# Fileset [s41467-022-32493-9.pdf](https://mdr.nims.go.jp/filesets/19f59a2f-fd61-459a-ba82-4c18c0e51811/download) ## Creator Dongxue Chen, Zhen Lian, Xiong Huang, Ying Su, Mina Rashetnia, Li Yan, Mark Blei, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Sefaattin Tongay, Zenghui Wang, Chuanwei Zhang, Yong-Tao Cui, Su-Fei Shi ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Tuning moiré excitons and correlated electronic states through layer degree of freedom](https://mdr.nims.go.jp/datasets/e5b1d365-b565-47f9-bad8-a98763ad782f) ## Fulltext Tuning moiré excitons and correlated electronic states through layer degree of freedomnature communicationsArticle https://doi.org/10.1038/s41467-022-32493-9Tuning moiré excitons and correlatedelectronic states through layer degreeof freedomDongxue Chen 1,2,10, Zhen Lian2,10, Xiong Huang 3,4,10, Ying Su 5,10,Mina Rashetnia3, Li Yan2, Mark Blei6, Takashi Taniguchi 7, Kenji Watanabe 8,Sefaattin Tongay 6, Zenghui Wang 1 , Chuanwei Zhang 5 ,Yong-Tao Cui 3 & Su-Fei Shi 2,9Moiré coupling in transition metal dichalcogenides (TMDCs) superlatticesintroduces flat minibands that enable strong electronic correlation and fasci-nating correlated states, and it also modifies the strong Coulomb-interaction-driven excitons and gives rise to moiré excitons. Here, we introduce the layerdegree of freedom to theWSe2/WS2moiré superlattice by changingWSe2 frommonolayer to bilayer and trilayer. We observe systematic changes of opticalspectra of the moiré excitons, which directly confirm the highly interfacialnature of moiré coupling at the WSe2/WS2 interface. In addition, the energyresonances of moiré excitons are strongly modified, with their separationsignificantly increased in multilayer WSe2/monolayer WS2 moiré superlattice.The additional WSe2 layers also modulate the strong electronic correlationstrength, evidenced by the reduced Mott transition temperature with addedWSe2 layer(s). The layer dependence of both moiré excitons and correlatedelectronic states can be well described by our theoretical model. Our studypresents a new method to tune the strong electronic correlation and moiréexciton bands in the TMDCs moiré superlattices, ushering in an excitingplatform to engineer quantum phenomena stemming from strong correlationand Coulomb interaction.In a strongly correlated electronic system, Coulomb interactionsamong electrons dominate over kinetic energy. Recently, two-dimensional (2D) moiré superlattices of van der Waals materials haveemerged as a promising platform to study correlated physics andexotic quantum phases in 2D, such as the correlated insulating statesand superconductivity in graphene moiré superlattices1–14, the Mottinsulator state at half band filling and various generalized Wignercrystal states at fractional fillings of the moiré superlattices based ontransition metal dichalcogenides (TMDCs)15–23. The key to the strongcorrelation in these systems is the enhanced Coulomb interaction inReceived: 14 November 2021Accepted: 29 July 2022Check for updates1Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, China. 2Department ofChemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 3Department of Physics and Astronomy, University of California,Riverside, CA 92521, USA. 4Department of Materials Science and Engineering, University of California, Riverside, CA 92521, USA. 5Department of Physics,University of Texas at Dallas, Dallas, TX75083, USA. 6School for Engineering ofMatter, Transport and Energy, ArizonaStateUniversity, Tempe, AZ85287, USA.7International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 8Research Center forFunctional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 9Department of Electrical, Computer & Systems Engi-neering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 10These authors contributed equally: Dongxue Chen, Zhen Lian, Xiong Huang, Ying Su.e-mail: zenghui.wang@uestc.edu.cn; Chuanwei.Zhang@utdallas.edu; yongtao.cui@ucr.edu; shis2@rpi.eduNature Communications | (2022) 13:4810 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/0000-0003-2035-8387http://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/0000-0001-7847-1142http://orcid.org/0000-0001-7847-1142http://orcid.org/0000-0001-7847-1142http://orcid.org/0000-0001-7847-1142http://orcid.org/0000-0001-7847-1142http://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/0000-0003-3743-7567http://orcid.org/0000-0003-3743-7567http://orcid.org/0000-0003-3743-7567http://orcid.org/0000-0003-3743-7567http://orcid.org/0000-0003-3743-7567http://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/s41467-022-32493-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-32493-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-32493-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-32493-9&domain=pdfmailto:zenghui.wang@uestc.edu.cnmailto:Chuanwei.Zhang@utdallas.edumailto:yongtao.cui@ucr.edumailto:shis2@rpi.edu2D and greatly reduced kinetic energy in the flat moiré minibands. InTMDC-based moiré superlattices, the combination of large effectivemass and strong moiré coupling renders the easier formation of flatbands and stronger electronic correlation, compared with graphenemoiré superlattices. For example, the 0- or 60-degree angle-alignedWSe2/WS2 exhibits Mott insulating states with transition temperaturesexceeding 150K18,19, the highest among all 2Dmoiré systems studied sofar. It alsohosts various correlated insulating states at fractional fillingsof the moiré lattice18,19, indicating strong and long-range electroninteractions.Meanwhile, the strong Coulomb interaction in 2D also leads totightly bound excitons with large binding energy in TMDCs24–27. Themoiré coupling in the TMDC moiré superlattices is expected to gen-erate excitonic flat minibands28, beyond the single-particle electronicflat bands in the conduction and valence bands. Recently, the moiréexcitons have been reported in the angle-aligned WSe2/WS2heterojunction17,18, in which correlated insulating states alsooccur15,17–19. The excitonic flat band is promising for realizing topolo-gical exciton states and correlated exciton Hubbard model28,29, ush-ering in exciting opportunities for engineering correlated quantumstates. However, there are key questions that remained to be addres-sed. For example, how is the moiré coupling’s extension in the out-of-plane direction? How could one systematically tune both the electro-nic flat bands and moiré exciton bands in the TMDCs moirésuperlattice?In this work, we investigate these questions utilizing the layerdegree of freedom, inspired by the layer-layer coupling in TMDCs thatleads to the abrupt direct-to-indirect bandgap transition from mono-layer to bilayer TMDCs30,31. We demonstrate a general approach tuningboth electronic and moiré exciton bands by increasing the layernumber of WSe2 in the angle-alignedWSe2/WS2 heterojunction. As thelayer number of WSe2 varies from monolayer (1 L) to bilayer (2 L) andtrilayer (3 L), the optical spectra of the moiré exciton change system-atically in a way that suggests the moiré coupling is highly interfacial,strongly confined at theWSe2/WS2 interface andbarely affects thenextneighboring WSe2 layer(s). However, the added WSe2 layer(s) couldmodify moiré excitons in theWSe2 layer interfacingWS2, resulting in asignificant increase in the resonance energy separations betweenmoiré excitons. This observation can be well described by a phe-nomenological model. Our work, to our best knowledge, reports thefirst sensitive tuning of moiré excitons via layer degree of freedom.The correlated electronic structure is also sensitive to the numberof layers in WSe2. TheMott insulator state at the filling of one hole permoiré unit cell (n = −1) is found to have a transition temperaturedecreased from 180K in 1 L/1 L WSe2/WS2 to 120 K in 2 L/1 L WSe2/WS2and 60K in 3 L/1 LWSe2/WS2. The correlated states at fractionalfillings(fractional charge per moiré supercell) are significantly quenched inthe 3 L/1 L WSe2/WS2 heterojunction. The reduced Mott transitiontemperature, however, is still significantly higher than that of graphenemoiré superlattices (~4 K1). Our study, therefore, also demonstrates anew knob to tune the strong electron correlation in TMDC moirésuperlattices that can be further exploited for engineering new cor-related quantum states.Results and discussionThe back-gated angle-aligned WSe2/WS2 heterojunction device isschematically shown in Fig. 1a, which includes three different regionsin the same device: 1 L/1 L WSe2/WS2, 2 L/1 L WSe2/WS2, and 3 L/1 LWSe2/WS2. The device was constructed through a dry pickup methoddescribed previously13 (also seeMethods), and the heterojunctions areaWSe2WS2h-BNFLGSiO2SiAu AuFig. 1 | Angle-aligned multilayer WSe2/monolayer WS2 moiré superlattice.a Schematic of the multilayer WSe2/monolayer WS2 heterojunction devices, withthe heterojunctions encapsulated with flakes of BN on both sides. The few-layer-graphene (FLG) works as the back gate electrode. bDifferential reflectance spectraof different regions at zero gate voltage. c–e are the differential reflectance spectraas a function of the gate voltage (density of carriers) at the region of 1 L/1 L, 2 L/1 L,and 3 L/1 L WSe2/WS2. All data were taken at 4.5 K.Article https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 2encapsulated with flakes of boron nitride (BN) and gated through few-layer graphene flakeworking as the back gate electrode.WSe2 andWS2have a lattice mismatch of ~4%, resulting in a moiré superlattice with aperiodicity of ~8 nm32,33 when they are angle-aligned (0- or 60-degreetwisted). Having the three regions (1 L/1 LWSe2/WS2, 2 L/1 LWSe2/WS2,and 3 L/1 L WSe2/WS2) in the same device is advantageous as thesethree regions have the same twist angle since the WSe2 for all thesethree regions are from the same flake. As a result, the moiré latticeconstant in these three regions are about the same, and we can com-pare our measurements from these different regions directly.The 1 L/1 LWSe2/WS2 heterojunction has a type-II band alignment,with the conduction band minimum located in the WS2 layer and thevalance band maximum in the WSe2 layer15. Strong moiré couplingleads to a band folding in the mini-Brillouin zone and generates moiréexciton bands32, which will split the A exciton resonance of WSe2 intothree moiré exciton peaks, as demonstrated in the previousexperiments17,32. Here we measure the reflectance spectra in the threedifferent regions of the WSe2/WS2 heterojunction as a function of thegate voltage, with results shown in Fig. 1c–e. There are two majordifferences between the moiré exciton spectra from the 1 L/1 LWSe2/WS2 and multilayer WSe2/monolayer WS2 (2 L/1 L WSe2/WS2 or3 L/1 L WSe2/WS2) heterojunctions. First, it is evident that near thecharge-neutral region (gate voltage ~0 V), there are three moiré exci-ton resonances in the 1 L/1 LWSe2/WS2 region (Fig. 1c) but four in both2 L/1 L (Fig. 1d) and 3 L/1 L (Fig. 1e) WSe2/WS2 regions. Second, themoiré exciton energy difference between the lowest and highestenergy moiré excitons increases significantly in both 2 L/1 L (Fig. 1d)and 3 L/1 L (Fig. 1e) WSe2/WS2 regions. These observations are betterillustrated in Fig. 1b, which plots the differential reflectance spectra atthe gate voltage of 0 V for the three different regions (line cuts at zerogate voltage in Fig. 1c–e. For the 1 L/1 L WSe2/WS2 region, we observethreemoiré exciton peaks at ~1.662 eV (X 1LI ), 1.715 eV (X 1LII ), and 1.753 eV(X 1LIII ), consistent with the previous reports32. However, in the 2 L/1 LWSe2/WS2 region, one additional exciton resonance emerges, addingup to a total of fourmajor excitons peaked at ~1.642 eV (X2LI ), ~1.693 eV(X2LIV ), 1.728 eV (X2LII ), and 1.793 eV (X2LIII ). In the 3 L/1 LWSe2/WS2 region,there are also four major exciton resonances at ~1.645 eV (X3LI ),~1.677 eV (X3LIV ), 1.730 eV (X3LII ), and 1.785 eV (X3LIII ). The largest moiréexciton energy difference, defined as the energy difference betweenX III and X I, is ~90meV for the 1 L/1 LWSe2/WS2 region but ~150meV for1 L/2 L WSe2/WS2 region and ~140meV for 1 L/3 L WSe2/WS2 region, anincrease of more than 50%. Similar behaviors have been observed forall the devices we have studied (details in Supplementary Note 5).Our observations suggest that the moiré potential is highly loca-lized at the WSe2/WS2 interface and has a limited extension along theout-of-plane direction. As a result, the moiré coupling only significantlymodifies the first WSe2 layer in contact with the monolayer WS2. Thenewly developed exciton resonances in the 2 L/1 L and 3 L/1 LWSe2/WS2heterojunctions (X2LIV and X3LIV ), therefore, arise from thebarelymodifiedintralayer A exciton in the upper WSe2 layers away from the interface(also see Supplementary Note 1). Our interpretation is supported by thefact that the energies ofX2LIV (1.693 eV) andX3LIV (1.677 eV) are close to theintralayer A exciton energy of monolayer WSe2 (~1.70 eV), and it is fur-ther corroborated by the stronger reflectance intensity from the newmoiré exciton in 3 L/1 L WSe2/WS2 (X3LIV ) compared with that in 2 L/1 LWSe2/WS2 (X2LIV ). Moreover, there is a redshift in the moiré excitonresonance X I and blueshifts in X II and X III in both 2 L/1 L and 3 L/1 LWSe2/WS2 compared with those in 1 L/1 L WSe2/WS2 (Fig. 1b). And theshift of X II and X III is more significant in magnitude than that of X I.Our results can be understood with a phenomenological model(details in SupplementaryNote 2), considering themoiré excitons in thefirst WSe2 layer interacting with a exciton state in the addedWSe2 layer(s) that has the resonance energy between X I and X II. The resulting levelrepulsion naturally explains the redshift of X I and blue shift of X II andX III in the 2 L/1 L (3 L/1 L)WSe2/WS2 comparedwith 1 L/1 LWSe2/WS2. Tounderstand the phenomenological model, we propose a possiblemicroscopic mechanism by considering the hybridization betweenmoiré excitons and interlayer-like hybrid exciton (iX) in multilayerWSe2/1 L WS2 (details in Supplementary Information Note 2). Thehybridization can increase the energy separation between moiré exci-tons and is enabled by the moiré-potential-induced Umklappscattering34–36. The interlayer-like hybrid exciton arises from the inter-layer tunneling in multilayer WSe2 that hybridizes the valence bands indifferent layers37. However, it has much weaker oscillator strength thanthe intralayer-like hybrid exciton and cannot be resolved in theexperiment. In the absence of hybridization betweendifferent excitonicstates, the energy dispersion of bare intralayer A excitons in 1 L WSe2and moiré excitons in 1 L/1 L WSe2/WS2 are shown in Fig. 2a, b, respec-tively. Here we fold the energy bands of A excitons into the mini-Brillouin zone to compare directly with that of moiré excitons. Thebright A exciton state at the mini-Brillouin zone center (which isdenoted as γ point as shown in the inset of Fig. 2a) is marked as XA inFig. 2a, and the bright moiré exciton states are marked as X 1LI , X 1LII , andX 1LIII in Fig. 2b. The optical absorption spectrum ofmoiré excitons in 1 L/1 L WSe2/WS2 is shown in Fig. 2c, with the three resonances corre-sponding to the three bright moiré exciton states. For the absorptionspectrum of 2 L/1 LWSe2/Ws2 in Fig. 2d, we introduce the hybridizationbetween moiré excitons and interlayer-like hybrid excitons (see Sup-plementary InformationNote 2). The hybridization induces a redshift inX2LI and blueshifts in X2LII and X2LIII compared with those of 1 L/1 LWSe2/Ws2 in Fig. 2c. The larger shift in the magnitude of X2LII and X2LIIIindicates stronger hybridization with the interlayer-like hybrid exciton,which is consistent with the proposed mechanism (see SupplementaryInformation Note 2).Moreover, the intralayer-like hybrid exciton in the second WSe2layer leads to another resonance X2LIV between X2LI and X2LII , as shown inFig. 2d, which is consistent with our experimental observation (Fig. 1b,d). In 3 L/1 L WSe2/WS2, additional hybrid excitons can be induced bythe interlayer tunneling between valence bands in the 2nd and 3rd WSe2layers. In this case, the additional hybrid excitons away from theWSe2/WS2 interface do not affect the moiré excitons. Therefore, themoiré excitons in 3 L/1 L WSe2/WS2 are nearly identical to those in 2 L/1 L WSe2/WS2 (Fig. 2d), also consistent with our experimental results(Fig. 1b). On the other hand, the additional hybrid excitons from upperWSe2 layers will contribute to the resonant peak X3LIV which should beconsisted of two sub-resonances. This is also consistent with ourexperimental data, as X3LIV (Fig. 1e) is broader than X2LIV (Fig. 1d). Inter-estingly, although these two resonances in X3LIV cannot be resolved atthe charge-neutral region, likely due to linewidth broadening, they canbe revealed in the p-doping region (Fig. 1e). The exact mechanism willbe investigated in the future.The moiré excitons in the three regions show distinct gatedependence, which also confirms the interfacial nature of the moirécoupling in the WSe2/WS2 superlattice. Our theoretical model, whichconsiders the interfacial nature of the moiré coupling, shows that thevalence bands due to the added layers are higher in energy than themoiré electronic flat band from the WSe2/WS2 interface, as shown inFig. 3a–c (detailed calculations in Supplementary Information Note 3).When carriers are added to the 1 L/1 L WSe2/WS2 heterostructure, theywill fill the first moiré valence band in theWSe2 layer and the first moiréconduction band in the WS2 layer. The first flat moiré miniband has astrong electron correlation due to their narrow bandwidth, and at thehalf-filling states (one electron/hole per moiré unit cell, n = +1 or −1),Mott insulator states will occur, as demonstrated in several recentexperiments15–20. The optical reflectance spectra are expected to bemodulated by these correlated states. In the 1 L/1 LWSe2/WS2 region, allthree excitons are modulated, with X 1LI being the most obvious one(Fig. 1c). In the 2 L/1 L and 3 L/1 L WSe2/WS2 regions, the excitons at thelowest energy (X2LI and X3LI ) are also strongly modulated (Fig. 1d, e).Figure 3d–f plots the gate voltage dependence of the lowest energyArticle https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 3moiré exciton for the three different regions (X 1LI , X2LI and X3LI ), whichclearly shows intensitymodulations at n = −1 and +1. On the other hand,the additional excitons in 2 L/1 L (X2LIV ) and 3 L/1 L (X3LIV ) WSe2/WS2regions are barely affected by the formation of the Mott states at n = ±1(Fig. 1d, e). These behaviors can also be explained by the interfacialnature of themoiré coupling, which confines the correlated electrons atthe interface ofWSe2/WS2. Themodulation of themoiré excitons at then = ±1 is likely due to the dielectric constant change and gap openingassociated with the Mott insulator states. Due to the small radius of thestrongly bound exciton24, only themoiré excitons in the firstWSe2 layerimmediately interfacing with the WS2 monolayer can sensitively detectthe dielectric constant change at the interface. In the 2 L/1 L and 3 L/1 Lregions, the additional excitons originated from intralayer excitonslocalized in the added layers, are thus barely affected.To better investigate the tuning of the electron correlation by thelayer degree of freedom, we perform microwave impedance micro-scopy (MIM) measurements to study the correlated insulating states inthe three different heterostructure regions (Fig. 4a). MIM probes thelocal conductivity of the sample and has been successfully employed toreveal a rich structureof correlated insulating states in the angle-aligned1 L/1 L WSe2/WS2 device8. In the multilayer WSe2/1 L WS2 device, weprimarily focus on the features on the hole side, as the holes reside inthe WSe2 layer due to the type-II alignment, and we introduce the layerdegree of freedom by modulating the layer number of WSe2. At tem-perature T = 10K, the MIM spectra in both 1 L/1 L and 2 L/1 L WSe2/WS2regions show similar pronounced features at various fillings, includingthe Mott insulator states at n = −1, the generalizedWigner crystal statesat fractional fillings of n = −1/3 & −2/3, −1/2, −1/4 & −3/4, etc. The 3 L/1 LWSe2/WS2 data show fewer and less pronounced dips: other than theMott insulator state atn = −1, only two fractionalfillingsn = −1/3 and−1/2can be resolved. There is also a small difference in the twist angle in the3 L/1 LWSe2/WS2 region (~1.3°) compared to that in the 1 L/1 L and2 L/1 Lregions (~0.9°), which results in different gate voltage positions forthese insulating states in the 3 L/1 L WSe2/WS2 region (details inmethod). Since the formation of the correlated insulating states atfractional fillings depends on long-range Coulomb interaction amongelectrons in neighboring moiré unit cells, our results suggest that theinter-site electron interaction strength is weaker in 3 L/1 L than in 1 L/1 Lor 2 L/1 L WSe2/WS2. The difference in the on-site interaction, corre-sponding to theMott insulator state at n = −1, can be further revealed inits temperature dependence. As shown in Fig. 4b–d, as the temperatureis raised, the features at fractional fillings disappear at ~30K in both 1 L/1 L and 2 L/1 L WSe2/WS2 regions and at ~15 K in the 3 L/1 L WSe2/WS2region. The Mott insulator state at n = −1 survives at much higher tem-peratures in 1 L/1 L WSe2/WS2, persisting to above 180K, the highestMott transition temperature reported in all 2D moiré superlatticestructures so far. In the 2 L/1 L WSe2/WS2 region, the Mott transitiontemperature is ~120K,while it ismuch lower, ~60K, in the 3 L/1 L region.As the correlation strength is determined by the ratio of the Coulombinteraction to the kinetic energy, the reduction of electron correlationstrength from 1 L/1 L or 2 L/1 L WSe2/WS2 is likely due to the increaseddielectric screening from the addedWSe2, which reduces the Coulombcbde1L/1L WSe2/WS23L/1L WSe2/WS22L/1L WSe2/WS2Absorbance (a.u.)0.80.60.40.200.40.30.20.10Absorbance (a.u.)Absorbance (a.u.)1.60 1.65 1.70 1.75 1.80E (eV)1.60 1.65 1.70 1.75 1.80E (eV)1.60 1.65 1.70 1.75 1.80E (eV)0.80.60.40.20aFig. 2 | Theoretical simulation of moiré excitons. a, b are the energy bands ofbare intralayer A excitons in 1 L WSe2 and moiré excitons in 1 L/1 L WSe2/WS2,respectively. a The A exciton bands are folded into the mini-Brillouin zone of themoiré superlattice to compare directly with that of moiré excitons in b. Inset ofa shows the schematic of the mini-Brillouin zone and the label of high symmetrypoints. The WSe2 bright intralayer A exciton state is marked by XA in a. The threebright Moiré exciton states are marked by X 1LI , X 1LII , and X 1LIII in b. Here, we set theenergy EA of XA as the energy reference. c–e Optical absorption spectra in 1 L/1 L,2 L/1 L, and 3 L/1 L WSe2/WS2. The interlayer hybridization between moiré excitonand intralayer A exciton is considered in d and e, with details elaborated in Sup-plementary Information Note 2.Article https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 4interaction at the interface. However, the further reduced correlationstrength in the 3 L/1 LWSe2/WS2 is facilitated by the additional increaseof kinetic energy, which arises from the increased bandwidth of the flatband, according to our calculation shown in Supplementary Informa-tion Fig. 2. We emphasize here that even the reduced electron corre-lation in the 2 L/1 L and 3 L/1 L WSe2/WS2 is still significantly strongerthan that in graphene moiré systems, which has a Mott transitiontemperature ~4K1. As a result, the layer degree of freedom can be uti-lized for engineering new correlated states.In summary, we have demonstrated a new moiré superlatticesystem based on multilayer TMDC heterojunctions. The added layershost additional intralayer excitons that interact with the moiré exci-tons residing at the moiré interface, and they can further modify thecorrelation strength of the correlated states. Considering the layer-valley-spin locking in TMDC38, these new TMDCs moiré superlatticesprovide an exciting platform to investigate emerging correlated valleyand spin physics.MethodsHeterostructure device fabricationWe use a dry pickup method20,39 to fabricate the WSe2/WS2 hetero-structures. We exfoliate monolayer WS2, multilayer WSe2, graphite,and BN layers on silicon substrate with a 285 nm thermal oxide layer.For angle-aligned heterostructures, we choose exfoliated WS2 andWSe2 layerswith sharp edges, whose crystal axes are further confirmedby second harmonic generation measurements. We then mount theSiO2/Si substrate on a rotational stage and clamp the glass slide withthin flakes to another three-dimensional (3D) stage. We adjust the 3Dstage to control the distance between substrates and thin flakes, andwe sequentially pickup different layers onto the pre-patterned Auelectrodes on SiO2/Si substrates. We fine adjust the angle of the rota-tional stage (accuracy of 0.02°) under a microscope objective to stackthe WSe2/WS2 heterojunction, ensuring a near-zero twist anglebetween the two flakes. The final constructed device is annealed at130 °C for 12 hours in a vacuum chamber. The pre-patterned Au con-tact electrodes are fabricated through standard electron-beam litho-graphy and e-beam evaporation processes (see SupplementaryInformation Fig. 3 for the optical microscope image of the device usedin themain text). More sample characterization details can be found inSupplementary Note 4.Optical spectroscopy measurementsTo perform differential reflectance contrast measurement, the sam-ples were mounted in a helium flow-controlled cryostat with a quartzoptical window and electrical feedthroughs. A super-continuum laser(YSL Photonics) was used as the white light source. The laser wasfocused onto the sample with a ×50 objective (the typical laser spotsize is ~2μm). The reflected light was directed into a spectrograph andcollected with a CCD camera (Princeton Instruments). The differentialreflectance is calculated as 4RR = R�R0R0by using the reflectance spectrumat the highest p-doping region as the reference R0.Microwave impedance microscopy measurementsThe MIM measurement is performed on a homebuilt cryogenic scan-ning probe microscope platform. A small microwave excitation ofabout 0.1μW at a fixed frequency ~10GHz is delivered to a chemicallyetched tungsten tip mounted on a quartz tuning fork. The reflectedsignal is analyzed to extract the demodulated output channels, MIM-Im andMIM-Re, which are proportional to the imaginary and real partsof the admittance between the tip and sample, respectively. Toenhance theMIM signal quality, the tip on the tuning fork is excited tooscillate at a frequency of around 32 kHz with an amplitude of ~8 nm.The resulting oscillation amplitudes of MIM-Im and MIM-Re are thenextracted using a lock-in amplifier to yield d(MIM-Im)/dz and d(MIM-Re)/dz, respectively. The d(MIM)/dz signals are free of fluctuatingbackgrounds, and their behavior is very similar to that of the standardFig. 3 | Layer dependence of the electronic flat miniband for WSe2/WS2 moirésuperlattices. a–c are calculated electronic bandstructure of the valence band in1 L/1 L WSe2/WS2, 2 L/1 L WSe2/WS2, 3 L/1 L WSe2/WS2, respectively (details in Sup-plementary Information Note 3), with the moiré flat band from the 1st layer WSe2labeled in red. d–f are differential reflectance intensity of the lowest energy moiréexciton (X I) as a function of the back gate voltage (carrier density) in Fig. 1c–e,respectively (vertical dashed line cuts), with the 2D color plots showing theenhanced reflectance spectra near the moiré excitons X II and X III .Article https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 5MIM signals. In this paper, we simply refer to d(MIM)/dz as the MIMsignal.Estimating the twist angleTwist angles of the moiré superlattices can be estimated by the carrierdensity corresponding to the correlated insulating state at n = ±1, witha bottom hBN of thickness ~52 nm and dielectric constant 3.5. The 1 L/1 L WSe2/WS2 and 2 L/1 L WSe2/WS2 regions have a similar moiré peri-odicity of 7.4 nm and twist angle of 0.9°. For the 3 L/1 L WSe2/WS2region, the moiré periodicity is 6.0 nm and the twist angle is 1.3°. Thisdifference is likely caused by a small distortion or wrinkle betweenWSe2 and WS2 layers.Data availabilitySource data are available for this paper. All other data that support theplots within this paper and other finding of this study are availablefrom the corresponding author upon reasonable request.Code availabilityThe source code for the numerical simulations is available from thecorresponding author upon reasonable request.References1. Cao, Y. et al. 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Nature 579, 56–61 (2020).-8 -6 -4 -2 0 2 4 6 8 103L/1L WSe2/WS22L/1L WSe2/WS2Filling factorMIM-Im (a.u.)Back gate (V)1L/1L WSe2/WS2-1 -2/3 -1/2 -1/3 0 1 -3/4 -1/4-8 -4 0 4 82L/1L WSe2/WS2Back gate (V)180 K150 K120 K90 K60 K40 K30 K24 K18 K14 K10 K7 K5 K3.7 K-8 -4 0 4 8024681012141L/1L WSe2/WS2Normolized MIM-Im (a.u.)Back gate (V)180 K150 K120 K90 K60 K40 K30 K24 K18 K14 K10 K7 K5 K3.7 K-8 -4 0 4 83L/1L WSe2/WS2Back gate (V)180 K120 K90 K60 K40 K30 K24 K18 K14 K10 K7 K5 K3.7 Ka b c dFig. 4 |MIMmeasurementsof correlated states indifferentmoiré superlattices.a MIM spectra as a function of gate voltage for the moiré superlattice of 1 L/1 LWSe2/WS2 (green), 2 L/1 L WSe2/WS2 (orange), and 3 L/1 L WSe2/WS2 (brown) at10 K.b–d are the temperature-dependentMIM spectra for themoiré superlattice of1 L/1 L, 2 L/1 L, and 3 L/1 L WSe2/WS2, respectively.Article https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 68. Shen, C. et al. 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Tailoring excitonic states of van der Waals bilayersthrough stacking configuration, band alignment, and valley spin.Sci. Adv. 5, eaax7407 (2019).38. Jones, A. M. et al. Spin–layer locking effects in optical orientation ofexciton spin in bilayer WSe2. Nat. Phys. 10, 130–134 (2014).39. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).AcknowledgementsWe thank professor Feng Wang and professor Chenhao Jin for theirhelpful discussions. The optical spectroscopy measurements are sup-ported by an AFOSRDURIP award throughGrant FA9550-20-1-0179. Thedevice fabrication was supported by the Micro and NanofabricationClean Room (MNCR) at Rensselaer Polytechnic Institute (RPI). Z. Lian andS.-F.S. acknowledge support from NYSTAR through Focus Center-NY–RPI Contract C150117. S.-F.S. also acknowledges the support fromNSF (Career Grant DMR-1945420 and DMR-2104902) and AFOSR(FA9550-18-1-0312). X.H. and Y.-T.C. acknowledge support from NSFunder award DMR- 2104805. Y.S. and C.Z. acknowledge support fromNSF PHY-2110212, PHY-1806227, ARO (W911NF17-1-0128), and AFOSR(FA9550-20-1-0220). D.C. acknowledges support from the NationalNatural Science Foundation of China, Grant number 62004032. S.T.acknowledges support from NSF DMR-1904716, DMR-1838443, CMMI-1933214, and DOE-SC0020653. K.W. and T.T. acknowledge supportfrom the Elemental Strategy Initiative conducted by the MEXT, Japan,Grant Number JPMXP0112101001 and JSPS KAKENHI, Grant Numbers19H05790 and JP20H00354. L.X. and D.S. acknowledge support fromthe U.S. Department of Energy (no. DE-FG02-07ER46451) for magneto-spectroscopy measurements performed at the National High MagneticField Laboratory,which is supportedby theNational Science Foundationthrough NSF/DMR-1644779 and the State of Florida.Author contributionsS.-F.S. and Y.-T.C. conceived the project. D.C. and Z.L. fabricated theheterostructure devices and performed the optical spectroscopy mea-surements. X.H. performed the MIM measurements. M.R. helped withdevice fabrication. M.B. and S.T. grew the TMDC crystals. T.T. and K.W.grew the BN crystals. C.Z. and Y.S. performed the theoretical calcula-tions. S.-F.S., Y.-T.C., C.Z., Y.S., D.C., Z.L., Z.W., X.H., and L.Y. analyzedthe data. S.-F.S. and Y.-T.C. wrote the manuscript with inputs from allauthors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-32493-9.Correspondence and requests for materials should be addressed toZenghui Wang, Chuanwei Zhang, Yong-Tao Cui or Su-Fei Shi.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of thiswork. 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If material is notincluded in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-32493-9Nature Communications | (2022) 13:4810 8http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Tuning moiré excitons and correlated electronic�states through layer degree of�freedom Results and discussion Methods Heterostructure device fabrication Optical spectroscopy measurements Microwave impedance microscopy measurements Estimating the twist angle Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information