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Mingfeng Chen, Runtong Li, Haonan Wang, Yuliang Yang, Yiyang Lai, Chaowei Hu, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Jiaqiang Yan, Jiun-Haw Chu, Erik Henriksen, Chuanwei Zhang, Li Yang, Xi Wang

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[Bichromatic moiré superlattices for tunable quadrupolar trions and correlated states](https://mdr.nims.go.jp/datasets/e76cca2c-0376-4e8c-bfb6-4249b80b1ac9)

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Bichromatic moiré superlattices for tunable quadrupolar trions and correlated statesArticle https://doi.org/10.1038/s41467-025-65342-6Bichromatic moiré superlattices for tunablequadrupolar trions and correlated statesMingfeng Chen 1,8, Runtong Li1,8, Haonan Wang1,8, Yuliang Yang1, Yiyang Lai1,Chaowei Hu 2, Takashi Taniguchi 3, Kenji Watanabe 4, Jiaqiang Yan 5,Jiun-Haw Chu 2, Erik Henriksen 1,6,7, Chuanwei Zhang 1,6,7, Li Yang1,6,7 &Xi Wang 1,6,7Moiré superlattices in transition metal dichalcogenide heterostructures pro-vide a platform to engineer many-body interactions. Here, we realize abichromatic moiré superlattice in an asymmetric WSe2/WS2/WSe2 hetero-trilayer by combining R- and H-stacked bilayers with mismatched moiréwavelengths. This structure hosts fermionic quadrupolar moiré trions—inter-layer excitons bound to an opposite-layer hole—with vanishing dipolemoments. These trions arise from hybridized moiré potentials enabling mul-tiple excitonic orbitals with tunable interlayer coupling, allowing control ofexcitonic and electronic ground states. We show that an out-of-plane electricfield could effectively reshape moiré excitons and interlayer-intralayer elec-tron correlations, driving a transition from interlayer to intralayer Mott stateswith enhanced Coulomb repulsion. The asymmetric stacking further enrichesexcitonic selection rules, broadening opportunities for spin-photon engi-neering. Our results demonstrate bichromatic moiré superlattices as areconfigurable platform for emergent quantum states, where quadrupolarmoiré trion emission may enable coherent and entangled quantum lightmanipulation.When twoormore 2D layers in a heterostructure have slightlydifferentlattice constants or are oriented in a way that their periodicities do notperfectly align, they create a moiré pattern, i.e., moiré superlattice. Itdictates various physical properties such as the electronic bandstructures and excitonic states et al.1–7. Moiré superlattices demon-strate significant potentials for studying many-body interactions,including excitonic complexes (e.g., trions, biexcitons)8–10, for quan-tum simulations such as Hubbard model physics11–15. The creation ofmoiré superlattices in transition metal dichalcogenide (TMD) hetero-structures has revealed or predicted a diverse range of phases in thesesystems, including generalized Wigner crystals16–23, Mottinsulators12,18,24, bosonic (excitonic) insulators20,25–29, charge transferinsulators30, as well as fractional31–34 and integer35 quantum anomalousstates.While enhancing the versatility of superlattice landscapes opensup a spectrum of possibilities, the inherent rigidity in these hetero-structuralmoiré superlattices presents a significant challenge for post-fabrication tuning. One promising method is to harness the inter-ference of distinct moiré wavelengths to craft intricate, tunablebichromatic patterns36. While theoretical insights have demonstratedthe potential of creating adjustable multi-chromatic superlatticeswithin TMD heterotrilayers to leverage moiré potentials fromReceived: 3 September 2025Accepted: 10 October 2025Check for updates1Department of Physics,WashingtonUniversity, St. Louis,MO, USA. 2Department of Physics, University ofWashington, Seattle,WA,USA. 3ResearchCenter forMaterials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 4Research Center for Electronic and Optical Materials, NationalInstitute for Materials Science, Tsukuba, Japan. 5Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA. 6Center forQuantum Leaps, Washington University, St. Louis, MO, USA. 7Institute of Materials Science and Engineering, Washington University, St. Louis, MO, USA.8These authors contributed equally: Mingfeng Chen, Runtong Li, Haonan Wang. e-mail: wxi@wustl.eduNature Communications |        (2025) 16:10359 11234567890():,;1234567890():,;http://orcid.org/0000-0001-8408-0359http://orcid.org/0000-0001-8408-0359http://orcid.org/0000-0001-8408-0359http://orcid.org/0000-0001-8408-0359http://orcid.org/0000-0001-8408-0359http://orcid.org/0000-0003-2071-0109http://orcid.org/0000-0003-2071-0109http://orcid.org/0000-0003-2071-0109http://orcid.org/0000-0003-2071-0109http://orcid.org/0000-0003-2071-0109http://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/0000-0001-6625-4706http://orcid.org/0000-0001-6625-4706http://orcid.org/0000-0001-6625-4706http://orcid.org/0000-0001-6625-4706http://orcid.org/0000-0001-6625-4706http://orcid.org/0000-0001-6222-1210http://orcid.org/0000-0001-6222-1210http://orcid.org/0000-0001-6222-1210http://orcid.org/0000-0001-6222-1210http://orcid.org/0000-0001-6222-1210http://orcid.org/0000-0002-4978-2440http://orcid.org/0000-0002-4978-2440http://orcid.org/0000-0002-4978-2440http://orcid.org/0000-0002-4978-2440http://orcid.org/0000-0002-4978-2440http://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/0000-0002-0641-0882http://orcid.org/0000-0002-0641-0882http://orcid.org/0000-0002-0641-0882http://orcid.org/0000-0002-0641-0882http://orcid.org/0000-0002-0641-0882http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65342-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65342-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65342-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65342-6&domain=pdfmailto:wxi@wustl.eduwww.nature.com/naturecommunicationsindependently controlled heterointerfaces across layered structures,the experimental realization remains absent. Key open questionsinclude how different moiré potentials interact and coevolve, howcharge redistribution and stacking order vary under distinct moiréperiodicities, and what role quasiparticle dynamics play in suchsynergistic superlattices.Here, we report an engineered heterotrilayer combining anR-stacked top bilayer and an H-stacked bottom bilayer with mis-matched moiré wavelengths, resulting in a bichromatic moiré super-lattice formed by the interference of two distinct moiré periods. Thisunique lattice geometry gives rise to emergent phenomena notaccessible in conventional moiré systems. First, the hybridized moirépotentials support a new class of charged excitons—fermionic quad-rupolar moiré trions—which are distinct from previously reportedbosonic quadrupolar excitons. These trions exhibit electrically tunabledipole moments, enabling controlled studies of quasiparticle dynam-ics in complex potential landscapes. Second, bichromatic interferenceenables in-situ tunability of the beating periodicity, dynamicallyreshaping the carrier-trapping landscape. We observe an electric-field-driven transition from an interlayer Mott insulating state to an intra-layer Mott state with enhanced on-site Coulomb repulsion. Furthertuning modifies the moiré potential profile and shifts the density ofground-state sites, allowing precise control over electron correlationsand establishing the asymmetric heterotrilayer as a reconfigurableplatform for exploring programmable correlated quantum states.Finally, the coexistence of R- and H-stacked domains enables tailoredcontrol of interlayer excitonic selection rules, advancing the engi-neering of spin-photon coupling for quantum optoelectronicapplications.ResultsStructures of R- and H-stacked WSe2/WS2/WSe2 heterotrilayersWe fabricated dual-gateWSe2/WS2/WSe2 heterotrilayer devices, whichallow independent control of doping levels and vertical electric field(Fig. 1a, see Methods). The structure of heterotrilayers investigated isshown in Fig. 1b inset. We highlight the layer alignments with arrows:parallel indicating R stacking and opposite indicating H stacking.Device 1 (Fig. 1b optical image) displays the topWSe2 layer alignedwiththe middle WS2 layer at an angle close to 1° (R stacking), while thebottom WSe2 layer is rotated 180° with a slightly different alignmentangle (H stacking). This device also includes a bilayer region for directcomparison.Moiré superlattices can be clearly identified in the PiezoresponseForce Microscopy (PFM) image of Device 1’s trilayer region (Fig. 1c).Fourier transform data (Fig. 1c inset) reveal two distinct moiré super-lattices with lattice constants approximately 7.4 nm ( ~ 0.9°) and6.7 nm ( ~ 1.5°). Besides, a larger superlattice background could beidentified in the PFM image emerging from the interference of thesetwo sets. This small, deliberate twist-angle offset of roughly 0.5° keepseach bilayer well aligned and prevents severe global disorder andfrustration, while preserving the beating patterns (see SupplementaryInformation Fig. S1).Fig. 1 | Structural characterization of trilayer heterostructure Device 1.a Schematic of a dual-gated WSe2/WS2/WSe2 heterotrilayer device, in which pre-evaporated and AFM-cleaned Cr/Pt is used as contacts to the TMD layers. bOpticalimage of Device D1 highlights the alignment of top WSe2 and bottom WSe2 layersrelative to the middle WS2 layer, with the topWSe2, middle WS2, and bottomWSe2outlined in purple, pink, and green, respectively. Inset: Schematic illustrating layeralignments with arrows indicating R stacking (parallel) and H stacking (opposite).c PFM image of Device D1’s trilayer region, revealing two distinct moirésuperlattices with lattice constants of approximately 7.4 nm ( ~ 0.9°) and 6.7 nm( ~ 1.5°), marked with red dashed circles in the inset Fourier transform image. d Anexemplary trilayer with a topmoiré with a 1° rotation (R-stack) and a bottommoiréwith a 1.56° rotation (H-stack), with high-symmetry sites A, B, C denoted by blue,red, and black circles; hollow symbols mark H-stack sites (AH, BH, CH) and filledsymbolsmark R-stack sites (AR, BR, CR). The R- andH-stackmoiré superlattices forma concatenated moiré pattern across the trilayer.Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 2www.nature.com/naturecommunicationsUnlike previous experimental studies focusing on symmetricalignment in the top and bottom heterostructures37–39, the intricateinterplay of high-symmetry stacking configurations in the R-H mis-aligned heterotrilayers unveils the elusive atomic registry textures. Asdepicted in Fig. 1d, an exemplary trilayer exhibits a top moiré with a 1°rotation (R-stack) and a bottom moiré with a 1.56° rotation (H-stack).Following the convention fromTong et al36, theseR- andH-stackmoirésuperlattices form a concatenated moiré pattern across the trilayer,delineated by nine distinct high-symmetry locales (SupplementaryInformation Fig. S2), each exhibiting different band hybridizationbetween the top andbottom layers. At locales suchasAR/AH (similar forBR/BH, CR/CH in Fig. S2), conservation of spin-valley degrees of freedomis anticipated to suppress tunneling and hybridization. By contrast,high-symmetry locales such as AR/CHmay allow stronger hybridization,depending on the local atomic alignment.In reported heterobilayers, the spatial distributions of band-edgeelectrons differ between R-stack and H-stack heterostructures40. InR-stack heterobilayers, electrons are localized predominantly at thehigh-symmetry locationCR, whereas inH-stack heterobilayers, they aremostly found at location AH. Combining R and H stackings in hetero-trilayers likely generates multiple orbital configurations for electronscentered in the middle layer, where both A and C serve as trappingsites. The physics inherent in R-H style heterotrilayers promises atapestry of intriguing phenomena.Multi-orbital nature of the bichromatic moiré superlatticeThe multi-orbital nature of the bichromatic moiré superlattice pro-motes the tunability of valley and spin degrees of freedom in TMDheterotrilayers. Experimentally, this manifests as multiple photo-luminescence (PL) peaks in the heterotrilayer structure. The PL spec-trum (Fig. 2a) reveals a dominant low-energy emission at ~1.39 eV and asecondary, weaker peak at ~1.46 eV. The energy separation of ~70meVbetween the two peaks significantly exceeds the expected excitondouble occupancy energy ( ~ 30meV) at a singlemoiré site26, indicatinga multi-orbital origin. Power-dependent PLmeasurements on Device 3(Fig. S3) show that both peaks persist even at the low excitation power,confirming their intrinsic origin from the heterotrilayer moirépotential rather than from power-induced filling effects. The normal-ized power dependence of the lower energy peak (Fig. S4) shows sig-nificant saturation behavior. The above evidence confirms that theemissive excitonic species from heterotrilayer regions are intrinsic tothe bichromatic moiré potential.To probe the origins of the dual PL peaks, we conducted out-of-plane electric field measurements while keeping the doping fixed.Upon applying an electric fieldwithout external doping, both PL peaksexhibit clear linear Stark shifts (Fig. 2b). These linear Stark shifts cor-respond to the emissions originating from the interlayer excitonspossessing significant out-of-plane dipoles.The emission energy of the high-energy peak decreasesmonotonically with the applied electric field. This peak is attributedto the interlayer exciton, with its dipole moment oriented down-ward. The interlayer exciton arises from the binding of holes in thebottom WSe2 layer and electrons in the middle WS2 layer. Polar-ization analysis, shown in Fig. 2c, further supports the identificationof this high-energy exciton. The peak exhibits cross-polarization(ρ < 0), indicating that the emission originates from an H-stackWSe2-WS2 heterobilayer40. This agrees with mid-bottom bilayerconfiguration.In contrast, the low-energy peak shows opposite slopes when thesign of the electric field is reversed. These opposing slopes, observedin Fig. 2b, c, correspond to dipole moments that flip direction. Thisbehavior confirms that the lower-energy exciton exhibits a bipolaremission characteristic. The dipole moment of this interlayer exciton(IX) flips dynamically with the applied electric field, with hole polar-ization occurring either in the top R-stacked layer or the bottomH-stacked layer (as shown in Fig. 2d, e).At a small electric field near E = 0.02 V/nm, the low-energy inter-layer excitons emitted from the top R-stacked and bottom H-stackedlayers exhibit identical energies. In this range, the local slope of thelow-energy peak is flat. This flat slope matches the quadrupolar exci-tons observed in symmetric heterotrilayers37–39. Despite differences inperiodicity and stacking order between the top and bottom moirésuperlattices, the identical energies and flat local slope are a signatureof a shared ground state in the R-H aligned heterotrilayers. AdditionalFig. 2 | Electric field dependence of interlayer PL peaks. a PL spectrum of thetrilayer heterostructure, displaying a dominant low-energy peak at 1.39 eV (low-energy peak) and a secondary peak at 1.46 eV (high-energy peak). b Interlayer PL asa function of electric fieldwithout external doping possesses different slopes of theStark shift across positive and negative electric field regimes. c The correspondingPLdegreeof circular polarizationρ = σ+ =σ+ �σ+ =σ�σ+ =σ+ +σ + =σ� in the sameconditions as inb. Thehigh-energy peak remains cross-polarized regardless of field direction, whereas thelow-energy peak flips from cross- to co-polarized when the electric field is reversedfrom positive to negative. d-e, Schematics of preferred sites of interlayer excitonemission with positive electric field (d) and negative electric field (e). The yellow,grey, and blue layers denote top WSe2 (R stacking), middle WS2, and bottomWSe2(H stacking). Blue and red spheres indicate electrons and holes, respectively. Thelow-energy peak originates from sites where holes can redistribute freely betweenthe top and bottomWSe2 layers (the left side ind, e), whereas the high-energy peakcomes from sites where holes remain localized in the bottomWSe2 layer (the rightside in d, e). In this study, positive electric field points from the top WSe2 to thebottom WSe2, and negative electric field points from the bottom WSe2 to topWSe2 layer.Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 3www.nature.com/naturecommunicationsdata from another Device D2 is present in Supplementary Informa-tion Fig. S5.The unique features of the PL peaks are attributed to the multi-orbital characteristics of the heterotrilayers. As illustrated in Fig. S2,the heterotrilayers feature multiple high-symmetry sites arising fromthe beating of the top and bottom moiré superlattices. Excitation ofintralayer excitons inWSe2 leads to rapid carrier relaxation to the bandedges, forming interlayer excitons. At minimally hybridized sites, theexcitons retain the same dipole moment. As a result, excitons emittedfrom these sites exhibit a single slope, as shown in Fig. 2b. By contrast,at strongly hybridized sites the lowest-energy state is shared by boththe top and bottom layers. In this case, an applied electric fieldpolarizes holes toward the bottom WSe2 layer (for E >0) or the topWSe2 layer (for E <0). Consequently, the bound excitons at these sitesdevelop a positive or negative dipole moment depending on thedirection of the electric field.Although the excitons share the same lowest-energy at specifichigh-symmetry locations, the distinct stacking orders of the top andbottom bilayers enforce opposing selection rules. The low-energy PLpeak for E <0, characterized by a positive slope, exhibits a positivedegree of polarization (Fig. 2c), which is consistent with the R-stackconfiguration in the upper heterobilayer of our device. In contrast,interlayer excitons in the lower heterobilayer, with negative slopes,display a negative degree of polarization, aligning with the H-stackconfiguration. This layer-polarized emission introduces an additionaldegree of freedom for manipulating circular polarization while main-taining fixed emission energies.Quadrupolar moiré trionsUnder hole-doping conditions, our experiments reveal the presence ofquadrupolar excitonic emission in the moiré trilayers, as shown inFig. 3a, b. Additional data across varying doping conditions fromDevice D1 are presented in Fig. S6. Furthermore, data from Device D2,tested under similar conditions, is included in Fig. S7. The formation ofquadrupolar excitonic species occurs immediately upon introducingexcess holes into the heterostructure. To confirm the formation ofinterlayer trions, we deliberately dope the heterotrilayer at fixedhole concentrations while sweeping the electric field. Figures 3a, bshow two hole-doping conditions at n = –2.25 × 1012cm2 andn = –3.75 × 1012cm–2. The low-energy peak exhibits minimal shifts inemission energy under low-field conditions (additional hole dopingscenarios are shown in Fig. S6). The flat slope confirms an almostnegligible out-of-plane dipole moment. In contrast, the high-energypeak shifts negatively with the electric field, consistent with thebehavior observed in Fig. 2b under intrinsic doping conditions. Thisshift is attributed to the fixed out-of-plane dipole moment of theexciton, whose position in the moiré superlattice results in a smallhybridization probability, as illustrated in Fig. 2d, e.Fig. 3 | PL peaks’ positions shift as a function of the electric field underfixed doping conditions. a n=–2.25 × 1012cm–2, b, n= –3.75 × 1012cm–2,c, n= 1.5 × 1012cm–2. Under hole doping (a and b), the peak energy of the low-energypeak remains nearly constant over a finite electric-field window, indicating the sta-bilization of a quadrupolar trion, whereas no such signature appears under electrondoping (c). The inset of a schematically present, from right to left, the carrier con-figurations that yield the low-energy peak: holes localized in the bottom WSe2 layerunder positive electric field and pair with an electron in themiddleWS₂ layer to forman interlayer exciton; holes shared between the top and bottomWSe2 layers create aquadrupolar trion; and holes once again confined to the top WSe2 layer bind to themiddle-layer electron under negative electric field, forming another interlayer exci-ton. The blue and red circles represent electrons and holes located in the WS2 andWSe2 layers, respectively. The blue, pink and green rectangles denote the top WSe2,middle WS2 and bottom WSe2 layers.Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 4www.nature.com/naturecommunicationsUnder electrondoping conditions, theflat slope of the low-energypeak is absent (Fig. 3c). The observed slopes are directly ascri-bed to the dipoles associated with the top and bottom interlayerexcitons.We attribute the excitonic species with nearly zero out-of-planedipole moments to the formation of quadrupolar moiré trions underhole-doped conditions. This interpretation is consistent with a sce-nario inwhich two holes are symmetrically distributed across theWSe2layers (Fig. 3a middle inset), regardless of whether the structure isR-stack or H-stack aligned. Strong Coulomb interactions drive theemergence of this unique three-particle complex, where two holes andone electron are strongly localized at the shared high-symmetrymoirésites. The resulting interlayer quadrupolar trion exhibits a nearly van-ishing out-of-plane dipole moment, and its energy remains stableunder varying electric fields, clearly distinguishing it from previouslyreported interlayer trions in heterobilayers8,9,41. Importantly, unlike thebosonic quadrupolar excitons observed in symmetric trilayers37–39 thatexist primarily under charge-neutral conditions, quadrupolar moirétrions appear only under doping. Furthermore, they require a sub-stantially larger electric field to polarize into dipole configurations.This enhanced robustness indicates that the formation of interlayerquadrupolar moiré trions is energetically favored in bichromaticheterotrilayers.When the electric field becomes sufficiently strong, holes in thebottom (top) WSe2 layer are polarized to the top (bottom) WSe2 layerto minimize the total energy, resulting in a well-defined out-of-planedipole moment. Specifically, for hole density below –2 × 1012cm–2( ~ ν = –1 for one moiré), a modest electric field of approximately±0.025 V/nm is sufficient to transform the quadrupolar trion into adipolar exciton (Fig. S6d, e). In this regime, polarized holes canredistribute across different moiré sites within the same WSe2 layer,effectively lowering the total energy. However, at higher hole fillingsν ≥ –1, polarizing all holes into the same layer forces them to sharemoiré sites, incurring strong on-site Coulomb repulsion. Conse-quently, a larger field exceeding ±0.05 V/nm is needed to overcomethis repulsion and achieve full dipolar polarization. These experi-mental findings demonstrate that the electric field can effectively tunethe ground states of holes bymanipulating their layer-specific degreesof freedom.Electric-field modulation of the moiré potential landscapeWe now deliberately tune the electric field to control the distributionof dopedholes. As shown in Fig. 4a, b, at E =0V/nm, the shared groundstate results in an even hole distribution across the top and bottomlayers, with both WSe2 layers experiencing the same moiré potentiallandscape.When the carrier density reaches 3.6 × 1012cm–2, we observea change in PL intensity (Fig. 4a) and enhanced polarization (Fig. 4b).This behavior alignswith the formation of an interlayerMott insulatingstate, as reported by Lian et al39. However, in our study, this phe-nomenon occurs in an asymmetric heterotrilayer, characterized bydistinct R-stack andH-stack layers, contrasting with the symmetric R-Rstack with identical lattice constants in the top and bottom layers asdescribed inpreviouswork39. It’s worth noting that, the interlayerMottinsulating state observed here differs from the behavior seen inregions with only bilayer R-stack heterostructure. In the R-stack het-erobilayer, as shown in Fig. S8, holes are strictly confined to the topWSe2 layer, and intensity variations occur at both fractional and inte-ger filling factors.Fig. 4 | PL intensity and polarization as a function of doping with afixed electric field. a–b, PL intensity (a) and polarization (b) versus densitywith E =0V/nm. c–d, PL intensity (c) and polarization (d) versus density withE = –0.05V/nm. e–f, PL intensity (e) and polarization (f) versus density withE = –0.1 V/nm. The PL intensity and polarization changes are used to identifythe integral filling and insulating states, ν =0 and ν = –1 can be clearly discernedandmarked by dashed lines in both the PL (white dashed lines) and correspondingpolarization (black dashed lines) 2D maps. The corresponding density in ν = –1under the electric field of 0 V/nm, –0.05 V/nm and –0.1 V/nm is 3.6 × 1012cm–2,4 × 1012cm–2 and 6.45 × 1012cm–2, respectively. Line cuts of the raw data illustratingthe polarization changes under specific conditions are provided in the Supple-mentary Information as Fig. S11.Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 5www.nature.com/naturecommunicationsWhen a fixed negative electric field (–0.05 V/nm) is applied, thedoped holes would predominantly occupy the top WSe2 layer. At ahole carrier density of 4 × 1012cm–2, strong intensity modulation(Fig. 4c), and a significant decrease in polarization (Fig. 4d) areobserved, as labelled by the dashed lines. The observed intensity andpolarization modulations are consistent with previously reported sig-natures of correlated states in TMDheterobilayers19,25–27,40,42. It is worthnoting that the emergence of integer-filling correlated states providescompelling evidence that the PL peaks originate from excitons loca-lized atbichromaticmoiré sites. The abrupt changes in PL intensity andpolarization with doping, as shown in Fig. 4 and Figs. S8-10, are indi-cative of strong interactions between interlayer moiré excitons andcorrelated electronic states, consistent with prior observations inmoiré systems19,25–27,40,42.By further tuning the electric field, themoiré potential profile issignificantly altered, as shown in Fig. 4e, f. For a fixed electric field of–0.1 V/nm, we observe a surprising increase in the doping densityrequired to reach the insulating state, rising to approximately6.45 × 1012cm–2. Furthermore, a distinct blueshift is observed at thispoint, indicative of the onset of on-site Coulomb repulsion.The substantial increase in carrier density needed to form theinsulating state strongly suggests a shift in the density of ground-state sites.Similar behavior is observed in Device D2 (Fig. S9). The electricfield required to reshape the entire moiré landscape is slightly differ-ent, owing to the variation in twist angles between the R-stack andH-stack layers. As shown in Fig. S10, the moiré superlattice of theH-stack heterobilayer is approximately 7.6 nm, which is slightly largerthan the value measured in Device D1 from the PFM data. However,qualitatively, the behavior with the applied electric field remains con-sistent with what we observed in Device D1.To gain insight into the experimental observations, we have cal-culated the moiré potentials for valence band holes in heterotrilayerbichromatic superlattices, following the methodology outlined byTong et al36. Detailed calculations are provided in the SupplementaryInformation. The concatenated moiré pattern is visualized by tracingseveral high-symmetry stacking sites, as shown in SupplementaryFig. S1, which includes both R-stack and H-stack high-symmetryregions. The calculated moiré potentials under various electric fieldconditions are presented in Fig. 5. The bright regions represent thelocal potential minima for holes (i.e., the valence band maximum).These regions will be first populated when the system is hole-doped.Considering the geometry of the trilayer moiré superlattice(Fig. 1d), we find that the heterotrilayer exhibits distinct moirépotential profiles compared to heterobilayers, with the added advan-tage of dynamic tunability via an applied electric field (Fig. 5). Thesimulations in Fig. 5 are performed under similar conditions to themeasurements in Fig. 4. In Fig. 4a, b, the applied electricfield is zero. Atthis condition, the hole density corresponding to thefirst integerfillinginsulating state, identified as an interlayer Mott insulator, is approxi-mately 3.6 × 1012cm–2, which is notably higher than the densityrequired to reach ν = 1 in the R-type heterobilayer with a moiré wave-length of 7.4 nm (n ~ 2.1 × 1012cm–2). In the absence of an electric field,the simulated moiré potential (Fig. 5a) shows bright regions slightlylarger than the R-type stacking domains (Fig. S12), with multiple high-symmetry sites available for hole occupancy. As shown in Fig. 5b, theholes are distributed across both the upper and lower WSe2 layers,forming a degenerate interlayer configuration. Laterally, the hole isconfined to a common moiré potential minimum shared betweenlayers, resulting in one hole occupying a shared ground state at thesame high-symmetry moiré site in the hybridized trilayer. This corre-lated state is referred to as an interlayerMott insulator39. In this regime,the holes can redistribute between the top and bottom WSe2 layerswithin the same vertical moiré cells.As the electric field increases (E-field pointing from the bottomgate to the top gate) to –0.05 V/nm, the hole density required for theMott insulating state increases to 4.0 × 1012cm–2 (Fig. 4c, d). The cor-responding simulation shows the area of the bright regions expandsslightly, indicating an enhanced capacity for hole occupancy (Fig. 5c).In this regime, holes preferentially occupy sites in the upper layer, withfewer holes residing in the lower layer (Fig. 5d). At an even higherelectric field of –0.1 V/nm, the hole density at ν = –1 further increase to6.45 × 1012cm–2 (Fig. 4e, f). The simulated potential landscape evolvesinto a honeycomb-like pattern (Fig. 5e), effectively doubling thenumber of sites available for hole localization, consistent with ourexperimental observations. In this regime, the electric field fullypolarizes the doped holes to localize in the upper layer (Fig. 5f), wherethe correlated states are now governed by intralayer hole interactionswith modified moiré periodicity and enhanced Coulomb repulsion.The strong on-site repulsion energy results in a significant blueshift inthe excitonic emission. Overall, these results demonstrate that theapplied electric field in a bichromatic moiré superlattice enables atunable transition from interlayer- to intralayer-dominated Mottinsulating states.Fig. 5 | Calculated electric-field modulation of moiré superlattice potentiallandscape in real space.Moiré superlattice potential in the heterotrilayer withoutelectric field (a), at electric field of –0.05 V/nm (c), and at electric field of –0.1 V/nm(e). The bright yellow locales are potential minima for holes. b,d,f, Schematicsshowing the preferred layer localization of holes under the corresponding electricfield conditions. As the out-of-plane electricfield is swept from0 to–0.05V/nmandthen to –0.1 V/nm, the number of hole-potential minima increase significantly, andthe hole distribution shifts toward the topWSe2 layer, accompanied by a transitionof theMott insulating state from interlayer to intralayer. The yellow, grey, and blueslabs represent the top WSe2 (R stack), middle WS2, and bottom WSe2 (H stack)layers, respectively. Colored spheres indicate holes localized in two WSe2 layers,with darker shading corresponding to higher hole density.Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 6www.nature.com/naturecommunicationsWe realize that the role of strain relaxation in real devices wouldaffect themoiré superlattice landscape. In complex trilayer structures,the R-stack and H-stack regions relax strain differently40. However, ourcalculations provide a qualitative physical framework for under-standing the role of the electric field in modulating moiré potentialsand hole distribution within the superlattices. These findings stronglysupport the realization of electrically tunable bichromatic moirépotentials.DiscussionIn conclusion, we have demonstrated tunable excitonic and electronicstates in uniquely engineered asymmetric R-H WSe2/WS2/WSe2bichromatic superlatticeswith two interferingmoiréwavelengths. Thisconfiguration provides access to previously unexplored physicalphenomena. First, the bichromatic superlattice hosts fermionicquadrupolar moiré trions, distinct from the bosonic quadrupolarexcitons reported earlier. Second, both excitonic states and electronicground states in these lattices can be highly tuned by external electricfields. Third, optical selection rules can be conveniently tailoredwithina single device. By carefully engineering stacking configurations inheterostructures, we demonstrate that quantum states in bichromaticmoiré superlattices can be controlled and reconfigured, opening newpathways for investigating many-body physics in quantum materials.Our findings open exciting possibilities for further investigationinto the dynamics of multi-orbital excitons and other quasiparticles inmore complex moiré superlattices. Future experiments would aim toexplore the coevolution of multiple moiré potentials, particularly intrilayer systemswith different stacking orders/angles, and their impacton charge/exciton interactions and quantum phases. The ability toindependently controlmultiplemoiré superlattices holds the potentialfor realizing dynamically tunable quantum systems, with applicationsin quantum simulation, topological phases, and novel optoelectronicdevices.The emission of these quadrupolar excitons and trions involves asuperposition of two excitonic species with dipole moments orientedin opposite directions. The investigation of the coherence and entan-glement could provide new avenues for the manipulation of quantumlight. Quadrupolar trions reported in this work are particularly robustagainst electrical noise under highly hole-doped conditions, whichcould emerge as promising stable sources.MethodsSample fabricationThe sample fabrication details can be found in Ref.43 In brief, a pre-fabricated bottom gate (a hexagonal boron nitride (hBN)/graphitestack) was transferred, and platinum contacts were defined above thestack using electron beam lithography. Subsequently, 3/7 nm of Cr/Ptwas deposited via electron beam evaporation to form the bottomcontacts. The bottom gate with contacts was then cleaned using anatomic force microscope (AFM) operated in contact mode.Monolayer WS2 and WSe2 flakes were mechanically exfoliatedfrom bulk crystals. The WSe2 crystals were grown using the fluxmethod, while theWS2 crystals were sourced fromHQGraphene. Priorto stacking, the crystal orientations of the monolayers were deter-mined via linear polarization-resolved second harmonic generation toensure accurate alignment. To achieve the desired R- and H-stackingconfigurations, the top and bottomWSe2monolayers were taken fromthe same large flake, which was precisely cut using an AFM probe tominimize strain introduced by conventional tear-and-stack methods.The monolayers were then assembled using a flat polycarbonate(PC)/polydimethylsiloxane (PDMS) stamp and transferred onto thecleaned bottom gate. Twist angles were confirmed using Piezo-response Force Microscopy (PFM)43,44. PFM was carried out using aBruker Dimension Icon AFM and Asylum Research Cypher S AFM withPt–Ir-coated conductive probes (SCM-PIT-V2, force constant ≈ 3N/m).An a.c. bias ( < 300mV, ≈700 kHz and 350kHz for lateral and verticalresonance frequencies, respectively) was applied between tip andsample, and the induced deformation amplitude and phase wererecorded to probe the local electromechanical response. Once themoiré wavelength was determined, a top graphite/hBN stack wastransferred for encapsulation and to complete the dual-gate geometry.Finally, Cr/Au electrodes for wire bonding were patterned using elec-tron beam lithography and deposited via e-beam evaporation(7/70 nm Cr/Au).Optical measurementsPL measurements were performed using a home-built confocalmicroscope in reflection geometry. The sample was mounted in aclose-cycled cryostat with temperature kept at 5 K (MontanaCryoAdvance 50), unless otherwise specified. A helium-neon laser(1.96 eV) was used in PL measurements. An additional 650 nm shortpass filter has been used to filter out any side bands. The excitationpower for PL measurement was kept at 1 µW. The incident polar-ization was set to be σ+ polarized using a linear polarizer andquarter-wave plate, while the photoluminescence was collected andpolarization-resolved to σ+ or σ– using another quarter-wave plateon a rotational mount and a linear polarizer. PL signals were dis-persed by a diffraction grating and detected on a silicon charge-coupled device camera. The PL was spectrally filtered from the laserusing a 700-nm long-pass filter before being directed into a spec-trometer. A pinhole was used in the collection path to exclude sig-nals from outside the laser spot area.Calculation of carrier density and electric fieldThe carrier density is estimated using a parallel-plate capacitor modelwith the gate voltage applied. The BN thickness of samples was mea-sured by AFM. D1 has 16 nm for top BN flake and 20nm for the bottomBN flake. And the top and bottomBN thickness of D2 are ~27.5 nm. Thecarrier density is calculated using Ct ΔVt +Cb ΔVb, where Ct (Cb) is thegeometric capacitance of top (bottom) gate, and ΔVt (ΔVb) is theeffective doping voltage (the relative voltage from band edge). Thevalue used for the dielectric constant of BN is εhBN ≈ 3. The moiréwavelength λ was derived directly from PFM images, and the corre-spondingmoiré density is given as n0 ≈ 2 / (√3 λ2). The filling factor wascalculated as ν = n/n0 and compared with the assignment of integerfilling factors based on gate-dependent photoluminescence in well-understood heterobilayer region in the same sample.The perpendicular electrical displacement field D is calculatedusing D = (Ct ΔVt – Cb ΔVb)/2 and the electric field is calculated asE =D/ε0.Theoretical calculationsThe moiré potential energies are described in terms of the lowestseveral harmonics36,45, wherein the parameters are determined by thehigh-symmetry stackings (See Supplementary Information for moredetails). All data for the high-symmetry stackings is extracted fromfirst-principles calculations that are performed using the Vienna abinitio Simulation Package (VASP)46.Data availabilityThe Source Data underlying the figures of this study are available withthe paper. 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Powe JuniorFaculty Enhancement Awards, partially supported by the Gordon andBetty Moore Foundation, grant https://doi.org/10.37807/gbmf11560.X.W. acknowledges equipment support by the Center for QuantumLeaps at WUSTL. X.W. acknowledges the use of the Cypher S atomicforce microscope for high-resolution PFM characterization of the moirésuperlattices. The fabrication used instruments in the Institute of Mate-rials Science and Engineering (IMSE) at WUSTL, with partial financialsupport from IMSE. BulkWSe2 crystalswere grown and characterized byC.H., J.C., and J.Y. Materials synthesis by C.H. and J.C. was supported aspart of Programmable Quantum Materials, an Energy Frontier ResearchCenter funded by the U.S. DOE, Office of Science, BES, under award DE-SC0019443. J.Y. is supported by the USDepartment of Energy, Office ofScience, Basic Energy Sciences, Materials Sciences and EngineeringDivision. K.W. and T.T. acknowledge support from the ElementalArticle https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 8https://doi.org/10.1038/s41567-021-01171-whttps://doi.org/10.1038/s41567-021-01171-whttps://doi.org/10.48550/arxiv.2309.14940https://doi.org/10.1103/physrevb.102.201115https://doi.org/10.1038/s41586-023-06536-0https://doi.org/10.1038/s41586-023-06536-0https://doi.org/10.37807/gbmf11560www.nature.com/naturecommunicationsStrategy Initiative conducted by the MEXT, Japan (Grant NumberJPMXP0112101001) and JSPS KAKENHI (Grant Numbers 19H05790,20H00354 and 21H05233). C.Z. is supported by the Air Force Office ofScientific Research underGrant No. FA9550-20-1-0220 and theNationalScience Foundation under Grant No. PHY-2409943, OSI-2228725,ECCS-2411394. H.W. and L.Y. are supported by the National ScienceFoundation (NSF) grant No. DMR-2124934. The simulation used Anvil atPurdue University through allocation DMR100005 from the AdvancedCyberinfrastructure Coordination Ecosystem: Services & Support(ACCESS) program, which is supported by National Science Foundationgrants #2138259, #2138286, #2138307, #2137603, and #2138296. E. H.acknowledges support by the Gordon and Betty Moore Foundation,grant https://doi.org/10.37807/gbmf11560.Author contributionsX.W. conceived the project. X.W., M.C., R.L. fabricated the samples.X.W., M.C., R.L., Y.Y., Y.L. performed the measurements. X.W. analyzedand interpreted the results. H.W., L.Y. and C.Z. performed the calcula-tions. T.T. and K.W. synthesized the hBN crystals. C.H., J.C., and J.Y.synthesized and characterized the bulk WSe2 crystals. X.W., M.C., H.W.,L.Y., C.Z., and E.H. wrote the paper with input from all authors. Allauthors discussed the results.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65342-6.Correspondence and requests for materials should be addressed toXi Wang.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-65342-6Nature Communications |        (2025) 16:10359 9https://doi.org/10.37807/gbmf11560https://doi.org/10.1038/s41467-025-65342-6http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Bichromatic moiré superlattices for tunable quadrupolar trions and correlated states Results Structures of R- and H-stacked WSe2/WS2/WSe2 heterotrilayers Multi-orbital nature of the bichromatic moiré superlattice Quadrupolar moiré trions Electric-field modulation of the moiré potential landscape Discussion Methods Sample fabrication Optical measurements Calculation of carrier density and electric field Theoretical calculations Data availability References Acknowledgements Author contributions Competing interests Additional information