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Aidan J. Campbell, Mauro Brotons-Gisbert, Hyeonjun Baek, Valerio Vitale, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Johannes Lischner, Brian D. Gerardot

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[Exciton-polarons in the presence of strongly correlated electronic states in a MoSe2/WSe2 moiré superlattice](https://mdr.nims.go.jp/datasets/a597ef18-b5de-4bb9-a1e7-d0937aa99a39)

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Exciton-polarons in the presence of strongly correlated electronic states in a MoSe2/WSe2 moiré superlatticeARTICLE OPENExciton-polarons in the presence of strongly correlatedelectronic states in a MoSe2/WSe2 moiré superlatticeAidan J. Campbell 1, Mauro Brotons-Gisbert 1, Hyeonjun Baek1, Valerio Vitale2, Takashi Taniguchi 3, Kenji Watanabe 4,Johannes Lischner2 and Brian D. Gerardot 1✉Two-dimensional moiré materials provide a highly tunable platform to investigate strongly correlated electronic states. Suchemergent many-body phenomena can be optically probed in moiré systems created by stacking two layers of transition metaldichalcogenide semiconductors: optically injected excitons can interact with itinerant carriers occupying narrow moiré bands toform exciton-polarons sensitive to strong correlations. Here, we investigate the behaviour of excitons dressed by a Fermi sealocalised by the moiré superlattice of a molybdenum diselenide (MoSe2)/tungsten diselenide (WSe2) twisted hetero-bilayer. At amultitude of fractional fillings of the moiré lattice, we observe ordering of both electrons and holes into stable correlated electronicstates. Magneto-optical measurements reveal extraordinary Zeeman splittings of the exciton-polarons due to exchange interactionsin the correlated hole phases, with a maximum close to the correlated state at one hole per site. The temperature dependence ofthe Zeeman splitting reveals antiferromagnetic ordering of the correlated holes across a wide range of fractional fillings. Our resultsillustrate the nature of exciton-polarons in the presence of strongly correlated electronic states and reveal the rich potential of theMoSe2/WSe2 platform for investigations of Fermi–Hubbard and Bose–Hubbard physics.npj 2D Materials and Applications            (2022) 6:79 ; https://doi.org/10.1038/s41699-022-00358-wINTRODUCTIONTwo-dimensional (2D) materials have emerged as a new play-ground to investigate many-body interactions and stronglycorrelated electronic phenomena. For example, due to a directbandgap1, huge exciton binding energies2, and straightforwardcontrol of carrier concentration3, monolayer transition metaldichalcogenides (TMDs) provide a platform to probe the interactionof an exciton with a Fermi sea (2D electron or hole gas) describedby the Fermi-polaron model4. With increasing Fermi energy, aneutral exciton evolves into two branches due to both attractive(lower energy) and repulsive (higher energy) interactions withcharge carriers4–8. By extension, TMD moiré heterostructuresprovide access to a highly tunable many-body physical systemconsisting of an exciton dressed by a Fermi sea which forms a seriesof charge-ordered (Mott insulating and generalised Wigner crystal)electronic states as the carrier concentration is tuned9.Stacking two monolayer TMDs with either a lattice mismatchand/or relative twist angle forms a moiré superlattice with aperiodicity that far exceeds the inter-atomic spacing of theconstituent crystals. Itinerant electrons in a Fermi sea can bespatially localised by the moiré potential, leading to the formationof flat bands. The suppressed kinetic energy of the charge carriersrelative to their on-site Coulomb repulsion energy, U, has led totheoretical predictions10–16 as well as experimental optical9,17–22and transport23–27 investigations of strongly correlated electronand hole phases for different TMD homo- and hetero-bilayersystems. In the simplest scenario, the highest flat valence band ina TMD moiré system can be mapped onto the 2D triangularHubbard model10,12,14. So far, evidence of Hubbard model physicshas only been observed experimentally for angle-aligned WSe2/WS2 hetero-bilayers which form a moiré superlattice due to latticemismatch17. However, the formation and behaviour of exciton-polarons as a function of fractional filling of the moiré lattice inHubbard model investigations has yet to be probed.While strongly correlated phenomena have yet to be observedin moiré hetero-bilayers formed from WSe2 and MoSe2, the systemremains compelling: it is predicted to form flat conduction andvalence minibands28,29 and is an excellent candidate for therealisation of a wide range of strongly correlated states includingWigner crystals12,13, Mott insulators10,11,14 and charge-transferinsulators16. Compared to TMD hetero-bilayers with differentchalcogen atoms, the energetic interplay between Coulombrepulsion and kinetic energy in the WSe2/MoSe2 system is moretunable with relative twist angle due to the small (0.2%) latticemismatch30. In addition, the moiré potential in WSe2/MoSe2hetero-bilayers has led to the observation of trapping of interlayerexcitons at specific atomic registries in the moiré lattice31–38. Todate, hetero-bilayer WSe2/MoSe2 remains the only moiré systemto conclusively exhibit exciton trapping.Here we optically investigate the formation and behaviour ofexciton-polarons, including their charge screening and Coulomband magnetic interactions, which are formed by intralayerexcitons dressed by a Fermi sea localised by a moiré superlatticein a MoSe2/WSe2 hetero-bilayer. As the Fermi level is tuned, weobserve ordering and re-ordering of itinerant carriers into amultitude of correlated states as evidenced by abrupt changes inthe oscillator strength, energy, and linewidth of the exciton-polarons. We observe these correlated states at positive (electron)and negative (hole) fractional fillings (ν) of the moiré lattice,including: ν= ±1/3, ±1/2, ±2/3, ±1, −5/4, where ∣ν∣= 1 representsa single carrier per moiré site. We assign the ±1 state to be aMott17,18,21 or charge-transfer16 insulator state and the rest to be1Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, UK. 2Departments of Materials and Physics and the Thomas Young Centrefor Theory and Simulation of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. 3International Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 4Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki,Tsukuba 305-0044, Japan. ✉email: B.D.Gerardot@hw.ac.ukwww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00358-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00358-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00358-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00358-w&domain=pdfhttp://orcid.org/0000-0002-1063-3536http://orcid.org/0000-0002-1063-3536http://orcid.org/0000-0002-1063-3536http://orcid.org/0000-0002-1063-3536http://orcid.org/0000-0002-1063-3536http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://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/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttps://doi.org/10.1038/s41699-022-00358-wmailto:B.D.Gerardot@hw.ac.ukwww.nature.com/npj2dmaterialsgeneralised Wigner crystals18,20,21,27. At ν=−1 we observe thatthe repulsive WSe2 exciton-polaron gains oscillator strength fromthe attractive, due to the reduced screening of the exciton bycarriers in the insulating state. After ν=−1, the oscillator strengthis then abruptly transferred to the attractive polaron. Furthermore,we observe filling-factor-dependent g-factors of these positively-charged attractive and repulsive polarons, with a maximum at ~1hole per site. Under the assumption that the g-factors areproportional to the magnetic susceptibility of the correlatedphases induced by exchange interactions, temperature dependentmeasurements for ν ≈−0.7 to −1.3 reveal an antiferromagneticspin coupling of the moiré pinned Fermi-hole sea. The experi-mental magnetic behaviour is theoretically explored using amodel that solves the Heisenberg Hamiltonian for charged-ordered hole states with antiferromagnetic next-neighbourinteractions. Our results highlight the behaviour of excitonsdressed by a Fermi sea which is spatially ordered in a series ofcorrelated states. This has importance for optical studies ofcorrelated electronic phenomena in 2D materials and demon-strates the potential of MoSe2/WSe2 heterostructures for futureinvestigations and implementations of highly tunable 2DFermi–Hubbard or Bose–Hubbard models39.RESULTSDevice structure and Fermi-polaronsFigure 1a shows a sketch of our dual-gated hetero-bilayer device,consisting of a monolayer MoSe2 and a monolayer WSe2 verticallystacked with a twist angle (Δθ) of ~57°. The relative twist anglefrom perfect H stacking (i.e., Δθ= 60°), estimated from the opticalmicrograph of the hetero-bilayer (see Methods) and confirmed byour gate dependent measurements (described later), is beyondthe proposed critical angle for lattice reconstruction40,41. Thehetero-bilayer was encapsulated by hexagonal boron nitride (hBN)layers with nearly identical thicknesses (~18 nm). Graphene layersact as electrical contacts for the top, bottom and hetero-bilayergates (see ref. 34 for more details). Moreover, the combination ofthe layer twist and the lattice mismatch between MoSe2 and WSe2results in the formation of a triangular moiré superlattice in ourdevice (see sketch in Fig. 1b) with a period of ~6 nm. This causes aperiodic variation in the interlayer hopping that results in aflattening of the conduction and valence bands in the type-II bandstructure characteristic of TMD hetero-bilayers (see Fig. 1c)42,43.The bare intralayer excitons of the constituent TMDs can beprobed via absorption spectroscopy. The moiré lattice carrierconcentration is tuned via the application of a gate voltage (Vg)between the top/bottom graphene contacts and the hetero-bilayer. As depicted by the schematic in Fig. 1b, these carriers arespatially ordered in a series of correlated states by the moirésuperlattice, whilst also dressing the photo-excited intralayerexciton to form attractive and repulsive exciton-polaron com-plexes (as shown in Fig. 1c).Correlated electronic statesTo investigate doping-dependent phenomena, we perform differ-ential reflection contrast (ΔR/R0) spectroscopy as a function of Vg,where ΔR= Rs− R0, and Rs (R0) is the intensity of the light reflectedby the hetero-bilayer (substrate). Figure 2a shows the Vgdependence of the first derivative of the reflectance spectra withrespect to photon energy (d(ΔR/R0)/dE). The doping dependence ofthe intralayer exciton-polarons in the MoSe2/WSe2 hetero-bilayer ismarkedly different to that observed for individual monolayers (seeSupplementary Fig. 1). At charge neutrality, we observe threeexcitonic resonances: X0W at higher energy, and two resonancesseparated by 36 meV in the spectral range corresponding to X0Mo,which we label as X0Mo;1 (low energy) and X0Mo;2 (high energy). Weassign the two MoSe2 peaks to be a consequence of the formationof moiré minibands, arising from the band folding at the edges ofthe reduced Brillouin zone44. Furthermore, with increasing electron(hole) doping X0W (X0Mo;1) dominate the spectrum, as expected for atype-II band alignment43,45.We employ the parallel plate capacitance model to estimate thedependence of the nominal carrier concentration n on the appliedVg. Using the density of moiré sites n0 corresponding to Δθ ~ 57°,we estimate the Vg-dependent nominal fractional filling ν= n/n0of the moiré lattice (see Methods). The excitonic features shown inFig. 2a exhibit strong modulations in their transition energy,linewidth and oscillator strengths for applied voltages close to thenominal Vg values corresponding to ν= 0 and ±1. Similarmodulations of the excitonic transitions, observed in WSe2/WS2hetero-bilayers17,20,21,46, have been attributed to the suppressedcharge screening originating from the formation of correlatedinsulator phases at different fractional fillings of the moirésuperlattice. In order to corroborate the presence of a robustmoiré lattice at the same spatial position in our sample where weobserve strongly correlated states, we measure the low-temperature (4 K) photoluminescence (PL) spectrum at chargeneutrality using confocal spectroscopy, revealing a series ofFig. 1 Device structure. a Sketch of the dual-gated WSe2/MoSe2 hetero-bilayer. Graphene layers are used as top, bottom, and hetero-bilayerelectrical contacts, while 18-nm-thick hBN layers are used as dielectric spacers34. b Illustration of the top view of a moiré superlattice with atwist angle Δθ and fractional filling of one hole per moiré unit cell. Fermi-polarons form between the photo-excited electron-hole pair andcharge-ordered Fermi sea. c Schematic type-II band structure of the H-WSe2/MoSe2 hetero-bilayer. Purple and orange curves denote bandsfrom MoSe2 and WSe2, respectively. The vertical wavy arrows represent the photon absorption by intralayer excitons in each monolayer. Whenthe Fermi level (EF) is tuned into the top valence band, the WSe2 attractive polaron forms due to interactions between the exciton in onevalley, dressed by holes in the opposite valley.A.J. Campbell et al.2npj 2D Materials and Applications (2022)    79 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;discrete peaks with narrow line-widths (<100 μeV) that demon-strate the existence of an underlying moiré lattice responsible forthe interlayer exciton trapping32–34 (see Supplementary Fig. 2).Moreover, Fig. 2a also reveals that each monolayer in the WSe2/MoSe2 hetero-bilayer is capable of sensing the doping-inducedchanges in their dielectric environment originating from thefractional filling of the other layer, similar to the effects observedusing a WSe2 sensor layer in proximity to a WSe2/WS2 hetero-structure21. Figure 2b shows an example of the sensingcapabilities of the MoSe2 layer for hole doping of the WSe2 layer:the transition energies of X0Mo;1 and X0Mo;2 blue-shift and peak atΔVg=−1.34 V, consistent with a decrease in the permittivity ofthe heterostructure arising from the formation of a correlatedinsulating state at 1 hole per moiré site in the WSe2 layer17,20. Inaddition to the modulation in the transition energy, the linewidthof X0Mo;1 also presents a clear minimum at ν ≈−1 (see Fig. 2c),which can be understood as the result of reduced charge disorderoriginating from a correlated insulating state19. These resultsdemonstrate the potential of intralayer excitons as sensors thatcan probe the formation of correlated states in the adjacent layer(see sketch in Fig. 2d) and corroborate the calibration of ν= ±1 inour device. To estimate the Vg values corresponding to otherfractional fillings of the moiré lattice, we assume a lineardependence of ν with Vg and extrapolate from the experimentalVg values determined for one hole/electron per site, as shown inthe right panel of Fig. 2e. To increase the sensitivity to doping-induced modulations of the reflectance signal, we plot the firstderivative of ΔR/R0 with respect to Vg (d(ΔR/R0)/dVg) as a functionof Vg (see left panel of Fig. 2e). The d(ΔR/R0)/dVg spectrumhighlights a series of abrupt changes in the reflected signal atν= 0, ±1/3, ±1/2, ±2/3, ±1, −5/4 (as indicated by the horizontallines in Fig. 2e), suggesting the formation of correlated states atthese fractional fillings of the triangular lattice. These results revealsymmetric loading of carriers, with an identical ΔVg= ±1.34 Vrequired to fill the moiré superlattice with either one electron(Vg= 1.34 V) or one hole (Vg=−1.34 V) per site, respectively. WeFig. 2 Correlated electron and hole states in the triangular moiré superlattice of a H-WSe2/MoSe2 hetero-bilayer. a Density plot of the firstderivative with respect to energy of the differential reflection contrast (d(ΔR/R0)/dE) of the MoSe2 and WSe2 intralayer exciton-polarons in theWSe2/MoSe2 hetero-bilayer. b Plot of Vg dependence of the estimated peak positions of the MoSe2 excitons. c Plot of the Vg dependence ofthe estimated linewidth Γ of X0Mo;1. d Sketch of the concept of dielectric sensing of correlated hole states. e Left: density plot of the firstderivative with respect to gate voltage of the ΔR/R0 in panel a. d(ΔR/R0)/dVg is multiplied by a factor of 2 for Vg < 0 for better visualisation.Right: plot of filling factor ν against Vg.A.J. Campbell et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    79 assign the stable phases at ν= ±1 to be either Mott17,18,21 orcharge-transfer16 insulator states and the remaining states to begeneralised Wigner crystals13,18,20,21,27.To gain deeper insight into the strength of the electroniccorrelations in our system, we investigate the melting temperatureof the different correlated states. Supplementary Fig. 9 shows thedependence of d(ΔR/R0)/dVg on Vg for temperatures ranging from 4 Kto 90 K. With increasing temperature, the abrupt changes in the d(ΔR/R0)/dVg spectrum (indicative of correlated state formation in both theelectron and hole doping regimes, see Fig. 2e) progressively smoothout until they can no longer be observed at 90 K. We quantitativelyestimate a melting temperature of ~55 K for the correlated state atone hole per moiré site (see Supplementary Fig. 10).Exciton-polaron behaviour at one hole per siteWe now investigate the behaviour of the WSe2 exciton-polarons asthe hole fractional filling of the moiré superlattice is tuned. Figure 3a,b shows the σ−- and σ+-helicity-resolved evolution of the d(ΔR/R0)/dE spectrum, respectively, for negative Vg under an applied magneticfield B of 5 T in Faraday configuration. The intensity colour scale inthese figures is saturated to improve the visibility of the WSe2intralayer repulsive and attractive exciton-polarons (labelled RPþW andAPþW, respectively), while the application of a magnetic field breaksthe energy degeneracy between the exciton transitions at ±K,helping to disentangle the behaviour of each excitonic species. Asfor the monolayer case, at Vg= 0 V only the neutral excitonresonance which becomes RPþW is present. As the hole fractionalfilling increases, an additional resonance gains oscillator strength at~10meV lower energy, in agreement with the formation of APþW47–49.The helicity-resolved results in Fig. 3a, b reveal additionalfeatures of the RPþW and APþW complexes for fractional hole filling.First, hole doping results in a larger blue-shift of RPþW compared toAPþW, as also observed for excitons interacting with a 2D fermionicsea in ML TMDs4,6,50. Second, the oscillator strength of the RPþWresonance shows a non-monotonic behaviour: for small gatevoltages it decreases with increasing hole doping, which can beunderstood as a progressive transfer of oscillator strength fromthe neutral exciton to the positive trion-like state as the Fermienergy moves deeper into the valence band. However, the RPþWresonance regains oscillator strength for hole doping levelscorresponding to ν ≈−1. This can be attributed to the suppressedcharge screening in the correlated insulating phase forming in themoiré lattice. For further hole doping (ν <−1), RPþW abruptlyquenches as the oscillator strength transfers to APþW. Third, uponhole doping the σ+-polarised transitions of both RPþW and APþWappear at a higher energy than their respective σ−-polarisedtransitions, indicative of a positive Zeeman splitting ΔE (accordingto the convention based on ΔE ¼ Eσþ � Eσ�, with Eσ±the energyof the transition with σ± polarisation). This behaviour contrastswith the negative g-factor of exciton-polarons in ML WSe2 basedon their spin and valley configurations51.To gain insight into the origin of the positive Zeeman splitting, weinvestigate the energies of RPþW and APþW as a function of the appliedB field for ν=−1. Figure 3c, d shows the σ−- and σ+-helicity-resolved evolution of the d(ΔR/R0)/dE spectrum for applied B fieldsFig. 3 Exciton-polaron behaviour at one hole per site. a, b σ−- (a) and σ+-helicity-resolved (b) evolution of the first derivative of ΔR/R0 withrespect to energy (d(ΔR/R0)/dE), as a function of the applied negative Vg (hole doping) under an applied magnetic field of 5 T. c, d σ−- (c) andσ+-helicity-resolved (d) evolution of d(ΔR/R0)/dE for applied magnetic fields between −2.5 and 2.5 T at ν=−1. The purple and black dotsrepresent the magnetic-field-dependent estimated energies of the RPþW and APþW, respectively, as extracted from the fits shown in (e). e Spectraof the bare ΔR/R0 at different applied magnetic fields (dots) for σ+- (red) and σ−-polarised (blue) collection. The solid lines represent fits of theexperimental ΔR/R0 to the analytical model described in the Supplementary text.A.J. Campbell et al.4npj 2D Materials and Applications (2022)    79 Published in partnership with FCT NOVA with the support of E-MRSbetween −2.5 and 2.5 T at ν=−1. Figure 3e shows linecuts of thebare ΔR/R0 spectrum at different B fields for σ+- (red dots) and σ−-polarised (blue dots) collection while the solid lines represent fitsfrom which we estimate the energy, linewidth, and oscillatorstrength of both RPþW and APþW as function of the applied magneticfield (see the Supplementary text for a detailed description of thefitting procedure). The B-field-dependent estimated energies of RPþWand APþW extracted from the fits are overlayed in Fig. 3c, d (purpleand black dots, respectively). A large positive Zeeman splitting isclearly observed, which suggests an interaction-enhanced magneticresponse of the correlated hole state at ν=−1. Finally, we note thatFig. 3a–e reveal a large spin polarisation of RPþW and APþW underapplied B fields. Such spin polarisation originates from the differenteffective hole doping in the ±K valleys induced by the large Zeemansplitting. APþW is an intervalley exciton complex in which themomentum-direct electron-hole pairs at ±K are dressed by holes inthe opposite valley52,53. On application of a positive magnetic fieldof 5 T, the valence band edge at +K is shifted to higher energyrelative to −K. Exchange interactions favour single valley occupancyof carriers, so nearly all the holes are doped in the +K valley, ratherthan the −K, leading to the observed spin polarisation6. When weprobe the exciton in −K using σ− light, there is a large population ofholes available to form APþW (see Fig. 3a). In contrast, there is asmaller population of holes at −K available to form APþW when weprobe the +K exciton using σ+, leading to a higher relative intensityof RPþW (see Fig. 3b). When we sweep the magnetic field frompositive to negative, we shift the band maximum from +K to −K,leading to the observed transfer in oscillator strength between RPþWand APþW (see Fig. 3c–e).Magnetic interactions probed by exciton-polaronsNext, we investigate the fractional-filling-dependence of theZeeman splitting of the RPþW and APþW resonances. Figure 4aFig. 4 Exciton-polaron magnetic interactions at different hole fractional fillings. a σ−- (blue) and σ+-resolved (red) ΔR/R0 spectra atrepresentative hole ν values under a B= 1 T. b B-field-dependent Zeeman splitting of APþW from −1 to 1 T at representative hole ν values.c Evolution of the g-factor of APþW as a function of the hole ν extracted from linear fits of ΔE in the range ∣B∣ ≤ 1 T (solid lines in panel b).d Valley Zeeman splitting of the APþW resonance at ν=−1 for different temperatures. e Evolution of the measured g-factor of APþW as a functionof temperature for ν=−1 in the temperature range for which the oscillator strength and linewidth of APþW are sufficient to enable a reliableestimate of the Zeeman splitting. The red solid line represents a fit of the experimental data (black dots) to a Curie–Weiss law from which theWeiss constant is estimated to be θ=−4.6 ± 0.9 K. The negative sign of the extracted Weiss constant reveals antiferromagnetic ordering ofneighbouring hole spins. f Theoretical prediction of the ν dependence of the g-factor based on a model that solves the HeisenbergHamiltonian for charge-ordered hole states with antiferromagnetic exchange interactions between nearest neighbour spins. For all panels theerror bars represent 68% confidence intervals.A.J. Campbell et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    79 shows σ−- (blue) and σ+-resolved (red) ΔR/R0 spectra atrepresentative hole ν values at B= 1 T. The dots representexperimental data while the solid lines are fits of the experimentalΔR/R0 to the model described in the Supplementary text, fromwhich we estimate the energy of the resonances. The spectra inFig. 4a reveal a clear positive ΔE for all hole doping levels,although with a magnitude that depends strongly on ν. Figure 4bshows the B-field-dependent Zeeman splitting of APþW from −1 to1 T at representative hole ν values. The estimated Zeemansplitting exhibits a linear dependence with B at small fields (i.e.,∣B∣ < 1 T). We note that RPþW shows a similar positive lineardependence with B at small fields, although it saturates at larger B(see Supplementary Fig. 6). The linear evolution of ΔE at small Bcan be associated to an effective exciton valley g-factor accordingto ΔE(B)= gμ0B, where μ0 is the Bohr magneton. Figure 4c showsthe evolution of the g-factor of APþW as a function of the hole νextracted from linear fits of ΔE in the range ∣B∣ ≤ 1 T (solid lines inFig. 4b). As already inferred from the results in Fig. 4b, the g-factorof APþW shown in Fig. 4c exhibits a strong dependence on ν,peaking around ν ≈−1, where it reaches a maximum value ofg ~ 145.Figure 4d shows the Zeeman splitting of APþW measured for∣B∣ ≤ 1 T at ν=−1 for different temperatures, where we observethe slope of the Zeeman splitting (and therefore the g-factor)decreases with increasing temperature. Figure 4e shows theevolution of the measured g-factor of APþW as a function oftemperature for ν=−1 in the temperature range in which theoscillator strength and linewidth of APþW enable a reliable estimate.We observe that the g-factor decreases by a factor ~5 when thetemperature increases from 4 to 39 K. We assume that theinteraction-induced enhancement of the attractive polaron g-factor is proportional to the magnetic susceptibility of thecorrelated states (e.g., χ∝ g) and observe that the decrease of g-factor with increasing temperature follows a Curie–Weiss lawχ−1∝ T− θ (red solid line in Fig. 4e), with T being the temperatureand θ the Weiss constant. From the fit in Fig. 4e we estimate aWeiss constant of θ=−4.6 ± 0.9 K, which suggests an antiferro-magnetic behaviour of the interactions between the localised holemoments for ν=−1. Supplementary Fig. 11 shows the tempera-ture dependence of the APþW g-factor for a range of hole fillingfactors from ν=−0.7 to ν=−1.37. The Weiss constants extractedfrom the Curie–Weiss fits are negative for all the explored holefilling factors, suggesting an antiferromagnetic phase for allcorrelated hole states. We note we observe no magnetic hysteresisin the Zeeman splitting at ν=−1 when the magnetic field isswept from negative to positive values followed by a subsequentpositive to negative sweep (see Supplementary Fig. 7). In contrastto the large attractive polaron g-factor enhancement observedunder hole doping, we only observe a modest g-factor enhance-ment in the electron doping regime (see Supplementary Fig. 8).DISCUSSIONThe extraordinary g-factors observed under hole doping can beunderstood by considering the effect of a magnetic field on alocalised hole in the triangular moiré superlattice. As a result ofexchange interactions with other holes in its environment, such ahole experiences an effective magnetic field which is the sum ofthe externally applied field and the field induced by the otherholes which in turn is proportional to the magnetisation M of thelocalised hole gas (i.e., ∝ λXM, with λX being a coupling constant).To calculate the induced field for a given fractional filling, we firstdetermine the configuration of localised carriers that minimises theelectrostatic repulsion energy using a simulated annealing techni-que (see Supplementary text for details). To describe the spinresponse of this arrangement of charges, we consider a HeisenbergHamiltonian with distance-dependent antiferromagnetic isotropicexchange interactions JðrÞ ¼ J0 expð�r=r0Þ with J0 denoting themagnitude of the exchange coupling at the characteristic lengthscale r0. For this Hamiltonian, the induced magnetic field and thecorresponding g-factor enhancement, g*/g, of a localised hole arecalculated within mean-field theory (see Supplementary text for adetailed description). To obtain the effective g-factor of theattractive exciton-polaron which is probed in our experiments, weassume that its g-factor enhancement due to exchange interactionswith localised holes is the same as that of a single hole, but that the‘non-enhanced’ g-factor g can be different. The experimental valueof this non-enhanced g is unknown since the g-factors of exciton-polarons are dependent on paramagnetic interactions and phase-space filling effects as carrier concentration is changed, even formonolayer TMDs6. Therefore, we treat g as an adjustable parameterchoosing its value such that the calculated and experimentallymeasured g-factors agree at ν=−1.Figure 4f shows that the filling dependence of the calculated g-factor is in good qualitative agreement with the experimentalresults. Specifically, it reaches a maximum at ν=−1, where theaverage number of occupied moiré sites around the localised holeis largest and the strong exchange interactions betweenneighbouring spins give rise to a large effective magnetic field.The model also captures the plateau-like feature between ν=−1/3 and −2/3. In contrast to the experimental findings, however, thecalculated g-factor is symmetric around ν=−1. Potential reasonsfor this discrepancy include (i) band structure effects and (ii) thedoping-induced reduction of frustration. Regarding (i), Tang et al.pointed out that the maximum g-factor occurs at a filling factorthat corresponds to a van Hove singularity of the density ofstates17. Regarding (ii), Zhang et al. carried out exact diagonalisa-tion studies of a triangular t-J model and found that at finitetemperatures the maximum spin susceptibility occurs at a holefilling higher than ν=−116. This is in agreement with a study byKoretsune et al. which employs a high-temperature expansion ofthe spin response function54. The increase in the spin suscept-ibility was explained in the work by the “release” of frustration bydoping. Further theoretical work is required to fully understandthe detailed behaviour of the g-factor.Finally, we estimate U/t in our device. The antiferromagneticcoupling between neighbouring spins due to the kinetic exchangemechanism can be estimated as J ≈− t2/U, where t is the hoppingamplitude between neighbouring moiré lattice sites. Using thevalue of θ at ν=−1 we estimate J ≈−0.4 meV. By combining Jwith the estimated melting temperature of the correlated state atν=−1 (~55 K) we obtain U/t ≈ 3.5 ± 0.4. This experimental valueagrees well with predicted values for MoSe2/WSe2 heterostruc-tures with stacking angles ~3° and ~57°10.Our results illustrate the properties of exciton-polarons in thepresence of correlated states in moiré heterostructures. Using thechanges in energy, oscillator strength, and linewidth of intralayerexcitons dressed by itinerant carriers occupying narrow electronicmoiré bands in a MoSe2/WSe2 hetero-bilayer, we observe theformation of correlated electron and hole states at a multitude offractional fillings of the moiré lattice. Upon hole doping, the WSe2attractive polaron transfers oscillator strength back to therepulsive polaron branch at 1 carrier per site, demonstrating thereduced screening of the exciton by the free charges in thepresence of the insulating state. In addition, we observe themagnetic interactions within the correlated hole states via boththe attractive and repulsive WSe2 exciton-polarons, which exhibitenhanced Zeeman splittings due to exchange interactions withthe moiré pinned carriers. Through temperature dependentmeasurements, the magnetic ordering of the correlated holes isshown to be antiferromagnetic in the range ν=−0.7 to ν=−1.37,and the U/t ratio of our device is estimated to be ~3.5. Furtherinvestigations could exploit the small lattice mismatch betweenMoSe2/WSe2, which enables a highly tunable moiré period, tosimulate condensed matter phase diagrams over a large range ofU/t ratios. Our observation of the formation of flat electronicA.J. Campbell et al.6npj 2D Materials and Applications (2022)    79 Published in partnership with FCT NOVA with the support of E-MRSbands compliments recent reports of moiré trapped interlayerexcitons in MoSe2/WSe2 hetero-bilayers32–38 and highlights theexciting prospects to investigate Fermi–Hubbard andBose–Hubbard physics in this system.METHODSSample fabricationThe sample was fabricated using the all-dry viscoelastic transfertechnique55. Bulk crystal was exfoliated onto PDMS stamps andmonolayer flakes were identified using an optical microscope. Asshown in a previous work for the same sample studied in thiswork, the zigzag edges of the TMD monolayers were identifiedusing optical images in order to achieve a nearly angle-alignedheterostructure (0° or 60°). Further details can be found in34. Theinterface between the two TMD layers is kept pristine (free ofpolymer contamination) by a transfer of one flake from its PDMSstamp onto the other flake on its PDMS stamp before subsequenttransfer onto the bottom hBN layer of the device. The twist angleis estimated to be ~57° from the optical images. Gold contacts tothe graphene layers were fabricated using standard lithographytechniques.Optical measurementsThe sample is held in a closed-cycle cryostat at 4 K unlessotherwise specified (for temperature dependent measurements).For differential reflectivity measurements, light from a powerstabilised tungsten lamp is collected by a multi-mode fibre. Thelight is collimated by a 20× objective and focused on the samplewith an achromatic objective (0.82 numerical aperture). Thereflected light is collected with the same objective and thenfocused onto a single-mode fibre and detected using a liquidnitrogen-cooled CCD spectrometer. The setup is confocal incollection due to the small diameter of the core of the collectionfibre. The incident and collected polarisation of the light iscontrolled using a series of linear polarisers, quarter-wave andhalf-wave plates.Filling factor calibrationThe carrier concentration n in the heterostructure can becalculated using the parallel plate capacitance model, n ¼ ϵϵ0ΔVgd1þϵϵ0ΔVgd2where ϵ is the permittivity of hBN, ΔVg is the voltage offsetbetween both the top and bottom gates and the heterostructuregate, and d1 (d2) is the thickness of the top (bottom) hBN layermeasured to be 17.4 ± 0.2 nm (18.2 ± 0.3 nm) using nullingellipsometry. For a small angular difference between two stackedlayers the moiré periodicity can be estimated using λM ¼ aSeffiffiffiffiffiffiffiffiffiffiδ2þθ2pwhere aSe is the lattice constant of WSe2, δ is the fractional latticemismatch between the two layers and θ is the twist angle inradians. For a triangular moiré pattern, the number of carriersrequired for one hole per site is given by n0 ¼ 2ffiffi3pλ2M. Using thelattice constants of 0.3280 and 0.3288 nm for WSe2 and MoSe2,respectively30 and a permittivity of 3.8 for the hBN56, andΔVg= 1.34 V for ν= ±1 as determined in the main text, wecalculate the twist angle in the main measurement location to be56.9°. This agrees well with the angle of ~57° estimated from theoptical micrograph.DATA AVAILABILITYData described in this paper are available online at https://researchportal.hw.ac.uk/en/persons/brian-d-gerardot/datasets/.CODE AVAILABILITYAll relevant codes are available from the corresponding author on request.Received: 18 May 2022; Accepted: 21 October 2022;REFERENCES1. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett.10, 1271–1275 (2010).2. Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series inmonolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).3. Baugher, B. W. 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Resonating-valence-bond states and ferromagneticcorrelations in the doped triangular Mott insulator. Phys. Rev. Lett. 89, 116401(2002).55. Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materialsby all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).56. Laturia, A., Van de Put, M. L. & Vandenberghe, W. G. Dielectric properties ofhexagonal boron nitride and transition metal dichalcogenides: from monolayerto bulk. npj 2D Mater. Appl. 2, 6 (2018).ACKNOWLEDGEMENTSWe thank Mikhail M. Glazov for fruitful discussions. This work was supported by theEPSRC (grant nos. EP/P029892/1 and EP/L015110/1), the ERC (grant no. 725920) and theEU Horizon 2020 research and innovation program (grant agreement no. 820423). M.B.-G. is supported by a Royal Society University Research Fellowship. B.D.G. is supported bya Wolfson Merit Award from the Royal Society and a Chair in Emerging Technology fromthe Royal Academy of Engineering. V.V. and J.L. acknowledge funding from the EPSRC(grant no. EP/S025324/1). K.W. and T.T. acknowledge support from the ElementalStrategy Initiative conducted by the MEXT, Japan (Grant Number JPMXP0112101001)and JSPS KAKENHI (Grant Numbers 19H05790, 20H00354 and 21H05233).AUTHOR CONTRIBUTIONSB.D.G. conceived and supervised the project. H.B. fabricated the sample. K.W. and T.T.supplied the hBN crystal. A.J.C. performed the experiment assisted by M.B.-G. A.J.C.analysed the data, assisted by M.B.-G. and B.D.G. V.V. and J.L. developed the theoreticalmodel. A.J.C., M.B.-G., V.V., J.L. and B.D.G. cowrote the paper with input from all authors.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-022-00358-w.Correspondence and requests for materials should be addressed to Brian D.Gerardot.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin 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 anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022A.J. Campbell et al.8npj 2D Materials and Applications (2022)    79 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-022-00358-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Exciton-polarons in the presence of strongly correlated electronic states in a MoSe2/WSe2 moir&#x000E9; superlattice Introduction Results Device structure and Fermi-polarons Correlated electronic states Exciton-polaron behaviour at one hole per site Magnetic interactions probed by exciton-polarons Discussion Methods Sample fabrication Optical measurements Filling factor calibration DATA AVAILABILITY References Acknowledgements Author Contributions Competing interests ADDITIONAL INFORMATION