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Jinjae Kim, Jiwon Park, Hyojin Choi, Taeho Kim, Soonyoung Cha, Yewon Lee, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jonghwan Kim, Moon-Ho Jo, Hyunyong Choi

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[Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell](https://mdr.nims.go.jp/datasets/31189a1a-a901-43db-b1f4-943e195dccc7)

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Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercellArticle https://doi.org/10.1038/s41467-024-47768-6Correlation-driven nonequilibrium excitonsite transition in aWSe2/WS2moiré supercellJinjae Kim 1,2,7, Jiwon Park1,2,7, Hyojin Choi1,2, Taeho Kim3,4, Soonyoung Cha5,Yewon Lee3,4, Kenji Watanabe 6, Takashi Taniguchi 6, Jonghwan Kim 3,4,Moon-Ho Jo 3,4 & Hyunyong Choi 1,2Moiré superlattices of transition metal dichalcogenides offer a unique plat-form to explore correlated excitonphysicswithoptical spectroscopy.Whereasthe spatially modulated potentials evoke that the exciton resonances are dis-tinct depending on a site in a moiré supercell, there have been no cleardemonstration how the moiré excitons trapped in different sites dynamicallyinteract with the doped carriers; so far the exciton-electron dynamic interac-tions were presumed to be site-dependent. Thus, the transient emergence ofnonequilibrium correlations are open questions, but existing studies are lim-ited to steady-state optical measurements. Here we report experimental fin-gerprints of site-dependent exciton correlations under continuous-wave aswell as ultrashort optical excitations. In near-zero angle-aligned WSe2/WS2heterobilayers, we observe intriguing polarization switching and stronglyenhanced Pauli blocking near theMott insulating state, dictating the dominantcorrelation-driven effects. When the twist angle is near 60°, no such correla-tions are observed, suggesting the strong dependence of atomic registry inmoiré supercell configuration. Our studies open the door to largely unex-plored nonequilibrium correlations of excitons in moiré superlattices.The intriguing phenomena of moiré superlattices emerge through thevertical alignment of two layers of two-dimensional (2D) materials,characterized by a relative twist angle or lattice mismatch. Thisstructural arrangement introduces an additional periodic potentiallandscape, influencing the behavior of electrons and holes within amoiré supercell. Excitons and charged particles in the moiré supercelloffer new avenues to explore profound correlation phenomena thatinclude unconventional superconductivity, ferromagnetism, and thetunable manipulation of Wigner crystal and Mott insulating states1–5.Because of the strong light-matter interaction features of transitionmetal dichalcogenides (TMDs), a rich spectrum of excitonic entitieshas been unveiled in this context, with optical spectroscopy. Examplesinclude the reflection contrast (RC), photoluminescence (PL), andhelicity-dependent magnetic circular dichroism, whereby interestingoptical characteristics encompassing moiré intralayer4 and interlayerexcitons6, trions7, moiré polarons8, spin-polarons9, and bosonic cor-related excitons10,11 have been studied.Despite these advancements, investigations on the microscopicnonequilibrium dynamics of these excitonic species are still infancy.While existing studies are limited to steady-state optical measure-ments, the transient emergence of nonequilibrium correlations andthe corresponding optical consequence remain unexplored. Exam-inations on such fields might provide new possibilities for the obser-vation of correlation-driven nonequilibriumdynamics. Particularly, theinvestigation within the charge-transfer insulating states that possessthe energetically favorable second local minimum potential in a moiréReceived: 27 October 2023Accepted: 10 April 2024Check for updates1Department of Physics, Seoul National University, Seoul 08826, Korea. 2Institute of Applied Physics, Seoul National University, Seoul 08826, Korea.3Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 37673, Korea. 4Center for van derWaals QuantumSolids, Institute for Basic Science (IBS), Pohang 37673, Korea. 5Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA.6Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 7These authors contributed equally: JinjaeKim, Jiwon Park. e-mail: hy.choi@snu.ac.krNature Communications |         (2024) 15:3312 11234567890():,;1234567890():,;http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://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/0000-0002-1467-3105http://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/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-7646-3269http://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-47768-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-47768-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-47768-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-47768-6&domain=pdfmailto:hy.choi@snu.ac.krsupercell offers a compelling opportunity to unravel the impact ofspatial atomic registry on the evolving spectral transients of excitons.In this Article, we report the observation of moiré exciton sitetransitions driven by the strong correlation between doped electronsand photoexcited excitons. We performed RC, interlayer exciton PL,and time-resolved pump-probe spectroscopy in a gate-controlled,angle-aligned WSe2/WS2 heterobilayer. Our findings reveal that, uponn-doping, the polarization switching and the strongly enhanced Pauliblocking phenomena are consistent with the dynamic site transition ofmoiré excitons,which eventuates only in theR-stacked (near 0°) device(R1) (Fig. 1a). Conversely, theH-stacked (near 60°) device (H1) does notmanifest such phenomena, indicating its strong dependence on amoiré supercell configuration. All measurements were conducted at atemperature of 4 K. We obtain consistent results from an additionalR-stacked device R2 and R3. The main text of results is primarily fromthe R-stacked heterobilayer R1 and the H-stacked heterobilayer H1.ResultsSteady-state optical spectroscopyIn our experiment, we fabricated both R- and H-stacked WSe2/WS2heterobilayers. A single-gated device is employed for both bilayers, asdepicted in Fig. 1b.Notably, we opted for a gold bottomgate insteadofthe conventional graphene-based dual gate configuration. This stra-tegic choice aimed tomaximize the signal-to-noise ratio for our pump-probe spectroscopy while avoiding any possible nonequilibrium arti-facts from graphene dynamics. In Fig. 1c, we presented an opticalmicroscopy image of the device R1. The twist angle was confirmedusing the second harmonic generation (SHG) spectroscopy (Supple-mentary Fig. 1).First, we examined the gate-dependent RC near the WSe2 A exci-ton resonance (~1.7 eV) of the device R1 (Fig. 2a). Three distinct intra-layer exciton peakswereobserved at the gate voltageVG =0V, labelledas X 1,X2, and X3. With changing VG, we have discerned a series ofinsulating states at integer fillings (ν) that are consistent with manyprior reports4,12–14. The same plots near the WS2 A exciton resonance(~2.0 eV) are presented in Supplementary Fig. 2.Given the type II band alignment characteristics of the WSe2/WS2heterobilayer, we have proceeded to investigate the PLmeasurementsof the interlayer excitons around the photon energy of 1.4 eV (Fig. 2b)under 632.8 nm continuous-wave laser excitation. Specifically, Fig. 2cshows the degree of circular polarization ρð= σ + =σ +�σ + =σ�σ + =σ + + σ + =σ�Þ derivedfrom the polarization-resolved PL measurements. When 0<ν<1, the PLemission is co-circularly polarized, but makes a transition into thelinearly-polarized PL when ν>1. In contrast, the cross-circularly polar-ized PL features are seen across the entire negative ν. The asymmetricPL peak shift, observed as a function of VG, arises from the differencesin the Stark effect15. These differences are specifically linked to ourdevice structure, where the WS2 layer is positioned closer to the backgate in our stacking configuration of heterobilayer (SupplementaryFig. 3). Due to the type-II alignment, when electrons are induced by thepositiveVG, they areprimarily populated in theWS2 layer. This, in turn,screens the electric field between WSe2 and WS2 layers, resulting in areduced Stark effect. To establish a comparative scope, we have con-ducted identical measurements on a device H1. Figure 2d and e showsFig. 1 | Schematics of the moiré exciton site transition in WSe2/WS2 devices.a Schematic shows the strong correlation induced moiré exciton site transition. Atcharge neutrality, the interlayer excitons occupyRXh site where the optical selectionrule for the interlayer exciton renders the co-circularly polarized PL emission (left).When dopedwith electrons, the Coulomb repulsion (Ue�ex) between electrons andinterlayer excitonsmakes the interlayer excitons transfer to the Rhh site which is thesecondary energy minimum of the moiré potential (right). Consequently, thepolarization switching of the interlayer excitons occurs into the linearly-polarizedPL. Correspondingly, the enhanced Pauli blocking is observed by both steady-stateand ultrashort optical measurements. b A device schematic showing the hBNencapsulated WSe2/WS2 with a gold bottom-gate. c Optical microscopy image of anear-0° twisted WSe2/WS2 heterobilayer (device R1).Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 2theVG-dependent RC andPL, performedon the deviceH1. The PL peakshows a sudden blueshift, and the absorption shows a spectral kink atν = 1. As seen in Fig. 2f, ρ does not show the polarization switching, butmaintains the cross-polarized character.Subsequently, we have investigated the laser intensity I depen-dent ρ of the interlayer PL emission on the device R1 (Fig. 3a). Here, wedefine the “threshold voltage”, at which the circular polarizationswitching occurs – from the co-circularly polarized PL emission to thelinearly-polarized (cross-circularly polarized) one. These thresholdvoltages are determined by the VG-dependent valley polarization(Supplementary Fig. 4). Figure 3b summarizes the threshold voltage asa function of I. Here, we note that the threshold voltage for then-doping case displays a relatively weak dependence on I, while itexhibits a much stronger I-dependence for the p-doping case; itrepresents that a higherVG is required for thepolarization switching tooccur for the p-doping case with increasing I.Suchdistinct dopingdependenceof PLpolarization arises from thecontrasting atomic arrangements between the R- and the H-stackedheterobilayers. It has been well established that the absence of out-of-plane mirror symmetry leads to a unique optical selection rule for theinterlayer electron-hole recombination16–20. This rule, governing notonly the spin-valley indices but also the local stacking, plays a pivotalrole in the PL polarization. The corresponding optical selection rules ofinterlayer transition are summarized in Supplementary Table 1 andSupplementary Table 2. In the case of the H-stacked device, where theinterlayer electrons and holes experience lateral separation, the inter-layer excitons experience two types of sites for the recombination tooccur, namelyHhh orHXh. These sites possess opposite selection rules butmaintain the spin preserving configuration. The observed cross-polarized PL suggests a higher recombination rate at the Hhh site bythe optical selection rule18. Because the site transitions are not observedon the device H1, the emitted light helicity remains unchanged.Fig. 2 | Twist-angle-dependent degree of circular polarization of interlayerexcitons. a VG-dependent reflection contrast (RC) spectrum of a R-stackedðθ≈1:2� ±0:6�Þ WSe2/WS2 moiré superlattice (Device R1). Positive (negative) VGrefers to electron (hole) doping. Filling factor ν refers to the number of dopedcarriers per moiré unit-cell (moiré density n0 = 2:19 × 1012cm�2). b VG-dependentinterlayer exciton PL (log scale) of device R1 when the incident laser and detectedPL are co-circularly polarized. c The corresponding degree of circular polarization(ρ= σ + =σ + �σ + =σ�σ + =σ + + σ + =σ�) measured from the polarization resolved PL. Polarizationswitching phenomena are observed near Mott insulating states (ν = 1) at VG = 2V aswell as VG = � 0:24V. d–f The same plots as a–c but for the H-stacked device H1.f Polarization switching is not observed but the cross-circularly polarized feature isseen for the entire VG.Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 3For the R-stacked device, the recombination of the electron andhole takes place at the RXh site, resulting in the co-circularly polarizedPL. After σ + excitation, the photogenerated electrons in the K valleyof WSe2 undergo relaxation into both K and �K valleys of WS2through the spin-flip and the valley-flip scattering. A recent study18has elucidated such a feature in the p-doping regime; when thepopulation of doped holes surpasses the imbalanced electronpopulation via efficient valley-flip relaxation, polarization switchingoccurs from the co-circularly polarized PL to the cross-circularlypolarized one. This polarization switching, attributed to the popu-lation imbalance, requires a higher VG to counteract when I isincreased (Fig. 3b).Our main discovery emerges when VG is positive. In contrast tothe p-doping case, we see the following observations in Fig. 3. Thepolarization switching displays a weak I-dependence for the n-dopingcase. Interestingly, the threshold voltage is close to theMott insulatingstate (ν = 1) where electrons occupy the moiré unit cell in a one-to-onecorrespondence triggered by on-site Coulomb repulsion (Ue�e). Thepolarization switching (from the co-circularly polarized to the linearly-polarized PL) cannot be understood by the valley-flip scattering; itdoes not add any additional polarization switching mechanisms in then-doping case18. Rather, we consider two scenarios when additionalelectrons are doped into the lattices, i.e., for ν ≥ 1. First, the extraelectron may occupy the same orbital as the former one with anopposite spin, resulting in both electrons occupying the same site.Second, whenUe�e exceeds the energy differences between twomoirélocal minimums (ΔEg), the extra electron avoids double-occupancyand resides at the second local minimum site. In this case, the corre-lation lead to a charge transfer insulating state and we put the strongcorrelation-induced moiré exciton site transition as the key con-tributor for polarization switching,which is in linewith the fact that theWSe2/WS2 heterobilayer is indeed a charge transfer insulator11,21,22for ν>1.Ultrafast nonequilibrium optical spectroscopyTo gain dynamic information on the polarization switching phenom-ena, we have explored the photoinduced nonequilibrium excitondynamics, by employing ultrafast pump-probe spectroscopy. Thetime-resolved experiments have been conducted using a 250 kHzTi:sapphire regenerative amplifier system (Coherent RegA 9040). Thepump pulses, whose photon energy is tunable from 1.65 eV to 2.3 eV,are generated by using anOptical Parametric Amplifier (Coherent OPA9450). Meanwhile, the white-light probe pulses are generated byfocusing the 50-fs, 1.55-eV pulse onto a 0.5-mm thick sapphire disk.Typical excitation fluences F (7∼ 70μJ=cm2) employed in our experi-ment yield 2D carrier densities in the range from 1011 to 3 × 1012cm�2which are below the 2D Mott density of TMDs ( ~ 1013cm�2)23–27, sug-gesting that excitons can be formed from the photoexcitation withoutforming the electron-hole plasma. First, wemonitor the K valley moiréintralayer exciton, i.e. the one at 1.684 eV (X 1), under co- and cross-circularly polarized photoexcitation at 1.75 eV (see the inset of Fig. 4a).The contour plots in Figs. 4a and 4b show the measured temporalevolution of the differential reflectance ΔR=R0 of the moiré intralayerexciton, and the corresponding line-cut spectra at selected pump-probe time delayΔt are shown in Fig. 4c. A distinct shape of theΔR=R0spectrum is apparent when comparing the co- and cross-circularlypolarized data. Clear exciton-resonance blueshift is observed for thecase of the co-circularly polarized pump-probe experiment, whereasthe cross-circularly polarizedpump-probedata display a redshift in theexciton resonance. Themeasured ΔR=R0 spectra remain such featuresover 3 ns except at the early Δt<0:1 ns.We now discuss the possible scenarios behind the observedspectral transients for early- Δt<0:1 ns and long-delay Δt>0:1 nsdynamics. For the early-delay dynamics, there are several carrierscattering processes involved such as hot-phonons, carrier-carrierinteractions and interlayer exciton transients. Upon ultra-short pulseexcitation, high-temperature carriers are generated, experiencingFig. 3 | Excitation intensity dependent threshold voltages. a VG-dependentdegree of circular polarization ðρ= σ + =σ + �σ + =σ�σ + =σ + +σ + =σ�Þ is shown for the two selected I. Thered dashed lines indicate ν = 1 and the black dashed lines indicate the thresholdvoltage when VG<0. b Threshold voltage as a function of I. The red and black linesindicate the threshold voltage for the polarization switchingwhenVG>0 andVG<0,respectively. The polarization switching exhibits a strong dependence on I whenVG<0; the higher I, the larger VG is required to switch the polarization. Such phe-nomena are due to the efficient valley-flip scattering as demonstrated in ref. 18.When VG>0, however, we suggest a different mechanism, namely a correlation-driven exciton site transition. In this regime, the polarization switching shows aweak I-dependence. See the main text for more details.Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 4thermalization relaxations through hot-phonon and carrier-carrierinteraction in a few hundred femtoseconds24,28. In addition, ultrafastcharge transfer in a type II band alignment occurswithin a fewhundredfemtoseconds, whose time scales depend on the stackedmaterials29,30.Subsequently, the intralayer exciton is formed within a few picose-conds in typical monolayer TMDs31–33, and the interlayer exciton isformed within 1 ps34. Thus, until a few picoseconds, the spectral tran-sients are influenced by the combined effects of the photoexcited hot-carriers, hot-phonons and the interlayer exciton formation. However,because the interlayer excitons exhibit long-lived lifetimes (~1.8 ns)35and ultralong valley lifetimes (~40 μs)36,37, the longer time delay (e.g.,Δt = 2 ns) is appropriate for studying thedynamics of interlayer excitonwithout considering the early transient effects. We first focus ourdiscussions on the longer time delays to elucidate the interlayer exci-ton site transition dynamics. Subsequently, we address the early timedelays, where the relaxation dynamics is primarily dominated by hot-phonon cooling processes.The co-circularly polarized exciton resonance displays a blueshiftat all the long-time delays (Fig. 4a). This can be attributed to theBurstein-Moss effect-induced Pauli blocking of the band-edgetransition38,39. The ultralong valley lifetime36,37 in WSe2/WS2 ensuresthat the co-circularly polarized signal is primarily influenced by thiseffect, because the photoexcited carriers tend to remain within thesame valleywhere theywere initially excited. Conversely, for the cross-circularly polarized case, the Pauli blocking subdues significantlybecause most of the carriers reside in the opposite valley. Of course,the valley-independent effects, such as bandgap renormalization31,38 orlattice heating40, can still induce the absorption changes. These factorslead to a redshift in the resonance energy, consistent with ourresults (Fig. 4b).Novel aspects of our study are the ν-depednent nonequilibriumΔR=R0 spectra. Supplementary Fig. 5a depicts the ΔR=R0 spectra fordifferent filling, ν from −2 to +2, where we have tuned the pump-photon energy of 2.0 eV, near the resonanceof theWS2A exciton. Akinto Figs. 4a and 4b, no significant spectral re-shaping is observed in theΔR=R0 spectra after a sufficient time delay of around 0.1 ns. Thisconfirms that our data represent the exclusive dynamics of the inter-layer excitons. A comparison between ν =0 and ν =2 case shows thatthe latter exhibits a more pronounced blueshift than the former. Weobserve similar behaviors across various F ’s with a lower photo-excitation energy of 1.75 eV (Supplementary Fig. 6). Figure 4d showsthe ν-dependent interlayer exciton ΔR=R0 spectra at Δt =2ns. TheΔR=R0 spectral transients of X 1 start to exhibit an abrupt change and astrongblueshiftwhen ν is above zerofilling, i.e.VG is larger than 1 V.OnFig. 4 | Strongly enhanced Pauli blocking of X1 in the n-doping regime. ΔR=R0spectra are shown under the pump excitation of _ω= 1:75eV (a, inset) whenVG =0V. a Co-circularly polarized and b cross-circularly polarized ΔR=R0, respec-tively. c ΔR=R0 at selected Δt are shown. When Δt =0 ns, ΔR=R0 are similar whenthe pump and the probe pulses are co-circularly (black solid) and cross-circularlypolarized (red solid), indicating the valley-independent hot-carrier dynamics nearzero-time delay. However, when Δt>0:1ns, the ΔR=R0 spectra show the valley-dependent interlayer exciton dynamics. d VG-dependent ΔR=R0 measured atΔt = 2ns for the device R1. Prominent blueshift is observed when ν>0 (inset). Thepump photon energy is 2.0 eV and F is 12μJ=cm2. Corresponding photoexcitedexciton density, estimated using a transfermatrixmethod (Supplementary Note 3),is 2:79 × 1012cm�2. This is the same order of moiré density n0 = 2:19 × 1012cm�2.Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 5the other hand, signals from X2 and X3 exhibit blueshifts at VG =0V,and they eventually subside without noticeable spectral changes evenwhen ν is larger than the zero (VG>1V) (see Supplementary Note 1 forthe detailed discussion about the X 1, X2, and X3 dynamics and Sup-plementary Fig. 7 for same contour plots resulted from device R3across various F ’s).The enhanced blueshift observed near the Mott insulating state(ν = 1) can be understood on the basis of the large-scale first-principlescalculations. Recent theory and experiment have demonstrated thatthe lowest energy moiré exciton (X 1 in our case) is a Wannier-typeexciton, featuring tightly bounded electrons and holes localized at theRhh site in the moiré supercell13. In contrast, the highest energy moiréexciton (X3 in our case) is characterized as an intralayer charge-transfer excitonwith electrons andholes spatially separated. It has alsobeen pointed out that the doped electron occupies the RXh site in themoiré supercell, which is the same site of interlayer excitons in theneutral regime. When n-doping is introduced, it naturally invokes aCoulomb repulsion (Uex�e) between the doped electrons and thephotoexcited interlayer excitons, causing the latter to dynamicallyshift to a more energetically favorable second local minimum site, i.e.Rhh. In Supplementary Note 2, we discuss the exciton site transition bycomparing energy differences ofΔEg andUex�e. Within the frameworkof a site transition in amoiré supercell, themeasured ΔR=R0 spectra atν ≥ 1 clearly represent the avoided double occupancy of Pauli blockingexperienced by the localized exciton X 1. In fact, the observed polar-ization switching from the circularly polarized PL to the linearlypolarized one is consistent with the standard optical selection rule ofthe interlayer exciton PL (Supplementary Table 1). In SupplementaryFig. 8, we have shown extensive temperature dependent ΔR=R0spectra. The measured critical temperature for the enhanced Pauliblocking is comparable with the thermal-activation temperature ofMott-Hubbard gap in WSe2/WS2. This implies that such phenomenaoriginate from the correlation-driven effects.In the case of H-stacking, the moiré potential exhibits differentpotential landscapes in comparison to the R-stacking. This distinc-tion arises from the differences in atomic configuration stemmingfrom different twist angles. Here, the excitons and doped electronsare localized at a different site in contrast to the R-stacking. Whilerecent studies10,18 have investigated the site of interlayer excitonsand doped electrons in the H-stacking, the site of the moiré intra-layer exciton (for the case of H-stacking) has not been clearlyresolved. Nevertheless, a natural expectation is that the enhancedPauli blocking shall result in a blueshift of the spectral transient ifinterlayer excitons and moiré intralayer excitons occupy the samesite. If not, we may observe a spectral redshift due to bandgaprenormalization or lattice heating. The transient redshift or blueshiftis mainly determined by how these exciton wavefunctions arespread out in a moiré supercell. We substantiate this scenario byperforming the same experiment on the device H1, and have foundthat the competing processes between the blueshift and the redshiftmechanisms yielded a modest blueshift without abrupt changes(Supplementary Fig. 10b). While a comprehensive theoretical workis necessary, the spectral transients without the abrupt changesindicate the absence of polarization switching in the device H1 withno moiré exciton site transition.To focus on the population dynamicswhile excluding the effect ofspectral shift, we perform spectral integration on the differentialreflectance ΔR=R041,42 (Fig. 5a). We use a biexponential fit function toexamine the decay of population (see Supplementary Note 4 for moredetails). The fast and slow components of decaying dynamics aredenoted as τfast and τslow, respectively.We choose an excitation energyof 1.75 eV, which is in resonance with X2. We investigate the F depen-dence of τfast and τslow for various fillings ν from -2 to 2. Upon a rela-tively small F of 7:2μJ=cm2, we extract τfast of 0:44±0:2 ps whenVG =0V and (Fig. 5b). With a high F of 36:2μJ=cm2, τfast increases to avalue of 0:49±0:04 ps. While a similar F dependence is observed foreach filling, the noticeable changes are seen at VG =4V, and the Fdependence is almost negligible at VG = 2V. The observed behavior isconsistent with the hot phonon effect24,43,44, where a substantial pho-non population is induced by the elevated lattice temperature, whichprevent the photoexcited carriers from being cooled via phononemission. This effect contradicts with the carrier-carrier scatteringprocess, where the sub-picosecond relaxation is known to becomefaster with increasing F . In prior studies24,45, A1g and/or E12g opticalphonons are proposed as the candidates in the cooling process withina time scale of 0.5 ps. Meanwhile, the modulation of optical phononsfrequency and intensity through the carrier doping is reported byprevious studies46–48, whichmay lead to different values of τfast and thedependency in various ν’s.The slow decay component τslow is on the order of ns, whichrepresent an effective lifetime of interlayer excitons in R-stackedWSe2/WS2 heterobilayers (Fig. 5c). When VG =0V and F = 7:2μJ=cm2,the measured τslow is a value of 3:38±0:33ns. This time constant doesnot match with recent studies49,50 of reporting relatively short inter-layer exciton lifetime of ~1 ns for R-stacked WSe2/WS2 hetero-structures. The discrepancy may arise because our experiments wereperformed at a temperature of 4 K, minimizing the non-radiativerecombination49,51.With increasingVG, the extracted τslow is 2:24±0:19ns atVG = 2V and 2:25±0:23 nsVG =4V, respectively, which are furtherdecreased compared to the neutral regime. This is consistent with thestudy11 reporting a decrease in the radiative lifetime of interlayerexciton inWSe2/WS2 whenmore n-doping is introduced. Interestingly,no significant F dependence is observed. It suggests a negligibleexciton-exciton annihilation process due to the minimal density ofphotoexcited interlayer exciton. However, in the case of p-doping,τslow not only strongly depends on F , but also exhibits opposite Fdependencies for VG = � 2:3V and VG = � 3:9V. Assuming the radia-tive decay rate remains relatively unchanged throughout thep-doping11, we can infer that the non-radiative decay and the relatedprocesses undergo significant changes, particularly due to gap open-ing at each insulating state, as previously observed in WSe2/MoS2heterobilayers52.We now turn to the rise dynamics of the population. Note that ourindependent measurement shows that a temporal resolution of ourpump-probe signal is limited to 132 fs (Supplementary Fig. 11). Tomonitor and quantify the site transition time (i.e., τsite in Fig. 5d), wefocus on the rise dynamics of the ΔR=R0 signals for X 1 exciton underthe photoexcitation on X2. When VG =0V, τsite is measured to be267± 58 fs (Fig. 5d). We note that this site transition dynamics pre-cedes the charge transfer dynamics, which occurs within 383 ± 10 fs(see Supplementary Fig. 12 for full VG-dependent charge transferdynamics). Thus, the dynamics of electrons and holes cannot be dis-tinguished in this case, because it occurs before the separation ofelectrons and holes in different layers. Upon p-doping, τsite slightlyincreases to 339± 87 fs at VG = � 3:9V. Conversely, upon n-doping, itsignificantly decreases, reaching our temporal resolution limit(represented by the dashed line) at VG = 2V (Fig. 5e). These trends areconsistently observed with various F (Supplementary Fig. 13). Recenttheoretical and experimental studies17,53 suggest that the electrostaticdoping can alter the landscape of moiré potentials. The asymmetricdependency of τsite on doping may reveal this signature of site-dependent dynamics of carriers. One possible scenario is that, withincreasing the n-doping, the site of ground exciton state experiences adynamic transition from RXh to Rhh, leading to the efficient carrierscattering into the Rhh site, which is the energetically favorable site. Infact, this is in line with our finding of exciton site transition that occursexclusively in then-doping, not in the caseof p-doping.However,moretheoretical studies for R-stacked WSe2/WS2 heterobilayers arerequired to understand the experimental results, which is beyond thescope of the current study.Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 6We have observed the correlation-driven nonequilibrium excitonsite transition in near-zero angle-aligned WSe2/WS2 heterobilayers.Beyond the conventional steady-state optical measurements, the site-dependent exciton correlations have been evidenced by the ultrafastoptical spectroscopy, whose effects enable to explain the polarizationswitching and strongly enhanced Pauli blocking when the doping isclose to theMott insulating regime. These findings, with the long-livedinterlayer excitons, are expected to facilitate future researches intothe unexplored nonequilibrium correlations in TMDs heterobilayerssuch as temporal dynamics of Bosonic correlated states and exciton-phonon interaction perturbed by the correlated electrons, whichhave been challenging to explore using conventional opticalspectroscopy.MethodsSample fabricationWe exfoliate monolayers of WSe2 and WS2 from bulk crystals (HQgraphene) and transfer them onto a SiO2/Si substrate. We thenconduct polarization-resolved second harmonic generation (SHG)measurements to identify the crystal orientation. Next, we transfer theWSe2 and WS2 monolayers onto a polyethylene terephthalate (PET)stamp. We assemble a near zero-degree-twist-angle heterostructureusing these materials, with few-layer graphite (FLG) acting as theelectrical contact. This heterostructure is enclosed by the top andbottom hexagonal boron nitride (hBN) dielectric layers, whose thick-ness are 17 nm and 25 nm confirmed by atomic force microscopy(AFM). High-quality single-crystal hBN has been provided by AdvancedMaterials Laboratory (National Institute for Materials Science, Japan).For our experimental setup, we create a back gate using a standarde-beam deposition system, comprising a 5 nm thick Ti layer and a45 nm thick Au layer. Following the fabrication process, we have per-formed additional polarization-resolved SHG measurements. We usethese measurements to precisely determine the twist angle in themonolayer regions of the sample and to distinguish between sampleswith near-zero and near-sixty-degree twist angles in the hetero-structure region.Fig. 5 | VG-dependent nonequilibrium decaying and rising dynamics. a Themeasured early- and long-delay ΔR=R0 spectra (top) and the spectrally integratedΔR=R0 (bottom) as a function of time delay at VG = 4V, showing a temporal evo-lutionof the carrier population.b, c Fast (τfast) and slow (τslow) decay time constantsas a function of VG under three different F ’s. The black, red and green circle cor-respond to the different F ’s of 7.2, 14.5, and 36.2 μJ=cm2, respectively. Each integerfilling ν from −2 to 2 is represented by dashed lines. We propose that the observeddecaying dynamics of τfast shows the carrier cooling dominated by hot phononeffects. Meanwhile, τslow shows 4-order longer dynamics than τfast, which is directlyrelated to the lifetimeof interlayer excitons. Distinct F dependence is evident whenVG<0V, while no significant change is observed when VG ≥0V. d Temporal evolu-tion of carrier population (open black circles). The red line is the fit to the data. Wecorrelate the rise dynamics of X 1 (1.68 eV) under photoexcitation resonant with X2(1.75 eV) to the site transition dynamics (τsite). e VG-dependent evolution of τsite(black circles) with F of 14.5 μJ=cm2. A dashed black line indicates the temporalresolution limit of 132 fs (Supplementary Fig. 11). Vertical error bars inb, c, and e areobtained from the fits.Article https://doi.org/10.1038/s41467-024-47768-6Nature Communications |         (2024) 15:3312 7Optical measurementsA halogen lamp (Thorlabs OSL2) was used as a white-light source forthe reflection contrast (RC)measurements.Theoutput of the lampwaspassed through a single-mode fiber (Thorlabs P1-630P-FC) and colli-mated by a triplet collimator (Thorlabs TC18FC). Then the beam wasfocused onto the sample with a 50× long working distance objective(Mitutoyo Plan Apo SL, NA=0:42). The beam diameter on the samplewas about 1μm, with a beam power of less than 5nW. The reflectedbeam from the samplewas collectedusing the sameobjective and thendispersed using a diffraction grating with 150 grooves per millimeter.This dispersed beamwas then detected using a charge-coupled devicecamera (Oxford Newton 970 EMCCD). The RC spectrum, defined asRC � ðR� R’Þ=R’, was obtained by comparing the reflected lightintensity from the sample (R) to that of a spectrum (R’) from thebackground. The measurement sensitivity is about 0.1%. For the PLmeasurements, we used a 632.8 nmdiode laser, which shares the sameoptical path of the RC measurements. A 633 nm notch filter (ThorlabsNF633-25) was used to spectrally filter out the laser line.Ultrafast pump-probe spectroscopy was conducted using a250kHz Ti:sapphire regenerative amplifier system (Coherent RegA9040). In this system, the 1.55 eV pulses that have a duration of 50femtoseconds were generated and thenwere separated into twopathsusing a beam splitter for the pump-probe spectroscopy. The pumppulses, with variable photon energy ranging from 1.65 eV to 2.3 eV,were produced through Optical Parametric Amplification (CoherentOPA9450).Meanwhile, thewhite-light probepulsesweregeneratedbyfocusing the 1.55 eV pulse on a 0.5-mm thick sapphire disk. Prism pairs(Thorlabs SF10) were placed in both paths to compensate the disper-sion introducedbydispersive optical elements. A dual-slotted chopper(Stanford Research Systems SR 540) was utilized to simultaneouslyrecord the reflectance without pump (R0) and the differential reflec-tance (ΔR) with pump via the dual lock-in detection technique (Stan-ford Research Systems SR 830). The probe beam reflected from thesample was passed through a monochromator (Dongwoo optronMonoRa 512i) before reaching an avalanche photodiode (ThorlabsAPD410A). We recorded ΔR of the probe beam while varying thepump-probe time delay (Δt) and the probe wavelength. Laser polar-ization and power were controlled using a proper set of waveplates(AQWP05M, AHWP05M-580, 10RP52-2) and a linear polarizer (GL10-A,GL10-B, 10GT04) depending on the laser wavelength. The entireexperiment was performed in a closed-cycle Montana cryostat(Cryostation s50) while keeping the base temperature of 4 K.Determination of moiré densityThe moiré density n0 is given by n0 = 2=ðffiffiffi3pa2M Þ for a triangularsuperlattice and the filling factor ν is given by ν =n=n0. Here aM is themoiré superlattice constant which is determined by the twist angle (θ)and lattice mismatch δ = ðaSe � aSÞ=aSe betweenWSe2 and WS2, whereaSe of 0.328 nm is the lattice constant ofWSe2 and aS of 0.315 nm is theone of WS2. We obtain aM ∼ 7:53nm by using the relationaM =aSe=ffiffiffiffiffiffiffiffiffiffiffiδ2 +θ2p. Corresponding moiré density n0 is 2:19 × 1012cm�2for θ= 1:2�.Data availabilityThe data that support the findings of this study are available from thecorresponding author upon request. The full set of pump-probe datagenerated in this study are provided in the Supplementary Informa-tion file.References1. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43–50 (2018).2. Wang, X. et al. Light-induced ferromagnetism in moiré super-lattices. Nature 604, 468–473 (2022).3. Park, H. et al. Observation of fractionally quantized anomalous Halleffect. Nature 622, 74–79 (2023).4. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2moiré superlattices. Nature 579, 353–358 (2020).5. Regan, E. C. et al. Mott and generalized Wigner crystal states inWSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).6. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons inMoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).7. Liu, E. et al. 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Mater. 9, 8 (2023).AcknowledgementsThis research was supported by the National Research Foundation ofKorea (NRF) through the government of Korea (Grant No.2021R1A2C3005905), Scalable Quantum Computer Technology Plat-form Center (Grant No. 2019R1A5A1027055), the Institute for Basic Sci-ence (IBS) in Korea (Grant No. IBS-R034-D1), Global ResearchDevelopment Center (GRDC) Cooperative Hub Program through theNational Research Foundation of Korea (NRF) funded by the Ministry ofScience and ICT (MSIT) (Grant No. RS-2023-00258359), and the corecenter program (2021R1A6C101B418) by the Ministry of Education.Author contributionsJinjae Kim, J.P., and Hyojin Choi fabricated samples. T.K., S.C. and Y.L.performed the device characteristics examination. K.W. and T.T. pro-vided high-quality hBN crystal. Jinjae Kim and J.P. performed the mea-surements. Jinjae Kim, J.P., Jonghwan Kim, M.-H.J. and Hyunyong Choiperformed data analysis and discussed the results. Hyunyong Choisupervised the project. Jinjae Kim and J.P. wrote the manuscript withinput from all co-authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-47768-6.Correspondence and requests for materials should be addressed toHyunyong Choi.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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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/s41467-024-47768-6Nature Communications |         (2024) 15:3312 9https://doi.org/10.1038/s41467-024-47768-6http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Correlation-driven nonequilibrium exciton site transition in a WSe2/WS2 moiré supercell Results Steady-state optical spectroscopy Ultrafast nonequilibrium optical spectroscopy Methods Sample fabrication Optical measurements Determination of moiré density Data availability References Acknowledgements Author contributions Competing interests Additional information