer quadrupolar exciton in asymmetric TMDC heterostructure: angle-aligned WSe2/WS2/WSe2 tri-layer. The interlayer excitons in the top and bottom bilayers haveopposite polarities, which restores the symmetry. Their hybridizationthen forms a superposition state of interlayer excitons, canceling thedipolar moments and giving rise to a quadrupolar exciton, which hasbeen predicted to enable intriguing quantumphase transition26,28–30. Inthe presence of moiré coupling, this hybridization further gives rise toa new type of correlated electronic state, hybridized interlayer Mottinsulator, in which the correlated holes are shared between the twoWSe2 layers, and the layer population can be continuously tuned by anelectric field.Results and discussionQuadrupolar exciton in angle-aligned t-WSe2/WS2/b-WSe2trilayerThe typical device structure is schematically shown in Fig. 1a, whichcontains three regions of different stackings among the three mono-layers: (I) WS2 over the bottomWSe2, whichwe denote asWS2/b-WSe2;(II) top WSe2 over WS2 (t-WSe2/WS2); and (III) the t-WSe2/WS2/b-WSe2trilayer. The whole device is gated by the top and bottom gateelectrodes made of few-layer graphene (FLG), which provides inde-pendent control of the electric field and doping.In the bilayer regions I and II, the WSe2/WS2 moiré superlatticeshost both correlated electrons and interlayer excitons due to the type-II band alignment (Fig. 1c). The interlayer excitons, with holes residingin the WSe2 layer and electrons in the WS2 layer (Fig. 1c), interact withthe correlated electrons and can be used to read out the transitions atthe correlated insulating states17,31–34. The doping-dependent photo-luminescence (PL) spectra in these regions (Fig. 1e, f) clearly revealthese features: the interlayer exciton PL peak has a strong intensity atthe charge neutrality point (CNP), which decreases quickly upondoping; the PL energy and intensity are also modulated by correlatedinsulator states such as the Mott insulator states at both n = 1 and −1,consistent with the previous studies12,31.In the trilayer region III, we expect quadrupolar excitons asschematically plotted in Fig. 1b. The quadrupolar exciton is thesuperposition of the two dipolar excitons of opposite polaritiesthrough the hybridization of the valence bands in the top and bottomWSe2 layers, which leads to the splitting of valence bands, Δ± , asshown in Fig. 1d, similar to the formation of bonding and antibondingstates in a double-well system29. As a result, the quadrupolar excitonswill have two branches: one at lower energy than the dipolar excitonand the other at higher energy, assuming that all have similar bindingenergies29. Figure 1g plots the PL in this region, which indeed exhibits amajor PL resonance at energies below the dipolar excitons in Fig. 1eand f. We have not observed any PL resonance corresponding to thehigher energy quadrupolar exciton yet, while some devices show highenergy exciton PL with different nature that we are going to explore inthe future (details in Supplementary Information Section 18). Thedoping dependence is also drastically different: the intensity of theWS2WSe2SiSiOWS2WSe2+-+-++-WSe2WS2 WSe2WSe2 Bilayer TrilayerVBdBilayere f ga bcE > 0Au2FLGFig. 1 | Excitons in different stacking structures of the trilayer device.aSchematicsof thedevice structurewith threedifferent regions: (I)WS2/b-WSe2 (II)t-WSe2/WS2/b-WSe2 (III) top bilayer, t-WSe2/WS2. b Schematics of the dipolar andquadrupolar excitons configuration. c Type-II alignment of the angle-alignedWSe2/WS2 heterobilayer. d Valence band hybridization in the trilayer region, comparedwith the flat valence band of WSe2 in the WSe2/WS2 moiré bilayer regions. e–g aredoping-dependent PL spectra for regions I, II, and III. The PL data were taken fromdevice D5.Article https://doi.org/10.1038/s41467-023-40288-9Nature Communications |         (2023) 14:4604 2lower energyPLpeak retains uponhole doping andonly starts todecayat n = −1 (we will discuss this in more detail later).The quadrupole nature of the excitons in the trilayer region isconfirmed by the electric field-dependent PL spectra. In regions I(Fig. 2a) and II (Fig. 2b), the interlayer exciton PL peaks both shiftlinearly as a function of the out-of-plane electricfield butwith oppositesigns of the slope. The slope is −0.72 e � nm for WS2/b-WSe2 (region I)and0.66 e � nm for t-WSe2/WS2 (region II), consistentwith the previousresults21,35–39. In contrast, the PL from the trilayer region III is symmetricabout the electric field, and the resonance energy exhibits a quadraticdependence on the electric field, as shown in Fig. 2c, d, clearlydemonstrating that the trilayer PL is from quadrupolar excitons. ThePL resonance energy can bewell fitted by a quadrupolar excitonmodel(orange curves in Fig. 2d, details in Supplementary Information Sec-tion 9). It is worth noting that at large electric fields, the quadrupolarexciton approaches the linear Stark shift of dipolar excitons with aslope around 0.7 e � nm (dashed lines), matching what we extractedfrom the data in the bilayer regions I and II. We further extract theΔDQ,the energy difference between dipolar excitons and quadrupolarexcitons under net zero electric field, to be about 12meV from thefitting in Fig. 2d (Supplementary Information Section 9), consistentwith the theoretical calculation for a similar trilayer structure(10–30meV in WSe2/MoSe2/WSe2)29. We have also reproduced similarquadrupolar exciton behaviors in other angle-alignedWSe2/WS2/WSe2devices, which show a ΔDQ about 30meV (device D2, SupplementaryInformation Section 10) and 9meV (device D1 and D3, SupplementaryInformation Section 14). We note that the dipolar exciton resonanceenergies in regions I and II only serve as a guide for the two dipolarexcitons involved in forming the quadrupolar excitons due todielectric environment difference and possible spatial inhomogeneity.The energies of the two dipolar excitons that form quadrupolar exci-tons in region III can be extracted from the fitting and are similar invalues, typically less than 7meV (detailed discussion in SupplementaryInformation Section 14). In fact, the electric field dependence of thequadrupolar exciton can be used to extract the energy differencebetween the two dipolar excitons involved in the hybridization, whichdictates the hybridization to occur at a finite electric field that tunesthe two dipolar exciton energies into resonance (details in Supple-mentary Information Section 14). We also want to mention that thehigher energy mode of the predicted quadrupolar excitons (asym-metric quadrupolar exciton mode29) is missing in Fig. 2, likely due tothe excited state or even dark state nature40 of the quadrupolar exci-ton, which leads to the absence of PL.The quadrupolar excitons show distinctively different powerdependence compared with that from dipolar excitons, as shown inFig. S5. The integrated PL intensity of quadrupolar excitons exhibitsmore nonlinear dependence than dipolar excitons, likely due to theirlarger size. In addition, the PL peak blueshifts as a function of theexcitation power (Fig. S5b, e) or exciton density (Fig. S6) is smaller forquadrupolar exciton compared with that of dipolar excitons, con-sistent with our expectation of reduced exciton-exciton repulsion forquadrupolar excitons. The estimation of the exciton density can befound in Supplementary Information Section 16.Evidence of an interlayer Mott insulatorNext,we study the interactionbetween thequadrupolar exciton and thecorrelated electrons in the moiré flatlands. We first revisit the dopingdependence of the quadrupolar exciton at zero electric field. Here, theFig. 2 | Electricfield-dependentPLspectraofdipolarandquadrupolarexcitons.a–c are electric field-dependent PL spectra of the region I, II, and III, respectively.d Fitting of the quadrupolar excitons PL resonances (orange curve) on extracted PLpeak energy (purple spheres) as a function of the electric field from (c). The PL peakpositions are extracted by fitting each PL spectrum with a single Lorentzian peak.The PL data were taken from device D5.Article https://doi.org/10.1038/s41467-023-40288-9Nature Communications |         (2023) 14:4604 3filling factor denotes the number of holes per moiré unit cell (“−” signfor holes), the same as those in the moiré bilayer regions I and II.However, since the trilayer consists of two moiré superlattices, both ofwhich can be filledwith carriers, we define their individual filling factorsas nt and nb, respectively, and the total filling factor n =nt + nb.We focuson the lowenergymodeof the trilayer quadrupolar exciton andobservetwomain features in its PL spectra, at n = −1 and n = −2, respectively. Atn = −1, the PL peak energy exhibits a kink (Fig. 3b), and the PL intensitydrops sharply upon further hole doping (Fig. 3c). At n = −2, the PLenergy exhibits a blueshift. These features correspond to the emer-gence of insulating states, similar to the previous studies17,31–34.The behaviors at these two fillings evolve systematically as afunction of the external electric field. Since the device structure issymmetric, the observed PL behaviors are also symmetric with respectto the electric field direction. Figure 3d–g plot examples of PL spectraat selected negative electric fields (direction definition in Fig. 1a), whiledetailed data at both electric field directions are available in Supple-mentary Information Section 8.Note that the labeled values of externalelectric fields are calculated based on voltages applied on the top andbottom gates (see Methods). The effective electric fields between thetop andbottomWSe2 layerswill bedifferent due to carrier populationsand layer chemical potentials (Supplementary Information Section 11).As an electric field is applied, the PL spectra of the low energy quad-rupolar mode remain largely unchanged concerning the two mainfeatures described above in the low field regime (Fig. 3d, e). However,it changes drastically at high electric fields (Fig. 3f, g): the PL intensitydrops quickly when doped away from CNP, and the PL energy exhibitsa blueshift at n = −1 instead of n = −2. In fact, the PL spectra at highelectric fields resemble that of dipolar excitons in a moiré bilayer(Fig. 1e, f, as well as our previous study26). Therefore, the observedchange in the PL spectra signals the transition from a quadrupolarexciton to a dipolar exciton. Similar results were reproduced inanother device with the same structure (device D3), as shown in Sup-plementary Information Section 12.With the understanding of the quadrupolar to dipolar excitontransition, we now discuss the nature of the n = −1 and −2 states andtheir evolution under electric fields. Figure 4a, c plot the PL intensityand peak energy as a function of both doping (filling factor) andexternal electric field, respectively. At n = −1, the PL energy andintensity both change abruptly above a certain threshold externalelectric field Ec,�1 (about 44mV/nm), while at n = −2, the PL blueshiftdisappearswhen the external electricfield exceeds Ec,�2 (about 32mV/nm). For the n = −1 state, in the absence of an external electric field,each hole is hybridized between the top and bottomWSe2 layers withFig. 3 | Evolution of doping-dependent PL spectra of the trilayer region atdifferent electric fields. a) the PL spectra as a function of the filling factor at thezero electric field. b PL peak energy and c integrated PL intensity, extracted from(a), plotted as a function of the filling factor. d–g are doping-dependent PL spectraat several external electric fields increasing in the negative direction. d, e are in thequadrupolar exciton regime, while f, g are transitioned to the dipolar excitonregime. The dotted white lines in the color plots are the extracted PL peak energiesthrough fitting (details in Supplementary Information Section 8). The PL data weretaken from device D1.Article https://doi.org/10.1038/s41467-023-40288-9Nature Communications |         (2023) 14:4604 4equal probability, i.e., the hole wavefunction is a superposition of thetop andbottomWSe2 valencemoiré bands. Laterally it is confined suchthat there is one hole in the twooverlappingmoiré unit cells combined(Fig. 4d). This state is a new type of correlated state in the trilayermoiré superlattice, an interlayer Mott insulator. The hole is allowed totunnel between the top and bottom WSe2 layers in the overlappingmoiré cells, but tunneling to neighboring moiré cells is prohibited bythe strong Coulomb repulsion. As the electric field increases, forexample, in the positive direction defined in Fig. 1a, the probability ofholes in the bottom WSe2 layer will increase. Above the thresholdelectric field Ec,�1, the hole will be 100% in the bottom WSe2 layer(nb = −1), leaving the top WSe2 layer empty (nt = 0). This state nowbecomes a Mott insulator in the WS2/b-WSe2 interface only, similar tothat in aWS2/WSe2moiré bilayer. The systemshould remain insulating,as seen in the behavior of the PL peak energy in Fig. 4c. This transitionis the result of the competition between the interlayer and intralayerhopping processes, which we characterize as energy t' and t, respec-tively. The interlayer (intralayer) hopping favors carriers populatingboth (individual) WSe2 layers. Based on the threshold electric field, weestimate the overall potential difference between the twoWSe2 layersis about 0meV at the transition, which suggests that t' is about thesame as t (See Supplementary Information Section 11: case 2 for adetailed discussion). We note that it is critical to have similar twistangles to observe the reported hybridized Mott insulator state here.The small difference in the twist angles of the reported device mightlead to amoiré superlattice of amuch larger period, which is not likelyto affect our experimental observation due to the corresponding lowdensity of carriers for the half-filling.At n = −2, the transition is different. Initially, at zero field, there isone hole per moiré unit cell in each of the two WSe2 layers, formingtwo separate Mott insulator states at both t-WSe2/WS2 and WS2/b-WSe2 interfaces (Fig. 4e). Application of an electric fieldwill create anenergy shift between the two Mott insulator Hubbard bands. How-ever, since both upper Hubbard bands (UHB) are fully occupied byholes, tunneling of holes between the two layers is forbidden, andthis carrier configuration (nt = nb = −1) will remain stable until theUHB of the top WSe2 layer starts to overlap with the lower Hubbardband (LHB) of the bottom WSe2 layer (Fig. 4g), and holes from thistop layer UHBwill start tomove to the LHB in the bottomWSe2 layer,resulting in partially filled bands in both layers such that the systemwill no longer be insulating (see the n = −2 evolution in Fig. 4c). Theenergy difference between the two WSe2 layer at the transitionshould be equal to the difference between the onsite Coulombrepulsion, U, and t'� t. This potential difference is estimated to be~20meV from the threshold field. As t'� t is about 0, this suggests avalue of about 20meV for U, consistent with the previous studies12,41.We note that the threshold electric field at n = −2 has a large uncer-tainty due to the weak PL signals, and the resulting estimation of U isa lower bound.Finally, the temperature-dependent PL spectra (Fig. S7) show thatthe interlayer Mott insulator transition temperature is about 80K,consistent with our expectation based on previous studies on MottFillingfactorn = -1 (Interlayer Mott Insulator) n = -2 (Mott Insulator)t-WSe2b-WSe2WS2t-WSe2 b-WSe2 t-WSe2 b-WSe2 t-WSe2 b-WSe2Ut-WSe2 b-WSe2UUHBLHBE=0 E=EC,-1E=EC,-2E=0a b cd ef g−80 −40 0 40 8046810Peakarea(arb.unit)External field (mV/nm)n = -1Fig. 4 | Interlayer Mott insulator at n = −1 and Mott insulator at n = −2. a Thecolor plot of integrated PL intensity as a function of filling factor and externalelectric field. b The linecut of (a) at n = −1. c The color plot of PL peak energy as afunction of the filling factor and external electric field. d, e are schematics of thehole configuration for the interlayer Mott insulator at n = −1 and Mott insulator atn = −2, respectively. f, g are the evolution of alignment and filling of the flat valencebands of the t-WSe2 and b-WSe2 layers as the electric field increases for n = −1 (f)and n = −2 (g). The PL data were taken from device D1.Article https://doi.org/10.1038/s41467-023-40288-9Nature Communications |         (2023) 14:4604 5insulator state in WS2/WSe2 moiré systems41,42. The quadrupolar exci-tons, however, are still obvious at 100K.We note that we have also observed quadrupolar excitons andcorrelated states in WS2/WSe2/WS2 trilayer moiré devices in which theconduction bands in the two WS2 layers are hybridized (Supplemen-tary Information Section 19). We choose to focus on the WSe2/WS2/WSe2 trilayer system in this work as the hybridization and interlayerMott insulator only involve one valence band in eachWSe2 monolayerinstead of two conduction bands in each WS2 monolayer, which sim-plifies the system.In summary, our study demonstrates a unique trilayer moirésystem that hosts both quadrupolar excitons and correlated states atn = −1 (interlayer Mott insulator) and n = −2 (Mott insulator). In parti-cular, the quadrupolar excitons and interlayer Mott insulator bothoriginate from the valence band hybridization and interact with eachother. Here, the flat valence band hybridization, combined with thelarge spin-orbit coupling, is promising for generating nontrivial topo-logical states and engineering quantum states such as quantumanomalous Hall43. The quadrupolar excitons in this unique trilayermoiré system are not only promising for realizing the quantum phasetransition of bosonic quasiparticles but also strongly interact withcorrelated electrons, setting up an exciting platform for engineeringnew correlated physics of fermions, bosons, and a mixture of both44.We also envision that further development in aligning the moiré tri-layer to allowdifferent stackingofmoiré sites (high symmetrypoints45)such asAAA, ABA, or ABCwill usher in unprecedented opportunities inelectronic and excitonic band engineering.Note: During the submission of this work, we became aware ofother works on quadrupolar excitons (ref. 46, ref. 47, and reference 29in ref. 47).MethodSample fabricationWeused the samedry pick-upmethod as reported in our earlier work32to fabricate TMDC heterostructures. 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. It is worth noting that typical largeTMDC flakes with one dimension exceeding 50 µmwere chosen for thedevice structure shown in Fig. 1. The polycarbonate (PC)/ poly-dimethylsiloxane (PDMS) stampwas used to pick up TMDCmonolayerand other flakes sequentially. The top WSe2 and bottom WSe2 arealigned with a 0-twist angle (R-stacked configuration). This is achievedeither through angle-aligned layer stacking and checking the secondharmonic generation (SHG) afterward or using the same WSe2 flakeand splitting it into two pieces via the tear and twist technique. Thealignment of each layer is achieved under a home-built microscopetransfer stage with the rotation controlled with an accuracy of 0.02degrees. The PC is then removed in the chloroform/isopropanolsequence and dried with nitrogen gas. The final constructed deviceswere annealed in a vacuum (<10−6 torr) at 250 oC for 8 h.Optical characterizationsDuring the optical measurements, the sample was kept in a cryogen-free optical cryostat (Montana Instruments). A home-built confocalimaging system was used to focus the laser onto the sample (with abeam spot diameter of ~2 µm) and collect the optical signal into aspectrometer (Princeton Instruments). During the measurements, thesamples were kept in a vacuum and cooled down to 6−10K. The PLmeasurements in Figs. 1, 2 are performed with 50 µW 633nm CWexcitation. All other PL measurements were performed with 633nmCWexcitationwith apower of 200 µWunless specified. The reflectancecontrast measurements were performed with a super-continuum laser(YSL Photonics). The polarized SHG measurements were performedwith a pulsed laser excitation centered at 900nm (Ti: Sapphire;Coherent Chameleon) with a repetition rate of 80MHz and a power of80mW. The angle between the laser polarization and the crystal axesof the sample was fixed. The SHG signal was analyzed using a half-waveplate and a polarizer. Additional PL measurements were per-formed with a 730 nm CW diode laser (Supplementary InformationSection 15), which showed similar results as the main text.Calculation of electric fieldThe external electric field is defined as 12ðVTGd1� VBGd2Þ, where VTG ðVBGÞ isthe top (back) gate voltage, and d1ðd2Þ is the thickness of the top(bottom) layer BN flake.The electric field in Fig. 2 is defined as the electric field in theTMDC heterostructure, which is given by εBN2εTMDCðVTGd1� VBGd2Þ.Data availabilitySource data are available for this paper. The data in Figs. 1–4 are pro-vided in the source data files. All other data that support the plotswithin this paper and other findings of this study are available from thecorresponding author upon reasonable request. Source data are pro-vided with this paper.References1. 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S.-F.S. also acknowledges the support from NSF GrantDMR−1945420, DMR−2104902, and ECCS-2139692. X.H. and Y.-T.C.acknowledge support from NSF under awards DMR-2104805 and DMR-2145735. The optical spectroscopy measurements were supported byDURIP awards through Grant FA9550-20−1-0179 and FA9550-23-1-0084. S.T. acknowledges support from NSF DMR-1904716, DMR-1838443, CMMI-1933214, and DOE-SC0020653. 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, OMR-2228725, ARO (W911NF17-1-0128), and AFOSR (FA9550−20−1-0220).Author contributionsS.-F.S. and Z.L. conceived the project. Z.L., D.C., and Y.M. fabricateddevices. Z.L., D.C., L.M., L.Y., X.H., and Q.W. performed measurements.M.B. andS.T. grew the TMDCcrystals. T.T. andK.W. grew theBNcrystals.S.-F.S., Y.-T.C., Z.L., D.C., X.C., Y.S., and C.Z. analyzed the data. S.-F.Sand Y.-T.C. supervised the project. S.-F.S. and Y.-T.C. wrote the manu-script with inputs from all authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-40288-9.Correspondence and requests for materials should be addressed toYong-Tao Cui or Su-Fei Shi.Peer review information Nature Communications thanks the anon-ymous, reviewer(s) for their contribution to the peer review of this work.A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-40288-9Nature Communications |         (2023) 14:4604 7https://doi.org/10.1038/s41467-023-40288-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Quadrupolar excitons and hybridized interlayer Mott insulator in a trilayer moiré superlattice Results and discussion Quadrupolar exciton in angle-aligned t-WSe2/WS2/b-WSe2 trilayer Evidence of an interlayer Mott insulator Method Sample fabrication Optical characterizations Calculation of electric field Data availability References Acknowledgements Author contributions Competing interests Additional information