# Fileset

[s41467-024-44739-9.pdf](https://mdr.nims.go.jp/filesets/c6a77ccf-3415-46c5-8f1a-a7228dd39e43/download)

## Creator

Elena Blundo, Federico Tuzi, Salvatore Cianci, Marzia Cuccu, Katarzyna Olkowska-Pucko, Łucja Kipczak, Giorgio Contestabile, Antonio Miriametro, Marco Felici, Giorgio Pettinari, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Adam Babiński, Maciej R. Molas, Antonio Polimeni

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Localisation-to-delocalisation transition of moiré excitons in WSe2/MoSe2 heterostructures](https://mdr.nims.go.jp/datasets/0287a8c3-1dc3-4459-9cf9-af89b7c1439e)

## Fulltext

Localisation-to-delocalisation transition of moiré excitons in WSe2/MoSe2 heterostructuresArticle https://doi.org/10.1038/s41467-024-44739-9Localisation-to-delocalisation transitionof moiré excitons in WSe2/MoSe2heterostructuresElena Blundo 1 , Federico Tuzi1, Salvatore Cianci 1, Marzia Cuccu1,Katarzyna Olkowska-Pucko2, Łucja Kipczak 2, Giorgio Contestabile1,Antonio Miriametro1, Marco Felici 1, Giorgio Pettinari 3, Takashi Taniguchi 4,Kenji Watanabe 5, Adam Babiński2, Maciej R. Molas 2 & Antonio Polimeni1Moiré excitons (MXs) are electron-hole pairs localised by the periodic (moiré)potential forming in two-dimensional heterostructures (HSs). MXs can beexploited, e.g., for creating nanoscale-ordered quantum emitters and achiev-ing or probing strongly correlated electronic phases at relatively high tem-peratures. Here, we studied the exciton properties of WSe2/MoSe2 HSs fromT = 6 K to room temperature using time-resolved and continuous-wave micro-photoluminescence also under a magnetic field. The exciton dynamics andemission lineshape evolutionwith temperature show clear signatures thatMXsde-trap from themoiré potential and turn into free interlayer excitons (IXs) fortemperatures above 100 K. The MX-to-IX transition is also apparent from theexciton magnetic moment reversing its sign when the moiré potential is notcapable of localising excitons at elevated temperatures. Concomitantly, theexciton formation and decay times reduce drastically. Thus, our findingsestablish the conditions for a truly confined nature of the exciton states in amoiré superlattice with increasing temperature and photo-generated carrierdensity.Two-dimensional (2D) heterostructures (HSs) can be formed bystacking two (or more) monolayers (MLs) of different van der Waalscrystals. 2D HSs offer a countless number of combinations thanks tothe nearly arbitrary choice of the chemical composition of the indivi-dual constituents and the control of their relative angular alignmentgiven by the twist angle θ1. Inherent to the stacking process is theformation of a moiré superlattice that superimposes on the topo-graphic and electronic structure of the single MLs. This phenomenonhas been particularly investigated in HSs made of transition metaldichalcogenide (TMD) semiconductors, which feature a sizeable bandgap2–8. The moiré potential can be as deep as 100 meV3,4,7 and canlocalise both intralayer excitons (Xs) residing in theMLs of theHS9 andinterlayer excitons (IXs)3–6 and trions10, in which different charge car-riers reside in the different layers of the HS. Moiré-confined IXs(hereafter, moiré excitons, MXs) are especially interesting as they canbe exploited as nanoscale-ordered arrays of quantum emitters3,11.Furthermore, their space-indirect character endows IXs, and specifi-cally MXs, with long lifetimes4,5 that, in conjunction with the depth ofthe moiré potential, make them suitable for the observation of high-temperature (>100 K) Bose-Einstein condensates, as shown in a WSe2/MoSe2 HS12. The topology of the moiré potential also induces stronglycorrelated electron and exciton states13,14 that led to the observation ofan exciton insulator surviving up to 90 K in aWS2/bilayer-WSe2 HS15. Inaddition, the MXs themselves were employed as a probe of theReceived: 24 April 2023Accepted: 2 January 2024Check for updates1PhysicsDepartment, SapienzaUniversity of Rome, PiazzaleAldoMoro5, 00185Rome, Italy. 2Institute of Experimental Physics, Faculty of Physics, University ofWarsaw, Pasteura 5, 02-093 Warsaw, Poland. 3Institute for Photonics and Nanotechnologies, National Research Council, 00133 Rome, Italy. 4InternationalCenter for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5Research Center for FunctionalMaterials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. e-mail: elena.blundo@uniroma1.it; antonio.polimeni@uniroma1.itNature Communications |         (2024) 15:1057 11234567890():,;1234567890():,;http://orcid.org/0000-0003-0423-4798http://orcid.org/0000-0003-0423-4798http://orcid.org/0000-0003-0423-4798http://orcid.org/0000-0003-0423-4798http://orcid.org/0000-0003-0423-4798http://orcid.org/0000-0003-4020-369Xhttp://orcid.org/0000-0003-4020-369Xhttp://orcid.org/0000-0003-4020-369Xhttp://orcid.org/0000-0003-4020-369Xhttp://orcid.org/0000-0003-4020-369Xhttp://orcid.org/0000-0003-1266-0201http://orcid.org/0000-0003-1266-0201http://orcid.org/0000-0003-1266-0201http://orcid.org/0000-0003-1266-0201http://orcid.org/0000-0003-1266-0201http://orcid.org/0000-0002-0977-2301http://orcid.org/0000-0002-0977-2301http://orcid.org/0000-0002-0977-2301http://orcid.org/0000-0002-0977-2301http://orcid.org/0000-0002-0977-2301http://orcid.org/0000-0003-0187-3770http://orcid.org/0000-0003-0187-3770http://orcid.org/0000-0003-0187-3770http://orcid.org/0000-0003-0187-3770http://orcid.org/0000-0003-0187-3770http://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/0000-0002-5516-9415http://orcid.org/0000-0002-5516-9415http://orcid.org/0000-0002-5516-9415http://orcid.org/0000-0002-5516-9415http://orcid.org/0000-0002-5516-9415http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-44739-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-44739-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-44739-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-44739-9&domain=pdfmailto:elena.blundo@uniroma1.itmailto:antonio.polimeni@uniroma1.itexistence of Mott insulators and Wigner crystals in WSe2/WS2 HSs atrelatively large temperatures16,17.For boson condensates and highly correlated charge systems, aswell as quantum photonics applications, the thermal stability of themoiré-induced confinement of the excitons plays a crucial role and afundamental question arises: Up to what extent can MXs be regardedas truly moiré-confined?In this work, we addressed this important aspect by investigatingthe effects of the lattice temperature and of the photo-generatedexciton density on the localisation of MXs, as resulting from their: (i)luminescence intensity and lineshape, (ii) temporal dynamics, (iii)magneticmoments. Specifically, we studied the emission properties oftwo exemplary WSe2/MoSe2 HSs by continuous-wave (cw) micro-photoluminescence (μ-PL) measurements, also under magnetic field,andby time-resolved (tr)μ-PL. Low-temperature (T =6K) tr-μ-PL showsthat the MX signal is characterised by different spectral components,with formation and recombination dynamics indicative of the pre-sence of a multi-level electronic potential4,6,18,19, as well as of MXslocalised at minima with different atomic registry as apparent fromtheir gyromagnetic factor20. The temperature evolution of the HSemission properties presents clear signatures of IX de-trapping fromthe moiré potential at Ts above 100 K and the ensuing spectral pre-dominance of free IXs at higher temperatures. Concomitantly,Zeeman-splitting measurements reveal an unexpected sign reversal ofthe exciton magnetic moment taking place with the temperature-induced MX transition to a free IX regime. This transition is paralleledby a strong reduction of both the emission rise and decay times, whichmirrors the faster formation and recombination dynamics, respec-tively, of the free IXs.ResultsMoiré exciton dynamics at low temperatureThe two investigated WSe2/MoSe2 HSs were fabricated by depositingthe first ML on the substrate (directly on a SiO2/Si substrate in one HS,and on a h-BN flake deposited on a SiO2/Si substrate in the other HS)and by then depositing the second ML on top. The HSs were thencapped with a thin h-BN layer; see Methods for other details. A com-parison of the PL properties before and after the h-BN capping (seeSupplementary Note 1) did not show sizeable variations of the HSoptical properties. Both HSs are characterised by a rather homo-geneous PL signal, both in terms of lineshape and intensity, see Sup-plementary Note 1. The twist angle between the MoSe2 and WSe2 MLswas estimated to be θ =0.46° in the first HS (hereafter HS1) and 0.74° inthe second (hereafterHS2), as detailed next. Such angles are close to0°and correspond to the configuration referred to as R-type (while HSswith θ close to 60° are named H-type). We will discuss mainly theresults obtained on HS1 with θ =0.46° and refer to HS2 (θ =0.74°) as acomparative case. Figure 1a shows an optical microscope image of HS1alongwith its sketch. Cw and tr-μ-PLmeasurementswere carried out atvariable laser excitation power Pexc and temperature using a confocalmicroscope setup. For μ-PL excitation (μ-PLE) measurements, weemployed the same setup using a wavelength-tunable laser as excita-tion source. Magneto-μ-PL measurements were performed at variabletemperature in a superconducting magnet up to 16 T, with the fieldperpendicular to the HS plane. Further details are reported in theMethods section.Figure 1 b shows the T = 6 K μ-PL spectrum (wine line) of HS1. Twobands are observed. The one peaked at 1.6 eV, labelled X, is due to agroup of localised (intralayer) exciton states originating from theMoSe2 ML with a small contribution from similar transitions in theWSe2 ML on the higher energy side of the band. The band centredat ≈ 1.36 eV, labelled MX, is due to MX recombination (with the elec-tron and hole being confined in the MoSe2 and WSe2 layer, respec-tively), as also reported in other works4,6,7,13. The blue line in Fig. 1b isthe μ-PLE spectrum obtained by monitoring the MX signal whilescanning the excitation laser wavelength. The MX signal shows aresonant contribution from the MoSe2 and WSe2 ML exciton states oftheHS, thus confirming the interlayer nature of theMXband.We pointout that, at variance with ref. 21, no MX-related absorption feature isinstead observed in the μ-PLE data due to the much smaller oscillatorstrength of the MX absorption. Figure 1c displays the MX spectrumrecorded at T = 6 K with Pexc = 5 nW (corresponding to 0.64 W/cm2).The spectrum can be deconvolved into several Gaussian components.The latter are equally spaced by (12.8 ± 1.3) meV, reflecting the quan-tised states of the moiré potential4,6,18,19. The Gaussian lineshape mapsonto the ensemble of MXs confined in randomly distributed moiréminima, due to the inevitable imperfections present in the HS plane.The very narrow lines superimposed on the multi-Gaussian lineshapeof the MX band likely correspond to single MXs confined in just onemoiré minimum7,22. The centroid energy of the MX band (1.357 eV)indicates that the investigated HS is R-type (θ ≈0°)4–6,13,23 with RXh localatomic registry3,7. In fact, for H-type HSs (θ ≈ 60°) the MX1.2 1.4 1.6 1.8 2.0 2.2 2.4XWSe2B6 KXMoSe2BXWSe2ANorm. PLE Int.Norm. PL Int.Energy (eV)MXXXMoSe2A1.32 1.35 1.38 1.4101.tnILP.mroNEnergy (eV)MXPexc = 5 nW6 K1.2 1.4 1.6 1.8MXX.tnILP.mroNEnergy (eV)x5IXcbMoSe 2WSe2hBN296 K100 K6 KdMoSe2WSe23 µmaFig. 1 | Optical properties of the WSe2/MoSe2 R-type HS1. a Optical micro-graph(left) and sketch (right) of HS1. b Low-T μ-PL and μ-PLE spectra of the HS, left andright axis, respectively. In the μ-PL spectrum (Pexc = 2 μW), X indicates the intralayerexciton recombination from localised states of the MoSe2 and WSe2 monolayers(lower- and higher-energy side, respectively). MX is the moiré exciton band. In theμ-PLE spectrum, four exciton resonances are observed. These resonances can beattributed to the A and B excitons (where the hole sits in the upper, A, and lower, B,spin-split valence band maximum at K, and the electron sits in the spin-split con-duction band minimum at K with same spin) of the MoSe2 and WSe2 layers. c μ-PLspectrumof theMXband acquiredwith very low laser power excitation (5 nW). Thespectrum can be reproduced byfiveGaussian functions (azure: single components;red line: total fit) that are spaced by (12.8 ± 1.3) meV. The very narrow lines thatmake up the broader Gaussian peaks correspond to single MXs recombining inmoiré minima. d μ-PL spectra recorded at different temperatures (and Pexc = 20μW). Themoiré/interlayer (MX/IX) exciton band is visible up to room temperature.X indicates the exciton band related to the single layer MoSe2 and WSe2 con-stituents of the HS.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 2recombination is centred at a higher energy —by about 40meV3,5,7,10,11,22,24–31— due to the shallower moiré potential for H-typeHSs with respect to R-type HSs7, see also Supplementary Note 1. Fromthe spacing between the MX states, as detailed in SupplementaryNote 2, we estimate a moiré superlattice period am of about 40 nm,which corresponds to θ= 0:46+0:05�0:04� ��10. Second harmonic generation(SHG) measurements confirm that estimation and provideθ =0. 1° ± 1. 5°, as reported in Supplementary Note 2. Given the largeuncertainty of the SHG data, we will assign to this HS the twist angleθ =0.46°, determined by the energy spacing of the moiré potentialresonances. From the HS period, we deduce that about 600 moiréminima are probed within the laser spot (radius equal to ≈ 500 nm).The excellent alignment leads to a sizeable signal of the HS IXs up toroom temperature, as shown in Fig. 1d. Note that the recombinationfrom the HS is indicated as MX at T = 6 K and as IX at T = 296 K,qualitatively hinting at a temperature-induced transition in the char-acter of the exciton. We investigated such transition by studying thetemporal evolution of the HS exciton signal, its dependence on thenumber of photo-generated carriers and by determining the excitongyromagnetic factor at different temperatures and photo-generatedcarrier densities.We first describe the tr-μ-PL results at T = 10 K, where most of theHS emission is due to the MX recombination in the RXh minima of themoiré potential3,7,32. Figure 2a shows the μ-PL spectrum of HS1 recor-ded at a power 200 times larger (Pexc=1 μW, i.e., 128 W/cm2) than inFig. 1c. This results in a non negligible contribution from a componentcentred at about 1.4 eV, which can be assigned (totally or partly) tomoiré excitons confined in the Rhh minima (as confirmed later). Indeed,the energy distance between this contribution and the lowest energycomponent (1.335 eV) of the HS emission at very low power density(see Fig. 1c) is about 65 meV. This value falls within the range of theband gap energy difference between the RXh and Rhh moiré evaluated inrefs. 3 (40 meV) and ref. 4 (70 meV). Three different spectral windowsare highlighted in Fig. 2a. For each of them, panel b and panel c displaythe correspondingμ-PL signal timeevolution fromthe laser pulseup to800 ns and in the time interval (0-1) ns, respectively (see also Sup-plementary Note 3, where the same data are compared to the laserpulse setting the resolution limit of our optical system). In the formerrange, the decay part of the data can be fitted byIdecayðtÞ=X3n= 1Ad,n � exp � t � t0τd,n� �, ð1Þwhere t0 is a reference time (from which the decay starts), and τd,n isthe decay time relative to the n-th component, whose weight is givenbywd,n =Ad,n/(Ad,1 +Ad,2 +Ad,3). The fitting curves are superimposed tothe data as solid lines in Fig. 2b and the τd,n values are displayed in thesame figure (the complete set of the fitting parameters, includingwd,n,can be found in Supplementary Note 3). The presence of differentcomponents (1, 2 and 3) indicates that different intermediate andintercommunicating levels are involved in the MX decay, possiblyincluding dark exciton states6,19. In any case, τd,n gets shorter for thehigher energy ranges considered; this is particularly true for the 1.4 eVcomponent, similar to recent results4,6,13,19. This finding supports thehypothesis that the structuredMXemission corresponds to a ladder ofdiscrete states arising from the moiré potential4,6,19. Indeed, higher-energy states may decay faster (due to the tendency of photo-generated carriers to occupy lower-lying states), with the ground statehaving the longest lifetime of several tens of ns, consistent with thespatially and k-space indirect characteristics of the MX transition. Werecall that in TMDMLs the intralayer exciton X is known to have muchshorter radiative decay times, on the order of a few ps to a few of tensof ps33,34, in contrast with MX. A similar behaviour is found in thesecond WSe2/MoSe2 HS investigated, or HS2, with energy spacingbetween the moiré resonances equal to (20.3 ± 3.4) meV and twistangle θ= ð0:74+0:16�0:11 Þ�10. The data for HS2 can be found in Supplemen-tary Note 2. As shown there, it is worth remarking that for HS2,featuring greater θ than HS1, longer decay times τd,n are found. This isin accordance with the larger momentum mismatch between thecharge pair of the moiré exciton in HS2 and agrees with the resultspresented in ref. 6.The different states of the moiré potential also exhibit a differentformation dynamics. Figure 2c shows the time evolution of the MXsignal in HS1 up to 1 ns after the laser pulse excitation. In this case, thedata are reproduced byIriseðtÞ= � Ar � exp � t � t0τr� �+ IdecayðtÞ ð2Þwhere τr is the luminescence rise time and Idecay represents the decaypart of the data. By fitting the decay part first, the data in the (0-1) nstime interval can be reproduced by Eq. 2, with only Ar and τr as fittingparameters. The τr values are displayed in panel c of Fig. 2 (the datacorresponding to the high-energy range, shown in the right-mostpanel, are close to the resolution limit and could not be fitted reliably).The data indicate that the highest-energy excited state of the moiré1.2 1.3 1.4 1.5 1.6 1.7X.tnI.mroNEnergy (eV)10 KMX10 100t (ns)d,2 = (1.03  0.01) nsd,3 = (13.5  0.1) nsd,1 < 0.23 ns10 100t (ns)d,2 = (15.2  0.2) nsd,3 = (77.0  0.3) nsd,1 = (1.59  0.01) ns10 10001d,2 = (14.0  0.6) nsd,3 = (51  4) nsd,1 = (2.27  0.09) ns.tnI.mroNt (ns)0.0 0.5 1.0t (ns)0.0 0.5r = (155  6) pst (ns)0.0 0.50.11r = (131  12) ps.tnI.mroNt (ns)bca Fig. 2 | Decay and rise of themoiré exciton band. a T = 10 K and Pexc = 1 μW μ-PLspectrum of HS1. MX indicates the moiré-trapped interlayer exciton, and X indi-cates the intralayer exciton recombination. Three different spectral regions arehighlighted on theMX band. On each of these regions, the μ-PL time evolution wasrecorded.bTime-evolution of the μ-PL signal recorded in theΔt = 0-800 ns intervalfrom the laser pulse on the three spectral regions highlighted in panel a (note alsothe colour code). The decay time τd,n values obtained by fitting the data via Eq. (1)(see solid lines) are displayed. c The same as b for Δt = 0–1.0 ns. The rise time τrvalues displayed in the panels are those used to reproduce the datawith Eq. (2) (seesolid lines). The data in the right-most panel could not be fitted reliably.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 3potential (together with the likely population of moiré excitons in therelative minimum at the Rhh registry) is populated faster (<100 ps),similar to what reported in ref. 19. Instead, the population of thelowest-energy state requires more time to reach its quasi-equilibriumoccupancy because of the extra contribution from higher-energylevels in addition to the direct excitation. Power-dependent tr-μ-PLmeasurements on both HSs, reported in Supplementary Note 4 and 5,showaprogressive shortening of the timedecay of theMXband as Pexcincreases. This is a likely consequence of exciton-exciton interactions,that tend to diminish the exciton lifetime35,36.Exciton recombination vs carrier density and temperatureThe X andMX recombination bands also exhibit quite distinct spectralbehaviours when the density of photo-generated excitons and thelattice temperature are increased. Figure 3a shows the cw μ-PL spectraof HS1 at T = 6 K for Pexc ranging from44 nW (i.e. 5.6W/cm2) to 100 μW(i.e. 1.3 ⋅ 104 W/cm2). TheMX band broadens and its centroid blueshiftswith increasing Pexc, likely as a consequence of the dipole-dipoleinteraction between MXs5,13,22,26,37,38. Following Ref. 13, we determinethat in the Pexc = (0.044-100) μWrange the density of photo-generatedelectron-hole pairs within the HS varies from ne-h = 1.1 ⋅ 1011 cm−2 to2.3 ⋅ 1013 cm−2 (see Supplementary Note 4). We note that the highestne-h achieved by us is smaller than the value necessary to observe anoptically induced Mott transition from IXs to spatially separatedelectron and hole gases13. Nevertheless, from the previously estimatedperiodof themoiré potentialam=40nm, the correspondingdensity ofmoiré minima is equal to 7.2 ⋅ 1010 cm−2 and a sizeable exciton-excitoninteraction is possible thus explaining the decrease in the emissiondecay time reported in Supplementary Note 4 and 5 as well as the MXband blueshift with Pexc13,22,38. Recent simulations based on the Green’sfunction formalism38 showed that exciton densities around 1011 − 1012cm–2 trigger intercell hopping and excitondelocalisation effects,whichreflect in a blue-shift and broadening of the moiré emission band. Inthe present case, we observe such effects starting from Pexc = 4.4 μW(see Fig. 3b), corresponding to ne-h ≈ 4 ⋅ 1012 cm–2, in good agreementwith ref. 38. On the other hand, the X band, which, as we recall, com-prises the MoSe2 and WSe2 intralayer excitons, does not changeappreciably its centroid. It instead gains significant spectral weightcompared to MX, which originates from recombination centres withfinite spatial density. Figure 3b shows the dependence of the inte-grated intensity Iof theHS exciton andXbands as a functionof Pexc forT = 6 K and T = 90 K. At 90 K, the HS exciton band is labelled MX-IX toindicate the contribution from IXs (or de-trapped MXs) occurring athigh Pexc and increasing temperature, as we are going to demonstrate.The integrated intensity was obtained by performing integrals oversuitable energy ranges (it cannot be reliably obtained by fitting thedata since the shape of the PL bands changes with power, comprisingthe appearance of narrow lines at low power). The data were fitted by:I =A � P αexc, ð3Þwhere A is a scaling constant. At T = 6 K, α is equal to 0.55 ±0.02 for MXand 0.89±0.02 for X. The smaller α found at low T for the MX signalfrom theHS (as opposed to that from intralayer excitons X in theMLs) iscompatible with the finite number of energy states available for excitonstrapped in the quantised levels of the moiré potential minima. Fur-thermore, the localised nature of MXs can lead to enhanced exciton-exciton interactions that act as a probable source of signal loss. Instead,the nearly linear behaviour of the X emission intensity is consistent withthe virtually unlimited number of intralayer excitons that can be photo-generated. Interestingly, Fig. 3b shows that the nearly linear dependenceof the X band on Pexc is maintained also at T = 90 K, while a majorvariation is found for the MX-IX band that can be explained byconsidering an increasingly higher spectral contribution of free IXs athigher T. As a matter of fact, the α value of MX-IX becomesapproximately equal to 1 at 90 K.102 103 104 105103104105106107 MX-IX, 90 K X, 90 K)stinu.bra(.tnILPPexc (nW) MX, 6 K X, 6 K1.2 1.3 1.4 1.5 1.6 1.7 1.8X6 K.tnILP.mroNEnergy (eV)MX0 50 100 150 200 250 3000.40.60.81.01.2 XTemperature (K)MX-IX1.20 1.25 1.30 1.35 1.40 1.45296 K.tnILP.mroNEnergy (eV)IXMX90 K.tnILP.mroNIX100 µW44 µW20 µW10 µW4.4 µW2.0 µW1.0 µW440 nW200 nW100 nW44 nW100 µW44 µW20 µW10 µW4.4 µW2.0 µW1.0 µW100 µW44 µW10 µW2.0 µW440 nW100 nW44 nWa bcdePexc =Pexc =Pexc =Fig. 3 | Photo-generated carrier density and temperature dependence of theexciton bands. a T = 6 K μ-PL spectra of HS1 recorded for different laser excitationpower values. MX indicates the moiré exciton band and X the intralayer excitonrecombination in the MoSe2 and WSe2 layers (lower- and higher-energy side,respectively). b PL integrated intensity dependence on the laser power Pexc forthe MX or MX-IX bands (azure symbols) and for the X band (light orange symbols)atT= 6K (full symbols) andT= 90K (open symbols), respectively. Solid anddashedlines are fits to the datawith Eq. (3) for T= 6K and90K, respectively. AtT=6K, theαcoefficient values are 0.55 ± 0.02 and 0.89± 0.02 for MX and X, respectively.AtT =90K, theα coefficient values are0.99 ± 0.02 and0.97 ± 0.03 forMX-IX andX,respectively. c Temperature variation of the α coefficient for the MX-IX and Xbands. In the former case, a clear transition from a sublinear to a linear behaviour isfound and ascribed to the transition from a moiré localisation regime to a freeinterlayer exciton one (hence the mixed label MX-IX). d T = 90 K μ-PL spectra fordifferent laser excitation powers in the energy region where the MX and IXrecombinations canbe simultaneously observed. IX takesoverMXupon increase ofthe photo-generated carrier density. e Same as d for T = 296 K, where only the IXtransition is observable.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 4Puzzled by this finding, we investigated the dependencies on Pexcof the integrated area of the MX-IX and X bands at different tem-peratures. The full set of power-dependent data can be found inSupplementary Note 6. Figure 3c summarises the variation of thecoefficient α with T, as obtained from Eq. (3). For the X band, a nearlylinear behaviour is observed at all temperatures. Instead, for theMX-IXband, α increases progressively from 0.55 to about 1 as T is increasedfrom 5 K to 120 K, with a linear behaviour observed at higher tem-peratures, up to room temperature. These results suggest a qualitativechange in the nature of the exciton-related bands in the HS at about120 K. A similarly comprehensive study was performed also for HS2,which has a larger twist angle of 0.74°. The results are shown in Sup-plementary Note 7. As for HS1, the X band shows a linear behavior (α =1) all over the temperature range. Although also inHS2 the coefficientαfor the MX-IX band exhibits a progressive increase from 0.5 to 1 (seeSupplementary Note 7), the plateau-value of 1 is reached at a tem-perature of about 100 K (lower than the 120 K value observed in HS1;see Fig. 3c) consistently with the shallower moiré potential at greatertwist angles39. On the one hand, these results strengthen the picturedescribed so far. On theother hand, they point to the crucial roleof thetwist angle in determining the thermal stability of moiré excitons andassociated phenomena in moiré superlattices.Figures 3d and e display a series of spectra recorded on HS1 atdifferent Pexc for T = 90 K and T = 296 K, respectively. In the first case,the lineshape of the MX band changes significantly as the density ofphotoexcited carriers increases. Indeed, we notice a considerablespectral weight transfer by about 100 meV from the structured bandaround 1.27 eV (at the lowest Pexc) to the single component peaked atabout 1.37 eV (at the highest Pexc). We ascribe this change to thesaturation of moiré-localised excitons in favour of moiré-de-trappedIXs (the related 100 meV band shift is indeed close to the moirépotential depth for R-type WSe2/MoSe2 HS3,4,7). This behaviour is notevident at the lowestT values (see, e.g., Fig. 3a), whenMXs are frozen intheir potential minima. Eventually, for T > 200 K, almost all MXs areionised and only IXs are observed, as shown in Fig. 3e, clearlydemonstrating the absence of a sizeable lineshape variation with Pexc.See Supplementary Note 7 for similar data recorded on HS2 (havinggreater θ).Moiré exciton de-trapping, magnetic moment and dynamicsvs TThe moiré exciton de-trapping is even more evident in Fig. 4a, whichshows the μ-PL spectra of HS1 for different T values and Pexc = 10 μW;similar studies for higher and lower Pexc are shown in SupplementaryNote 8. From T = 6 K to T = 120 K, the HS signal is dominated by the MXband, which undergoes a redistribution of the carrier populationbetween the different states of the moiré potential. Starting from T =120 K, a high-energy component due to IXs appears and becomesincreasingly important relative to the MX band, until the latter vanishesat about 220 K. Finally, at room temperature only IXs are visible. AtT≈ 160 K, the two contributions coexist so that their energy differencecan be estimated. The obtained value, equal to about 90 meV, fits wellwith the exciton barrier height of the moiré potential in R-typeWSe2/MoSe2 HSs3,4,7, where only the exciton singlet state is opticallypermitted (the MX-IX energy distance becomes 75 meV in the HS2 withgreater θ). Although qualitatively, also this observation agrees with theexpected shallower moiré potential depth for greater twist angles39; seeSupplementary Notes 6 and 7). In contrast, the exciton ground state inH-type HSs is in a triplet configuration, with the singlet state having anenergy 25 meV higher5,22,27. Also, we exclude that the two transitionscoexisting at intermediate T are ascribable to KCB-KVB (CB and VB standfor conduction and valence band, respectively) and ΛCB-KVB IXtransitions21, which differ by 55 meV21.It is worth mentioning that different results were reported in theliterature. In ref. 28, the MX de-trapping was observed by monitoringthe PL intensity and lifetime of WSe2/MoSe2 HSs with a transitiontemperature < 50 K that is in contrast with our results. On the otherhand, exciton diffusivity measurements7 showed the absence of MXde-trapping in a WSe2/MoSe2 HS with nearly perfect lattice alignment(θ = 0.15°), while a clear de-trapping was visible for θ > 2°7.In any case, the here observed temperature-induced change in thenature of the exciton in the HS should be reflected in the electronicproperties of the levels involved in the excitonic transition. In thisrespect, the exciton magnetic moment and the associated gyromag-netic factor gexc—embedding the spin, orbital and valley properties ofthe bands— turned out to be an extremely sensitive parameter of theelectronic structure of nanostructures40 and of 2D crystals41–44 andtheir HSs5,10,20,22–24,26,45–48. In WSe2/MoSe2 HSs, the lowest-energy exci-ton state is in a spin-singlet configuration for R-type HSs and in a spin-triplet configuration for H-type HSs49. The spin-singlet and spin-tripletexcitons feature a gexc value with a positive (≈+ 7) and a negative (≈−15)sign, respectively, the exact value depending on the specificsample5,20,22,24,25,46–48. Our HS is R-type, as discussed before, and there-fore we expect a positive gexc value. Figure 4b shows the magneticfield, B, dependent μ-PL spectra of HS1 in the HS exciton region atT = 10 K and Pexc = 10 nW (corresponding to ne-h = 2.0 ⋅ 1010 cm-2, seeSupplementary Note 4). For each field, the opposite circular polarisa-tions σ± were recorded simultaneously on two different regions of theCCD detector, see Methods. Figure 4b shows the σ+ and σ−-polarisedμ-PL spectra that exhibit several narrow lines due to different MXs.They all undergo a Zeeman splitting (ZS) given byZSðBÞ= Eσ + � Eσ�= gexc � μBB: ð4ÞEσ ±are the peak energies of components with opposite helicity σ+ andσ−, and μB is the Bohr magneton. The positive (negative) energy shiftwith B of the σ+ (σ−) component of the lines displayed in Fig. 4b indi-cates that gexc > 0 for the individual MXs. Then, magneto-μ-PL mea-surementswere performed also atT = 160K and Pexc=75 μW,where theHS exciton band is instead dominated by free IXs. Figure 4c shows theσ+ and σ− components of the IX spectra at different magnetic fields.Remarkably, the twocomponents shift withB accordingly to a negativeZS, i.e. opposite to that found atT = 10K for theMX lines (for IXs, the σ+red component is at lower energy than the σ− blue one). Figure 4dshows the ZS field dependence for the MX lines at 10 K and for the IXband at 160K, bothfitted by Eq. (4). The resulting gexc for the (trapped)MXs and (free) IXs are gexc,MX = + 6.73 ± 0.10 (this is an average valueover the 5 measured MXs) and gexc,IX = − 4.64 ± 0.10, respectively. Theformer is in close agreement with previous experimental5,23,46,47 andtheoretical20 results found for MXs in R-type WSe2/MoSe2 HSs. Asreported in Supplementary Note 9, we performed similar measure-ments and found similar results for HS2. For HS1, we also derived theZS of the five gaussians into which the moiré exciton band can bedeconvolved at low T and Pexc, as shown in Fig. 1c. As discussed inSupplementary Note 10, in comparison to the single MX lines ofFig. 4d, a smaller ZS is found for the Gaussian components, resulting inan average gexc = + 4.43 ± 0.89. The smaller gexc for the Gaussiancomponents might be caused by exciton-exciton interactions. In fact,the Gaussian lineshape could be the consequence not only of adistribution of an ensemble of singlemoiré lines, but also of an excitoninteraction-induced broadening of the themoiré emission itself. As forthe results at 160 K, to our knowledge there are no previous ZSmeasurements on HSs at high temperatures. We found a similarnegative gexc,IX value of about −5 also at T = 210 K and 100 K, asdescribed in Supplementary Note 11. The origin of the sign reversal ofgexc,IX must be then ascribed to the avoided effect of the moirépotential caused by the temperature-induced de-trapping of the MXs.As a matter of fact, we can estimate gexc,IX considering the separatecontribution of electrons and holes to the IX gyromagnetic factor, asusually done for excitons in semiconductors. Following an analogousArticle https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 5procedure to that employed in ref. 43 for strainedWS2MLs, for this HSwe usegexc,IX = 2 LCBðMoSe2Þ � LVBðWSe2Þ� �, ð5Þwhere the first and second terms are the expectation values of theorbital angularmomentumof theMoSe2 CB andWSe2 VB, respectively(the spin contribution cancels out because the band extrema involvedin the free IX transition have the same spin for R-typeHSs). As reportedin ref. 20, LCB(MoSe2) = 1.78 and LVB(WSe2) = 4.00 and from Eq. (5) weobtain gexc,IX = − 4.44 in very good agreement with the value we foundexperimentally for the free IX transition shown in Fig. 4d. To thisregard, it is relevant to add that a positive gexc is found for theMXbandalso at T = 80 K, as shown by μ-PL measurements on HS1 performed atB = 16 T and sufficiently low laser power (as low as 10nW) to emphasizethe contribution of theMX band at high T; see Supplementary Note 11.Interestingly, the suppression of the moiré potential in an R-typeWSe2/MoSe2 HS caused by inserting a h-BN layer between the con-stituent MLs leads to magneto-PL results similar to ours50. Indeed, inRef. 50 the spatial decoupling between the HS singleMLs determines asign reversal and a decrease of the gexc modulus analogous to thatfound here by increasing the lattice temperature.TheexcitonZS inWSe2/MoSe2HSsmaydependon the local atomicregistry, too20. Figure 5a shows a series of μ-PL spectra recorded on HS1with opposite circular polarisation (σ+ and σ−) at different magneticfields for T = 6 K and low laser excitation power Pexc = 0.2 μW. Severalnarrow lines due to moiré confined excitons can be observed, super-imposed on a continuum background. Like in Fig. 4b, the MX linesexhibit a positive Zeeman splitting with average gexc,MX = + 6.78 ±0.11(panel c of the figure). Figure 5b shows the same study of panel arecorded on the same point of the HS but with a Pexc value increased byabout a factor of 400. The narrow lines associated to moiré confinedexcitons merge forming a single band, whose maximum shows a blue-shift ofmore than 30meVwith respect to the low-energy side of theMXband at lower Pexc. Quite interestingly and unexpectedly, under thesecircumstances, theZS value reverses its sign resulting in a gyromagneticfactor gexc = −6.93, as shown in Fig. 5c. We also performed a PL study atfixedB = 16 T by varying Pexc overmore than three orders ofmagnitude.The data are described in Supplementary Note 12 for both HS1 and HS2and show how when increasing the density of excitons the initiallypositive ZS due to the singlemoiré excitons eventually goes negative asthe MX component broadens and blue-shifts. To interpret these resultswe note that: (i) the Pexc-induced blue-shift is significantly smaller than100meV (i.e., themoiré potential depth3,4,7) and (ii) themodulus of gexc(∣−6.93∣) found at high Pexc and T = 10 K is larger than that (∣ −4.64∣)0 3 6 9 12 15-4048121620SZ-SZ0(meV)B (T)1.35 1.36 1.37 1.38ytisnetnI.mroNEnergy (eV)ytisnetnI.mroN1.32 1.35 1.38 1.41ytisnetnI.mroNEnergy (eV)10 K, Pexc = 10 nW 160 K, Pexc = 75 µWIXb cdPexc = 10 µWaT (K)29628026024022020018016014012010090 80706050403020106IXIXMXMX12 T9 T0 T6 T3 T12 T0 T12 T0 TM5, 10 KM4, 10 KM3, 10 KM2, 10 KM1, 10 KIX, 160 KFig. 4 | Exciton magnetic moment sign reversal. a μ-PL spectra of HS1 recordedfor different temperatures and fixed Pexc = 10 μW focused via a 20× objective(NA=0.4). MX indicates the moiré exciton band and IX the free interlayer excitonrecombination. Note the major spectral transfer from MXs to IXs for T > 120 K.b Magneto-μ-PL spectra from 0 to 12 T (in steps of 1 T) of the MX band at T = 10 Kand Pexc = 10 nW (focused via a 100×objectivewithNA=0.82). The upper and lowerpanels correspond to the σ+ (red) and σ− (blue) circular polarisations, respectively.The data are stacked by y-offset. The positive and negative slopes of the σ+ and σ−polarisations with the field indicate a positive gyromagnetic factor. The arrowsdenote some specific MX lines. c Magneto- μ-PL spectra at T = 160 K and Pexc =75 μW of the free IX band for the σ + and σ − polarisations. A negative Zeemansplitting (ZS) can be observed, with the σ + and σ − spectra being at lower and higherenergy, respectively. d ZS of the fivemoiré-localised excitonsM1 toM5 highlightedby the arrows in panel b (M1 is the lowest energy one, M5 the highest) and of thefree IX exciton vsmagnetic fieldmeasured in panel c, resulting in the gyromagneticfactors displayed in the figure. The ZS data of the M2 to M5 lines were shifted byy-offset for ease of visualisation. Error bars are within the symbol size.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 6measured at high T (see Fig. 4c, d), where moiré de-trapped (and thusfree) excitons (IXs) dominate the emission spectrum.Thus,weconcludethat the main contribution to the MX band in Fig. 5b (high Pexc) comesfrom moiré excitons with Rhh local registry. Indeed, at low power, thelowest energy RXh states are first populated. When Pexc is increased, theRhh states, that lie just a few tens of meV at higher energy (see Fig. 5d),start to be populated and, for sufficiently high power, dominate theemission spectrum. TheRMh states, that lie at evenhigher energy, are notvisible due to their small oscillator strength20. This picture is corrobo-rated by theoretical calculations, showing that gexc = + 6.19 for the RXhregistry, while gexc = −6.15 for the Rhh registry20. Figure 5d summarisesthese findings and provide a comparison between experimental andtheoretical gexc values formoiré-localised aswell as free IX excitons. Thequantitative potential landscape for the moiré potential is also shown,as derived from ref. 3.These results demonstrate how magnetic fields represent a valu-able tool to determine the localised or delocalised status of chargecarriers in 2D HSs, which can be important for the understanding offundamental effects, such as the formation of highly correlated elec-tronic phases12,13,16,51.The sign reversal of the g-factor upon temperature increase isaccompanied by a change in the MX formation and recombinationdynamics when the de-trapping process starts to occur with increasingT. Figure 6a displays the time evolution of the μ-PL exciton signal inHS1 within 1 ns after the laser excitation, which corresponds pre-dominantly to the exciton formation process. Different temperatureswere considered with Pexc = 44 nW (ne-h=1.1 ⋅ 1011 cm–2).It is clear that the MX formation dynamics becomes faster withincreasing T (for T ≤ 100 K and Pexc = 44 nW, MXs dominate). Theexperimental data were fitted by Eq. (2) and the T dependence of τr isdisplayed in panel b for two different photo-generated carrierdensities. At T = 100 K, τr approaches the temporal resolution limit(notice that once the data get close to the resolution limit, the esti-mated rise time is affected by the system response and thus onlyqualitatively indicative). The higher temperatures and the ensuing MXionisation process result indeed in a decreased contribution of themoiré localisation step, and thus in a reduction of the time required tobuild up the exciton population contributing to the MX/IX band. Thisprocess ismore evident with increasing Pexc, as can be noted in Fig. 6b.As a matter of fact, a larger photo-generated carrier density tends tosaturate theMX states shifting the spectral centroid of theMX-IX bandtowards the faster-forming IX levels.The luminescence decay is also highly influenced by tempera-ture variations. Figure 6c shows the MX-IX band decay curves at Pexc= 1 μW (ne-h = 1.2 ⋅ 1012 cm– 2) and different temperatures. The curvescan be reproduced using Eq. (1) and the values of the fitting para-meters (τd,n andwd,n) are displayed in Fig. 6d. The three values of thedecay time τd,n decrease monotonically, with the shorter one (τd,1)reaching the resolution limit (0.23 ns) at T = 140 K, and the weightsof the slower components (wd,2 and wd,3) becoming less important.The latter are particularly relevant at low T, where decay time valuesof about 200 ns are observed, consistent with the space-indirectnature of MXs. The, yet small, k-space mismatch associated with thetwist angle may also contribute to the lengthening of the lumines-cence decay time6. The marked decrease of τd,n with T can beexplained by two simultaneous mechanisms. First, non-radiativerecombination channels are activated at higher temperatures,greatly shortening the luminescence decay time. Second, deloca-lised states are expected to have a larger recombination probability,because they are more likely to interact with other oppositelycharged free carriers, or with lattice defects acting as non-radiativechannels52.0 2 4 6 8 10 12-4-20246gMX = -6.93 0.08gM2= +6.76 0.08gM1= +6.90 0.10ZS- ZS 0(meV)B (T)gM3= +6.69 0.090306090E(meV)-8-404812g-factor1.32 1.34 1.36 1.38 1.40M1ytisnetnI.mroNEnergy (eV)M3M21.34 1.36 1.38 1.40Energy (eV)12 T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0 T12 T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0 TPPeexxeexcxxcca bcMXT = 10 K, Pexc = 0.2 µW T = 10 K, Pexc = 75 µWRhX Rhh RhMFree IXd RhXRhX Rhh RhM RhXexptheoryexptheoryWSe2MSe2Fig. 5 | Unveling the moiré atomic registry through g-factor measurements.a, b Helicity-resolved normalised μ-PL spectra of HS1 under magnetic field at T=6 Kfor two different laser excitation powers Pexc (focused via a 100×objective withNA = 0.82). The two sets of data were acquired in the same point of the HS. ForPexc =0.2 μW (a), many narrow lines can be seen. M1, M2 and M3 indicate three suchnarrow lines. At high powers Pexc = 75 μW (b) a continuous band can be seen. c ZS ofthe linesM1-M3of panel a andof theMXbandofpanelb, showing anopposite signofthe g-factor. The data of lines M2 andM3 are up-shifted by 1 and 2meV, respectively(as indicated by the double-sided arrows on the left) for sake of clarity. d Top: The-oretical g-factors (cyan stars) estimated for MXs confined in the RXh , Rhh, and RMhatomic registries20. The experimental g-factors calculated for the MX lines at lowpower (as an average of the g-factors estimated for theM1, M2 andM3 lines of panelc), and for the MX bandmeasured at high power (pink data in panel c) are displayedas orange pentagons, and —based on their value— are associated to the RXh and Rhhregistries, respectively. The cyan solid line and the orange dashed line provide theg-factor calculated based on Eq. (5) and that measured experimentally (Fig. 4c, d) forthe free IX, respectively. The insets show the atomic alignment corresponding to thethreeatomic registries. Errorbars arewithin the symbol/line size.Bottom:Variationofthe interlayer excitonpotential landscapewith respect to itsminimumat theRXh point(ΔE) in R-type MoSe2/WSe2 HSs. Adapted from the calculations of ref. 3.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 7In summary, we investigated the process of temperature-inducedexciton de-trapping from moiré minima in WSe2/MoSe2 HSs. Weobserved that at temperatures above 100 K moiré excitons turn intofree interlayer excitons with relevant consequences for quantumtechnology applications11 and for the observation of many-body phe-nomena, such as exciton condensation12 or Mott transition13,16,51. Thetemperature-induced transition from a moiré-confined to a free IXregime manifests itself in a sizeable variation of the power law gov-erning the exciton signal growth with photo-generated carrier density.The exciton magnetic moment too undergoes major variations withincreasing T. Indeed, the interlayer exciton g-factor exhibits aremarkable reversal of its sign anddecrease of itsmodulus (going fromabout + 7 to about − 5) concomitantly with the de-trapping of themoiré-confined excitons for T ≳ 100 K. This is likely to have relevantconsequences for valleytronic applications of TMD HSs. Within thesame T interval, we also consistently found that the formation time ofMXs is strongly reduced, as a consequence of the cross-over from alocalised to a free-like regime. This indicates that the excitoncapture inthe moiré potential requires an intermediate step that lengthens theluminescence rise time. Also, the decay time of the MX/IX states isgreatly reduced by increasing T due to the increased recombinationprobability of freely moving excitons as well as to exciton-excitoninteractions and to thermally activated non-radiative recombinationchannels. Our findings shed new light on the truly confined nature ofthe exciton states in a moiré superlattice with increasing temperatureand exciton density, thus setting the conditions for the observationand stability of highly correlated phases at elevated temperatures inmoiré superlattices.MethodsSample fabricationThe HSs were fabricated by the standard dry transfer technique. TMDflakes were mechanically exfoliated by the scotch tape method anddeposited onPDMS.MoSe2 andWSe2MLson the PDMSwere identifiedand deposited. For HS1, the MoSe2 ML was deposited first on a SiO2/Sisubstrate, and theWSe2was deposited atop of it. h-BNflakeswere thenexfoliated with the same approach and a thin h-BN flake was identifiedon the PDMS. The flake was then deposited in such a way to cap the HScompletely. The twist angle between the MLs was then estimated bySHGmeasurements. ForHS2, a h-BNflakewasfirst depositedona SiO2/Si substrate. TheWSe2MLwas then deposited atop. The orientation ofthe ML was checked by SHG. The orientation of the MoSe2 ML onPDMSwas also checked, and theMLwasdeposited aligned to theWSe2ML (virtually null twist angle). This HS was also subsequently cappedwith a thin h-BN flake. The twist angle of the two HSs was then deter-mined more precisely by optical studies (see Supplementary Note 2).10 1001E-30.010.11ytisnetnI.mroNTime (ns)0.0 0.5 1.00.51.tnI.mroNt (ns)0 35 70 105 14010-410-310-210-1100).nu.bra(htgieWT (K)0 35 70 105 140100101102)sn(emityaceDT (K)0.51.tnI.mroN0.51.tnI.mroN0.51.tnI.mroN0 20 40 60 80 10020406080100120140Resolution limit,emitesiRr(ps)T (K)44 nW200 nW10 K40 K70 K100 KabPexc = 44 nW7070 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKK1141444444444444444444444444444444444444440 0000 000   KKKKKKKKK140 K140 KRRRRRTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT666 KKKPexc = 1000 nWcdddd,3,3,3ddd,2,2,2ddd,1,1,1ddd,3,3,3ddd,2,2,2ddd,1,,1,1Fig. 6 | Rise and decay times with increasing temperature. a Time-evolution ofthe μ-PL signal of the investigated WSe2/MoSe2 heterostructure (HS1) recorded atdifferent temperatures (and fixed laser excitation power Pexc = 44 nW) in the Δt =0 − 1.0 ns interval from the laser pulse. The detection energy was set at the MX-IXband (see Fig. 3). The solid lines are fits to the data by Eq. (2). b Rise time τr valuesobtained by fitting the experimental data for different temperatures and two Pexcvalues. The setup time resolution is shown by the grey area. Notice that once thedata get close to the resolution limit, the estimated rise time is affected by thesystem response and thus only qualitatively indicative. cTime-evolutionof the μ-PLsignal of theMX-IX band (see Fig. 3) recorded in theΔt = 0-800 ns interval from thelaser pulse. The data were recorded at different temperatures, as indicated in thefigure, and fixed Pexc. The grey area indicates the instrumental response. d Decaytimes τd,n values used to reproduce the data of panel c via Eq. (1). The same for thespectral weights wd,n of the different time components, see Eq. (1).Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 8After everydeposition step, the sampleswereannealed in high vacuumat 150 °C for some hours.Continuous-wave μ-PL measurementsFor μ-PLmeasurements, the excitation laser was provided by a singlefrequency Nd:YVO4 lasers (DPSS series by Lasos) emitting at 532 nm.The luminescence signal was spectrally dispersed by a 20.3 cm focallength Isoplane 160 monochromator (Princeton Instruments)equipped with a 150 grooves/mm and a 300 grooves/mm gratingand detected by a back-illuminated N2-cooled Si CCD camera(100BRX by Princeton Instruments). The laser light was filtered outby a very sharp long-pass Razor edge filter (Semrock). A 100 × long-working-distance Zeiss objective with NA = 0.75 was employed toexcite and collect the light, in a backscattering configuration using aconfocal setup.For high resolutionmeasurements aimed at higlighting the moiréenergy levels (Fig. 1c and Supplementary Fig. 2.1), a 75 cm focal lengthActon monochromator was used.Time-resolved μ-PL measurementsFor tr μ-PL measurements, the sample was excited with a ps super-continuum laser (NKT Photonics) tuned at 530 nm, with a full width athalf maximum of about 10 nm and 50 ps pulses at 1.2 MHz repetitionrate. The sample was excited in the same experimental configurationused for continuous wave measurements. The signal was then col-lected in a backscattering configuration using a confocal setup. Thedesired spectral region was selected by using longpass and shortpassfilters. The signal was thus focused bymeans of a lens on an avalanchephotodetector from MPD with temporal resolution of 30 ps.μ-PL excitation measurementsFor μ-PL excitation (μ-PLE), we employed the sameps supercontinuumlaser used for tr μ-PL. The laser wavelength was automatically changedby an acousto-optic tunable filter and employing a series of shortpassand longpass filters to remove spurious signals from the laser. Thedetection wavelength was selected using the same monochromatorand detector employed for cw μ-PL measurements.Magneto-μ-PL measurementsMagneto-μ-PL measurements were performed at variable temperaturein a superconducting magnet reaching up to 16 T. x-y-z piezoelectricstages were used to excite the sample and collect the signal from thedesired point of the sample. A 515-nm-laser and a 100 ×microscopeobjective with NA = 0.82 were used. The same objective was used tocollect the luminescence. The circular polarisation of the PL was ana-lysed using a quarter-wave plate (that maps circular polarisations ofopposite helicity into opposite linear polarisations) and a Wollastonprism steering the components of opposite linear polarisation (andthus of opposite helicity) to different lines of the liquid-nitrogen-cooled Si-CCD we employed (100BRX by Princeton Instruments). Inthis manner, the σ+ and σ− components could be measured simulta-neously. A monochromator with 0.75 m focal length (PrincetonInstruments) and a 600 grooves/mm grating was used to disperse thePL signal.Second harmonic generation measurementsThe measurements were performed by using the 900 nm line of atunable pulsed Ti:Sapphire laser with a pulse width of <100 fs and arepetition rate of 80 MHz. The sample was excited and measuredunder a 50 × confocal objective lens (NA = 0.85), and the frequency-duplicated light was collected in a backscattering configuration.Linear polarisers were used to select laser light and SHG signalwith given polarisation states. The sample was placed on a rotationstage to collect the SH response in terms of relative polarisationangles.Data availabilityThe data that support the findings of this study are available from thecorresponding authors upon request.References1. Lau, C. N., Bockrath, M. W., Mak, K. F. & Zhang, F. Reproducibility inthe fabrication and physics of moiré materials. Nature 602, 41(2022).2. Zhang, C. et al. Interlayer couplings, moiré patterns, and 2D elec-tronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3,e1601459 (2017).3. Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: Fromprogrammable quantum emitter arrays to spin-orbit-coupled arti-ficial lattice. Sci. Adv. 3, e1701696 (2017).4. Tran, K. et al. Evidence for moiré excitons in van der Waals het-erostructures. Nature 567, 71 (2019).5. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons inMoSe2/WSe2 heterobilayers. Nature 567, 66 (2019).6. Choi, J. et al. Twist angle-dependent interlayer exciton lifetimes invan derWaals heterostructures. Phys. Rev. Lett. 126, 047401 (2021).7. Li, Z. et al. Interlayer exciton transport in MoSe2/WSe2 hetero-structures. ACS Nano 15, 1539 (2021).8. Du, L. et al. Moiré photonics and optoelectronics. Science 379,eadg0014 (2023).9. Zhang, N. et al. Moiré intralayer excitons in a MoSe2/MoS2 hetero-structure. Nano Lett. 18, 7651 (2018).10. Liu, E. et al. Signatures of moiré trions in MoSe2/WSe2 hetero-bilayers. Nature 594, 46 (2021).11. Baek, H. et al. Highly energy-tunable quantum light from moiré-trapped excitons. Sci. Adv. 6, eaba8526 (2020).12. Wang, Z. et al. Evidence of high-temperature exciton condensationin two-dimensional atomic double layers. Nature 574, 76 (2019).13. Wang, J. et al. Optical generation of high carrier densities in 2Dsemiconductor heterobilayers. Sci. Adv. 5, eaax0145 (2019).14. Huang, D., Choi, J., Shih, C.-K. & Li, X. Excitons in semiconductormoiré superlattices. Nat. Nanotechnol. 17, 227 (2022).15. Chen, D. et al. Excitonic insulator in a heterojunction moiré super-lattice. Nat. Phys. 18, 1171 (2022).16. Regan, E. C. et al. Mott and generalized Wigner crystal states inWSe2/WS2 moiré superlattices. Nature 579, 359 (2020).17. Xu, Y. et al. Correlated insulating states at fractional fillings ofmoirésuperlattices. Nature 587, 214 (2020).18. Wu, F., Lovorn, T. & MacDonald, A. H. Theory of optical absorptionby interlayer excitons in transition metal dichalcogenide hetero-bilayers. Phys. Rev. B 97, 035306 (2018).19. Tan,Q., Rasmita, A., Zhang, Z., Novoselov, K. S. &Gao,W.-B. Opticalsignature of cascade transitions betweenmoiré interlayer excitons.Phys. Rev. Lett. 129, 247401 (2022).20. Woźniak, T., Junior, P. E. F., Seifert, G., Chaves, A. & Kunstmann, J.Exciton g factors of van der Waals heterostructures from first-principles calculations. Phys. Rev. B 100, 235408 (2020).21. Barré, E. et al. Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures. Science 376, 406 (2022).22. Brotons-Gisbert, M. et al. Moiré-trapped interlayer trions in acharge-tunable WSe2/MoSe2 heterobilayer. Phys. Rev. X 11,031033 (2021).23. Li, W., Lu, X., Dubey, S., Devenica, L. & Srivastava, A. Dipolar inter-actions between localized interlayer excitons in van der Waalsheterostructures. Nat. Mater. 19, 624 (2020).24. Nagler, P. et al. Giant magnetic splitting inducing near-unity valleypolarization in van der Waals heterostructures. Nat. Commun. 8,1551 (2017).25. Wang, T. et al. Giant valley-Zeeman splitting from spin-singlet andspin-triplet interlayer excitons in WSe2/MoSe2 heterostructure.Nano Lett. 20, 694 (2020).Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 926. Li, W., Lu, X., Wu, J. & Srivastava, A. Optical control of the valleyZeeman effect through many-exciton interactions. Nat. Nano-technol. 16, 148 (2021).27. Zhang, L. et al. Highly valley-polarized singlet and triplet interlayerexcitons in van der Waals heterostructure. Phys. Rev. B 100,041402(R) (2019).28. Mahdikhanysarvejahany, F. et al. Temperature dependent moirétrapping of interlayer excitons inMoSe2-WSe2 heterostructures. npj2D Mater. Appl. 5, 67 (2021).29. Miller, B. et al. Long-lived direct and indirect interlayer excitons invan der Waals heterostructures. Nano Lett. 17, 5229 (2017).30. Troue, M. et al. Extended spatial coherence of interlayer excitonsin MoSe2/WSe2 heterobilayers. Phys. Rev. Lett. 131, 036902(2023).31. Parzefall, P. et al. Moiré phonons in twisted MoSe2-WSe2 hetero-bilayers and their correlation with interlayer excitons. 2D Mater. 8,035030 (2021).32. Shinokita, K., Watanabe, K., Taniguchi, T. & Matsuda, K. Valleyrelaxation of the moiré excitons in a WSe2/MoSe2 heterobilayer.Nano Lett. 22, 16862 (2022).33. Robert, C. et al. Exciton radiative lifetime in transition metaldichalcogenide monolayers. Phys. Rev. B 93, 205423 (2016).34. Blundo, E. et al. Evidence of the direct-to-indirect band gap transi-tion in strained two-dimensional WS2 and MoS2, and WSe2. Phys.Rev. Res. 2, 012024 (2020).35. Aivazian, G. et al. Many-body effects in nonlinear optical responsesof 2D layered semiconductors. 2D Mater. 4, 025024 (2017).36. Salehzadeh, O., Tran, N. H., Liu, X., Shih, I. & Mi, Z. Exciton kinetics,quantum efficiency, and efficiency droop of monolayer MoS2 light-emitting devices. Nano Lett. 14, 4125 (2014).37. Nagler, P. et al. Interlayer exciton dynamics in a dichalcogenidemonolayer heterostructure. 2D Mater. 4, 025112 (2017).38. Brem, S. & Malic, E. Bosonic delocalization of dipolar moiré exci-tons. Nano Lett. 23, 4627 (2023).39. Lin, B.-H. et al. Remarkably deep moiré potential for intralayerexcitons in MoSe2/MoS2 twisted heterobilayers. Nano Lett. 23,1306 (2023).40. Tedeschi, D. et al. Unusual spin properties of inpwurtzite nanowiresrevealed by Zeeman splitting spectroscopy. Phys. Rev. B 99,161204(R) (2019).41. Stier, A. V. et al. Magnetooptics of exciton Rydberg states in amonolayer semiconductor. Phys. Rev. Lett. 120, 057405 (2018).42. Molas, M. R. et al. Probing and manipulating valley coherence ofdark excitons in monolayer WSe2. Phys. Rev. Lett. 123,096803 (2019).43. Blundo, E. et al. Strain-induced exciton hybridization in WS2monolayers unveiled by Zeeman-splitting measurements. Phys.Rev. Lett. 129, 067402 (2022).44. Olkowska-Pucko, K. et al. Excitons and trions in WSSe monolayers.2D Mater. 10, 015018 (2023).45. Gobato, Y. G. et al. Distinctiveg-factor ofmoiré-confinedexcitons invan der Waals heterostructures. Nano Lett. 22, 8641 (2022).46. Ciarrocchi, A. et al. Polarization switching and electrical control ofinterlayer excitons in two-dimensional van der Waals hetero-structures. Nat. Photon. 13, 131 (2019).47. Joe, A. Y. et al. Electrically controlled emission from singlet andtriplet exciton species in atomically thin light-emitting diodes. Phys.Rev. B 103, L161411 (2021).48. Holler, J. et al. Interlayer exciton valley polarization dynamics inlarge magnetic fields. Phys. Rev. B 105, 085303 (2022).49. Yu,H., Liu,G.-B. &Yao,W. Brightened spin-triplet interlayer excitonsand optical selection rules in van der Waals heterobilayers. 2DMater. 5, 035021 (2018).50. Mahdikhanysarvejahany, F. et al. Localized interlayer excitons inMoSe2/WSe2 heterostructures without a moiré potential. Nat.Commun. 13, 5354 (2022).51. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2moiré superlattices. Nature 579, 353 (2020).52. Vinattieri, A. et al. Role of the host matrix in the carrier recombi-nation of InGaAsN alloys. Appl. Phys. Lett. 82, 2805 (2003).AcknowledgementsThe authors thank Andrey Chaves, Paulo E. Faria Jr and Tomasz Woź-niak for useful discussions about the magneto-photoluminescenceresults and are grateful to Daniele Sanvitto for support with the SHGmeasurements. E.B., A.P., A.B., and M.R.M. acknowledge support bythe European Union’s Horizon 2020 research and innovation pro-gramme through the ISABEL project (No. 871106). This project wasfunded within the QuantERA II Programme that has received fundingfrom the European Union’s Horizon 2020 research and innovationprogramme under Grant Agreement No. 101017733, and with fundingorganisations Ministero dell’Università e della Ricerca (A.P. and M.F.)and by Consiglio Nazionale delle Ricerche (G.P.). A.P. and M.F.acknowledge financial support from the PNRR MUR projectPE0000023-NQSTI. M.F. and G.P. acknowledge funding from thePRIN2022 project DELIGHT2D (Prot. 20222HNMYE). E.B. acknowl-edges support from La Sapienza through the grants Avvio alla Ricerca2021 (Grant no. AR12117A8A090764) and Avvio alla Ricerca 2022(Grant no. AR2221816B672C03). The authors acknowledge supportfrom the National Science Centre, Poland, through Grants No. 2018/31/B/ST3/02111 (K.O. P. and M.R.M.) and No. 2017/27/B/ST3/00205(A.B.). K.W. and T.T. acknowledge support from the JSPS KAKENHI(Grant Numbers 19H05790 and 20H00354).Author contributionsE.B. and A.P. conceived and supervised the research. E.B. and M.C.fabricated the heterostructures. E.B., F.T., S.C., M.C. andG.C. performedthe optical measurements and analysed the data. E.B., A.P., K.O.P., L.K.,and M.R.M. performed the magneto-optical measurements, with thesupport of A.B., andE.B. analysed thedata. A.M. provided support for theSHG measurements. M.F. provided support for the time-resolved mea-surements. G.P. contributed to the sample characterisation. T.T. andK.W. grew the hBN samples. E.B. and A.P. wrote the manuscript. Theresults and the manuscript were approved by all the coauthors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-44739-9.Correspondence and requests for materials should be addressed toElena Blundo or Antonio Polimeni.Peer review information Nature Communications thanks Xiaoxu Zhao,Fateme Mahdikhany and the other anonymous reviewer for their con-tribution to the peer review of this work. A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 10https://doi.org/10.1038/s41467-024-44739-9http://www.nature.com/reprintsOpen Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-44739-9Nature Communications |         (2024) 15:1057 11http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Localisation-to-delocalisation transition of�moiré excitons in WSe2/MoSe2 heterostructures Results Moiré exciton dynamics at low temperature Exciton recombination vs carrier density and temperature Moiré exciton de-trapping, magnetic moment and dynamics vs T Methods Sample fabrication Continuous-wave μ-PL measurements Time-resolved μ-PL measurements μ-PL excitation measurements Magneto-μ-PL measurements Second harmonic generation measurements Data availability References Acknowledgements Author contributions Competing interests Additional information