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[Eric A. Arsenault](https://orcid.org/0000-0002-5363-3229), Yiliu Li, [Birui Yang](https://orcid.org/0009-0000-2346-8173), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [James C. Hone](https://orcid.org/0000-0002-8084-3301), [Cory R. Dean](https://orcid.org/0000-0003-2967-5960), Xiaodong Xu, [X.-Y. Zhu](https://orcid.org/0000-0002-2090-8484)

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[Time-domain signatures of distinct correlated insulators in a moiré superlattice](https://mdr.nims.go.jp/datasets/7dbf6175-1742-4f15-9d0e-ab7cf194a007)

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Time-domain signatures of distinct correlated insulators in a moiré superlatticeArticle https://doi.org/10.1038/s41467-024-54886-8Time-domain signatures of distinctcorrelated insulators in a moiré superlatticeEric A. Arsenault 1, Yiliu Li1, Birui Yang 2, Takashi Taniguchi 3,Kenji Watanabe 4, James C. Hone 5, Cory R. Dean 2, Xiaodong Xu6 &X.-Y. Zhu 1Among expanding discoveries of quantum phases in moiré superlattices,correlated insulators stand out as both the most stable and most commonlyobserved.Despite the central importanceof these states inmoiré physics, littleis known about their underlying nature. Here, we use pump-probe spectro-scopy to show distinct time-domain signatures of correlated insulators at fill-ings of one (ν = −1) and two (ν = −2) holes per moiré unit cell in the angle-aligned WSe2/WS2 system. Following photo-doping, we find that the dis-ordering time of the ν = −1 state is independent of excitation density (nex), asexpected from the characteristic phonon response time associated with apolaronic state. In contrast, the disordering time of the ν = −2 state scales with1=ffiffiffiffiffiffiffiffiffinexp, in agreement with plasmonic screening from free holons and dou-blons. These states display disparate reordering behavior dominated either byfirst order (ν = −1) or second order (ν = −2) recombination, suggesting thepresence of Hubbard excitons and free carrier-like holons/doublons, respec-tively. Our work delineates the roles of electron–phonon (e–ph) versuselectron–electron (e–e) interactions in correlated insulators on the moirélandscape and establishes non-equilibrium responses as mechanistic sig-natures for distinguishing and discovering quantum phases.Moiré materials offer unprecedented and highly tunable plat-forms for understanding the emergence of quantum phases ofmatter and for exploring future device applications. Among thequantum phases realized in these systems, the correlated insula-tors stand out as the most commonly observed1–15. Other quan-tum phases, including mixed bosonic-fermionic states16–18,superconductors19,20, and various quantum Hall states21–28, areoften directly related to or appear in the vicinity of correlatedinsulators. Despite the obvious importance of correlated insula-tors in moiré systems, an understanding of the hierarchy of sta-bilizing/destabilizing interactions remains largely limited to areliance on simple models, such as the Hubbard Hamiltonian29,30.Establishing how correlated insulators differ mechanistically isessential to understanding their properties, such as varying cri-tical temperatures (Tc), and connections to other quantum pha-ses. We focus on the most robust quantum states discovered todate at moiré interfaces—correlated insulators at integer fillingfactors of moiré superlattices in transition metal dichalcogenideheterobilayers2–15. We choose the angle-aligned WSe2/WS2 moirésystem, where the ν = −1 and ν = −2 correlated insulator statesexhibit high Tc of ~150 K and ~80 K, respectively2,3,6,8,11. Recently,we suggested that the observed high Tc is, in addition to many-body e–e interactions, related to polaronic stabilization due toe–ph interactions31.Received: 15 June 2024Accepted: 21 November 2024Check for updates1Department of Chemistry, Columbia University, New York, NY, USA. 2Department of Physics, Columbia University, New York, NY, USA. 3Research Center forMaterials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 4Research Center for Electronic and Optical Materials, NationalInstitute for Materials Science, Tsukuba, Japan. 5Department of Mechanical Engineering, Columbia University, New York, NY, USA. 6Department of Physics,University of Washington, Seattle, WA, USA. e-mail: xz2324@columbia.eduNature Communications |          (2025) 16:549 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5363-3229http://orcid.org/0000-0002-5363-3229http://orcid.org/0000-0002-5363-3229http://orcid.org/0000-0002-5363-3229http://orcid.org/0000-0002-5363-3229http://orcid.org/0009-0000-2346-8173http://orcid.org/0009-0000-2346-8173http://orcid.org/0009-0000-2346-8173http://orcid.org/0009-0000-2346-8173http://orcid.org/0009-0000-2346-8173http://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/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0003-2967-5960http://orcid.org/0000-0003-2967-5960http://orcid.org/0000-0003-2967-5960http://orcid.org/0000-0003-2967-5960http://orcid.org/0000-0003-2967-5960http://orcid.org/0000-0002-2090-8484http://orcid.org/0000-0002-2090-8484http://orcid.org/0000-0002-2090-8484http://orcid.org/0000-0002-2090-8484http://orcid.org/0000-0002-2090-8484http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54886-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54886-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54886-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54886-8&domain=pdfmailto:xz2324@columbia.eduwww.nature.com/naturecommunicationsIn the angle-aligned WSe2/WS2 moiré system studied here, thereare two potential wells at high symmetry points in each moiré unitcell, leading to the formation of two narrow moiré bands32,33.Recently, this was experimentally confirmed by Park et al. viareflective magnetic circular dichroism measurements16. At half filling(ν = −1) of the first moiré band (lower energy), many-body correlationresults in gap opening near the top of the valence band and theformation of an upper and a lower Hubbard band (UHB and LHB,respectively). The secondmoiré band is believed to be located withinthe Hubbard gap of the first moiré band and the ν = −1 correlatedinsulator is properly called a charge-transfer (CT) insulator32 insteadof a Mott insulator34. At ν = −2, the inter-band Coulomb energy (U’,rather than the intra-band Coulomb energy, U) favors the half fillingof both bands and the result is a two-band Mott insulator16 ratherthan a trivial band insulator6. To understand these correlated insu-lators, we take a time-domain approach31 in which a pump pulsecreates holons and doublons across the correlated gap and a probepulse detects the disordering dynamics35 via exciton sensing of thedielectric environment2,3,6,8. Such an approach directly accesses thetimescales relevant to electronic or atomic motions that are notaccessible in steady-state spectroscopy or transport measurements.In particular, disordering of a correlated state occurs on a timescaleof the characteristic system response, linked to either electronhopping or the oscillation period of a relevant phonon mode,depending on whether e–e or e–ph interactions play the dominaterole in stabilizing the state36. Here, we apply such an approach cou-pled with fluence-dependent measurements. Through this lens, wemap the mechanistic regimes governing correlated insulator stabi-lity/instability in moiré systems as a function of photoexcitationdensity, nex.Results and discussionSteady-state and transient correlated state sensingFigure 1a illustrates the WSe2/WS2 heterostructure (AB stacked,θ = 60± 1°) featuring top and bottom gates, each consisting of a hex-agonal boron nitride (h-BN) dielectric spacer and a few-layer graphene(Gr) electrode. The dual-gate structure allows either hole (ν <0) orelectron (ν >0) doping from an applied gate voltage (Vg), while theelectricfield at themoiré interface canbemaintained at zero. Figure 1billustrates the static reflectance spectrumof the device as a function ofVg and moiré filling factor ν (defined here as charge filling per moiréunit cell). In the reflectance measurement, the excitonic oscillatorstrength, sensitive to changes in the dielectric environment, is aneffective probe of correlated state formation. We choose the lowestenergy moiré exciton of WSe2 as our dielectric sensor for its highoscillator strength and therefore high sensitivity. At ν = ±1, ±2, weobserve an increased exciton signal as the effective dielectric constantdecreases upon the formation of correlated insulator states2,3,6,8. Fur-ther device characterization can be found in Supplementary Fig. 1.By introducing pulsed laser excitation (and detection), we canfurther perform transient reflectance measurements on the samedevice architecture31. This allows us to obtain both time-resolved andgate-dependent reflectance spectra (see Supplementary Figs. 2–3). Forexcitation, we employ a pump with photon energy (1.55 eV) below theoptical gaps of WSe2 and WS2 to uniquely target the correlated states.This avoids pump-induced interlayer exciton formation which wouldresult in long-lived responses on the nanosecond time scale33. Theabsorption of a pump photon excites a hole from the LHB of the cor-related insulator deep into the valenceband(s). The excited holes relaxwithin this continuous manifold on ultrafast time scales, typically ofthe order of 10s–100s femtoseconds due to scattering with otheracΔt = 2 psdΔt = 8 pseFluence(μJ/cm2)371014285685Δt = 50 psbGrVtVbWSe2WS2h-BNh-BNGrGrFig. 1 | Steady-state and transient correlated state detection via exciton sen-sing. a Schematic of device architecture where the WSe2/WS2 heterobilayer issymmetrically encapsulated by top and bottom gates (Vt and Vb, respectively)consisting of hexagonal boron nitride (h-BN) and few-layer graphene (Gr). b Gated(Vg = Vt =Vb) steady-state reflectance spectrum of the lowest energy moiré excitonof WSe2. Here, ΔR =R –R0 where R is the reflected signal from the bilayer and dualgate region while R0 is the reflected signal from a region with gates and no bilayer.c–e Gated (Vg = Vt =Vb) transient reflectance response as a function of pumpfluence at Δt = 2, 8, 50ps, respectively. Shown is the integrated response cen-tralized around the lowest energy WSe2 moiré exciton sensor. The differentfluence-dependent responses have been offset and multiplied by −1 for clarity.Associated fluence labels are shown on the side of panel e and are consistentlycolored throughout the other panels. Here, ΔR =Ron –Roff where the subscriptindicates either pump-on or -off spectra. See Methods for further details. All datawere collected at 11 K.Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 2www.nature.com/naturecommunicationscarriers and optical phonons37, towards the upper unoccupied band(s)(the UHB or the CT band)32. The result is the formation of holon-doublon pairs across the correlation gap (see Supplementary Fig. 4 forschematic). The presence of holons and doublons leads to disorderingof the correlated insulator on characteristic timescales determined bye–e or e–ph interactions36. Recovery of the charge order reaches theso-called “bottleneck” on a timescale determined by recombination ofholons and doublons across the gap35. The timescale of disordering iscaptured by the transient increase in the effective dielectric constant,monitored through the exciton sensor covered by a probe pulse cen-tered at 1.65 eV (spanning the lowest energy moiré exciton of WSe2).We note that in the current measurements, we focus on the holedoping side because our transientmeasurements aremost sensitive tothe correlated states which reside exclusively in the same layer as theWSe2 excitonic sensor due to the type-II band alignment at the WSe2/WS2 interface2,3. Correlated state recovery is tracked through thesubsequent reduction in the effective dielectric constant as the origi-nal insulator behavior reemerges.Figure 1c–e show transient reflectance spectra integrated aroundthe lowest energy moiré transition of WSe2 as functions of bothapplied gate voltage, Vg, and pump-probe time delay, Δt, at varyingpump fluences. The pump fluence is increased until saturating beha-vior is reached in the transient response (Supplementary Fig. 5). Inagreement with the static reflectance spectra, correlated stateresponses at ν = −1, −2 are observed in the time-resolved spectra, withthe maximum response (disordering) in a few ps and recovery (reor-dering) in tens of ps. With increasing fluence, the magnitude of thecorrelated state response also increases. Intriguingly, the response ofthe ν = −2 state to pump-induced disordering occurs in a broader Vgrange than the ν = −1 state does (Fig. 1c–e), in contrast to the steady-state measurement (Fig. 1b). This may suggest that the transientmeasurements are particularly sensitive to an expanse of otherwisehidden states with varying charge ordering around ν = −2, as predictedfor lower filling factors38,39. In the present case, the magnitude of thetransient response around ν = −2 indicates a significant change in thedielectric environment and therefore a substantial non-equilibriumphotoinduced response. The states in this region also appear to havevarying recovery timescales (Fig. 1e) which can be seen as a narrowingin the transient response along the Vg axis at later Δt, particularly atlower pump fluence. In the following, we focus on the disordering andreordering dynamics at ν = −1, −2.Distinct temporal responses of correlated insulator statesFigure 2a, b show the transient reflectance responses of the ν = −1,−2 states for the indicated pump fluences (f = 3–85 µJ/cm2). Followingthe coherent artifact arising frompump-probe overlap atΔt = 0 ps, thenon-equilibrium response of the correlated states is initially related todisordering of the equilibrium charge configuration, as evidenced byan increase in the effective dielectric constant detected throughbleaching of the exciton transition. In each case, the disorderingreaches a maximum magnitude after a few ps and subsequentlyrecovers. The black solid curve in each case is a fit consisting of a singleexponential decay (disordering) and either a single exponential firstorder (ν = −1) or a second order (ν = −2) recovery (reordering); furtherfit details can be found in the Methods section (fit residuals shown inSupplementary Fig. 6 and unnormalized data and fits in Supplemen-tary Fig. 7). The chosen functional form for the recovery dynamics willbe explicitly discussed further below. Finally, an additional offset isalso included to account for the much longer timescale (»100 ps)recovery dynamics. This offset is negligible at low excitation fluencebut becomes significant at f > 14 µJ/cm2. As detailed in control experi-ments on the undoped charge neutral state (ν =0, SupplementaryFig. 8) the long-lived offset can be attributed to hole injection into theWSe2/WS2 moiré structure from thermionic emission of hot electronsin the unavoidably photo-excited Gr electrodes at sufficiently highexcitation densities (Supplementary Fig. 9)40,41. Concomitant with thedynamic responses from disordering and recovery are temporaloscillations of interlayer phonon modes which have been discusseda ν = -1Fluence(μJ/cm2)371014285685b ν = -2Fluence(μJ/cm2)371056851428cν = -1ν = -2Fluence (μJ/cm2)3 7 10 28 56 85143 7 10 28 56 8514Fl. (μJ/cm2)dτrτdFig. 2 | Non-equilibrium correlated insulator response. a, b Fluence-dependenttemporal response of the ν = −1, −2 states, respectively. The time traces wereaveraged in a narrowwindow about themaximumof the lowest energyWSe2moiréexciton sensor. Each fluence-dependent transient has been normalized for clearcomparisonof the dynamical response (see Supplementary Fig. 7 for unnormalizeddata where the overall signal trend is preserved). Data are shown in shaded colorswhile the fits used for time constant extraction are shown in black. See theMethodssection for further details. Throughout the panels, increasing pump fluence isshown from light to dark shades. All fluence-dependent data are colored con-sistently for each of the filling factors throughout the figure. All data were collectedat 11 K.c,dTomoreeasily anddirectly visualize the trends in thefluence-dependentdynamics (without the substantial interlayer phonon response), the normalized fitsfrom (a, b) are shown in (c, d), respectively. Arrows indicating the time constantsassociated with the disordering dynamics (τd) and recovery dynamics (τr) arelabeled in (d).Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 3www.nature.com/naturecommunicationselsewhere42. Thesemodes are coherent phononwavepackets launchedfrom strain fields induced by the pump at the Gr electrodes. Thesewavepackets propagate through the h-BN prior to impinging on theheterobilayer with an apparent delay as determined by the phonongroup velocity.To more clearly view the disordering and recovery dynamicswithout interference from the coherent phonon oscillations, we replotthe normalized fits independently from the data in Fig. 2c, d for ν = −1,−2, respectively. The disordering and recover dynamics of the ν = −1state are found to be independent of fluence in the entire investigatedrange (f = 3–85 µJ/cm2). In contrast, the ν = −2 state exhibits distinctbehavior—both the disordering and the recovery accelerate withincreasing fluence. To quantitatively compare the two correlatedinsulator states, we plot in Fig. 3a, b the disordering time (τd) for the atν = −1 and −2 states, respectively, as functions of fluence.For the ν = −1 state, disordering occurs with a time constantτd = 3.3 ± 0.2 ps, independent of the photoexcited carrier density, nex,of the correlated insulator (up to saturation of the observed transientresponse in the investigated pump fluence range). This result pre-cludes a pure electronically-driven disordering mechanism, the rate(=1/τd) ofwhich should increasewithnex due to carrier screening of themany-body electronic interactions. Instead, the constant τd suggests atime scale characteristic of e–ph interactions and rate-limited by theoscillation period of the relevant phonon mode(s), often described asthe amplitude mode in charge density wave (CDW) systems36,43. Ourinitial pump-probe measurements on the ν = −1 correlated insulatorstate in the WSe2/WS2 moiré superlattice revealed thermal activationbehavior in the disordering process, suggesting the polaronic natureof the correlated insulator, in agreement with an ab initio calculation31.The independence of disordering rate on nex observed here not onlyconfirms the polaronic interpretation, but also reveals the dominanceof e–ph interactions in stabilizing the charge order in the ν = −1 cor-related insulator. Such a polaronic and ordered correlated state issimilar to a CDW state44; however, unambiguous delineation betweenMott insulators versusCDWordering remains a subject of discussion45.The observed τd can be understood as relating to the oscillationperiod (typically taken as either a half or quarter period) of phononmode(s) involved, as shown in the related CDW systems36,43. The cor-responding mode frequency is consistent with the fact that the moirédeformation potential likely involves acoustic phonons accessible viathe momentum range defined by the mini-Brillouin zone of the moirésuperlattice31. Interestingly, in the fit residuals, a low frequency oscil-lation attributable to this phonon mode is potentially present at Δt <10 ps; however, this remains speculative as this feature is obscured bythe interlayer modes after only a single period (Supplementary Fig. 6).Further suggestive, this behavior is noticeably absent in the controlν =0 data (Supplementary Fig. 8).In stark contrast to the behavior of the ν = −1 state, the disorderingtime, τd, for the ν = −2 state displays a strong dependence on fluence(Fig. 3b). This is unexplainable by only consiring e–ph interactions andinstead suggests the importanceofmany-body electronic interactions.In particular, we find that the disordering time can be well-describedby the functional form τd / 1=ffiffiffiffiffiffiffinexp+ τconst (solid black curve inFig. 3b). The square root dependence on doping density is well-knownfor the 2D plasmon frequency36,43. In other words, disordering as aresult of photoexcited carrier screening occurs on a characteristictimescale inversely proportional to the plasmon frequency, ωp36, asreported for the ultrafast collapse of order in the excitonic insulator1T-TiSe243. We conclude that disordering of the ν = −2 correlatedinsulator at theWSe2/WS2moiré interfaceobservedhere isdeterminedby the electronic response, namely screening by photodoped holonsand doublons. Our previousmeasurement on temperature-dependentdisordering of the ν = −2 state shows a thermal activation energy lowerthan that of the ν = −1 state31. The current result, in combination withour previous finding, reveals that plasmonic screening overwhelmspolaronic stabilization in the disordering of the ν = −2 correlatedinsulator. We note that, while the observed τd is dominated byscreening as shown by the 1=ffiffiffiffiffiffiffiffiffinexpdependence, there seems to be afundamental limit to τd as captured by the offset, τconst = 2.2 ± 0.1 ps.The exact origin of this offset is not known, but we speculate it may beassociated with either additional e–ph interactions31 or a deviationfrom the pure 2D plasmon response in the moiré superlattice46. Papajand Lewandowski recently theoretically proposed that the coupling ofcharge order to the collective plasmon response can result in plasmonband folding and gap opening, leading to an upper bound in theplasmon frequency46. These issues deserve further investigations.The fundamental distinction between the ν = −2 and ν = −1 insu-lator states can be understood from the difference in charge occupa-tion of each moiré unit cell. In the ν = −2 state, there are two holes (ontwo different sites) within each moiré unit, giving rise to the Coulomba bν = -1 ν = -2Fig. 3 | Disordering in the polaronic versus plasmonic limits. aDisordering timeconstant (τd) for ν = −1 as a function of fluence. The linear fit trend line is shown inblack. bDisordering time constant (τd) for ν = −2 as a function of fluence. Shown inblack is the fit of the form / 1=ffiffiffiffiffiffiffiffiffinexp+ τconst. Throughout the figure, all error barsindicate 99% confidence intervals. Large circle outlines have been added to aidwithdata visualization. The fluence-dependent shaded colors for the ν = −1, −2 states areconsistent with the data shown elsewhere in the text. See the Methods section forfurther details.Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 4www.nature.com/naturecommunicationsrepulsion energy U’. For comparison, U’ is absent for the ν = −1 statewhere the second site remains unoccupied. The magnitude of U’ (onthe order of 50–100meV)16,32 dominates over the polaron stabilizationenergy (~13meV estimated from thermal activation)31. As a result,photodoping of the two-band correlated insulator, ν = −2, leads to afree carrier-like plasmonic response. In contrast, the stronger polaro-nic localization for the ν = −1 state diminishes the collective plasmoncharacter for holons and doublons.The fundamental distinction between ν = −1 and ν = −2 is alsoreflected in the recovery dynamics, which are determined by holon-doublon recombination across the correlation gap35. Figure 4a showsthe reordering time constants obtained from single exponential fits tothe recovery component of the data in Fig. 2. For the ν = −1 state, thereordering is captured as a first order process implied in the mono-exponential fit and verified by the approximate independence ofrecovery time constants τr on nex. Such a first-order kinetic processreveals that recombination of the perturbed ν = −1 state derives from a“single body”, i.e., a local holon-doublon pair called a Hubbardexciton47. This local holon-doublon pair is fortified by polaronic sta-bilization, which inhibits their separation into a free holon and a freedoublon.However, for ν = −2, the single-exponential recovery time con-stant τr decreases with nex, indicating the failure of the first orderkinetic model and that the recovery process is of higher order in nex(see Supplementary Fig. 10a). We find that the recovery for ν = −2 issecond order, i.e., the recovery rate is proportional to nex2. To fit therecovery to a second order kinetic scheme, we use the functional formAr/(1+Ar∙t/τr, eff), where Ar is a constant proportional to nex(0), the initialconcentration of photo-excitation as controlled via the pump fluence.Figure 4b shows the resulting effective second order recovery timeconstant, τr, eff, which is correctlynex-independent (see SupplementaryFig. 10b). The apparent second order process supports the two-bodyrecombination kinetics of a holon and a doublon, in excellent agree-ment with the free-carrier nature of photo-doping of the ν = −2 cor-related insulator state.In summary, we find distinct disordering and reorderingmechanisms for the ν = −1 and −2 states in the WSe2/WS2 moirésuperlattice. The non-equilibrium response of the ν = −1 state revealsits dominant polaronic nature, leading to disordering determined by acharacteristic phonon time and re-ordering by the first-order recom-bination of a localized holon-doublon pair. In contrast, in theν = −2 state, e–e interactions dominate over e–ph interactions. As aresult, photodoping of the ν = −2 state results in free carrier-like holonsand doublons, leading to disordering dominated by carrier screeningand re-ordering dominated by second-order recombination of freeholons and free doublons. The distinct non-equilibrium responses ofthe two correlated states define the richness of behavior accessible bya time-domain view. While we do possess sufficient sensitivity in theexperiments presented here to resolve the correlated insulators atfractional filling of the moiré superlattice6,8, further improvement insignal-to-noise ratio may allow us to resolve these states at fractionalfillings and reveal their distinct dynamics. This remains a key objectiveof our research program on time-domain views of moiré quantummatter. Overall, the delicate balance or competition between e–e ande–ph interactions may provide an additional angle in understandingand ultimately controlling quantum phases on the moiré landscape oreven in realizing otherwise hidden metastable phases.Methods60° device fabrication and gatingThe WSe2 and WS2 monolayers are mechanically exfoliated from flux-grown bulk WSe2 crystals and commercially purchased bulk WS2crystals (HQ Graphene), respectively. Prior to transfer, the crystalorientation of WSe2 and WS2 monolayers are first determined viapolarization-resolved second harmonic generation (P-SHG). Themonolayers are then stacked together by a dry-transfer techniquewitha polycarbonate stamp. To distinguish between R- and H-stackedconfigurations, P-SHG is again applied to the heterobilayer region afterthe device is fabricated, with results compared to individual mono-layers. The error bars for the angle determination are well within ±1°.The sample is grounded viaGr contacts connected to the heterobilayerand single crystal h-BN dielectrics andGr gates are used to encapsulatethe device and provide control of the carrier density and displacementfield (if desired) via external source meters (Keithly 2400). SF6 radio-frequency plasma is applied to the stack to etch the encapsulatingh-BN and create connection to the Gr gates contacts. All electrodes area bFirst Order Second Orderν = -1ν = -2ν = -2Ar ∙ exp[-t/τr] Ar 1 + (Ar ∙ t)/τr, effFig. 4 | Charge reordering of distinct correlated insulators. a Reordering timeconstant (τr) for ν = −1 and ν = −2 as a function of fluence. Here, τr was extractedbased on considering the recovery as a first order process (mono-exponentialfunctional form, inset ina). The black line for ν = −1 shows the linearfit trend line forτr as a function of fluence. The dotted black line for ν = −2 shows the linear inter-polation between data points to highlight the data trend. b Effective reorderingtime constant (τr, eff) for ν = −2 as a function of fluence. Here, τr, eff was extractedbased on considering the recovery for ν = −2 as a second order process (inset in b).The black line shows the linear fit for τr, eff as a function of fluence. Throughout thefigure, all error bars indicate 99% confidence intervals. Large circle outlines havebeen added to aidwith data visualization. The fluence-dependent shaded colors forthe ν = −1,−2 states are consistentwith thedata shownelsewhere in the text. See theMethods section for furtherdetails and Supplementary Fig. 10 forplots ofkr (= 1/τr).Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 5www.nature.com/naturecommunicationsdefined with electron beam lithography and made of a three-layermetal film of Cr/Pd/Au (3 nm/17 nm/60nm).Spectroscopic measurementsFor the spectroscopic measurements, the sample is cooled down toT = 11 K under vacuum (<10−6 torr) with a closed-cycle liquid heliumcryostat (FusionX-Plane,Montana Instruments).We note that no laser-induced continuous heating was observed at any of the employedpump fluences. Steady-state reflectancemeasurements are carried outwith a 3200K halogen lamp (KLS EKE/AL). A 715 nm low pass filter isemployed to avoid potential photodoping effects. Following collima-tion, the lamp light is focused onto the sample/substrate with a 100X,0.75NAobjective. The reflected light is collectedby the sameobjectiveand then dispersed with a spectrometer onto an InGaAs array (PyLoN-IR, Princeton Instruments). The steady-state reflectance spectrumis obtained by contrasting the reflected signal from the sample (R),which includes the bilayer and dual gate region, and the effectivesubstrate (R0), which includes a region with gates and no bilayer asfollows: (R-R0)/R0. For the spatially-resolved reflectance experimentsused for mapping of the bilayer, a dual-axis galvo mirror scanningsystem is employed48. Following spatial scanning of the sample ascontrolled via the angles of the galvo mirrors, the reflected light isspatially filtered through a pinhole and collected by the detector.The steady-state photoluminescence (PL) experiments are per-formed with a HeNe laser (Model 31-2140-000, Coherent). The exci-tation power is set to the range 50–100 nW and focused onto thesample. The PL signal was spectrally filtered from the laser using along-pass filter prior to dispersal with a spectrometer and detection(the same detection system described above is employed here).The pump-probe experiments are seeded by femtosecond pulses(250kHz, 1.55 eV, 100 fs) generated by a Ti:sapphire oscillator (Mira900, Coherent) and regenerative amplifier (RegA 9050, Coherent).The output is then split to form the pump and probe arms. For theprobe, a fraction of the fundamental is focused into a sapphire crystalto generate a white light continuum which is then spectrally filtered(750 ± 40 nm band pass filter) to cover the lowest energy WSe2 moiréexciton. The pump beam (800nm, fundamental) is then directedtowards a motorized delay stage to control the time delay, Δt, andpassed through an optical chopper to generate pump-on and -offsignals. Following this, the pump and probe arms are directed colli-nearly to the sample through an objective (100X, 0.75 NA). The pumpand probe spot diameters are ~2.36μm and ~0.9μm, respectively. Duetemporal broadening from the objective, our instrument responsefunction is ~200 fs. The same objective is used to collect the reflectedlight which is spectrally filtered to remove the pump and dispersedonto an InGaAs detector array (PyLoN-IR, Princeton Instruments). Thepump-on and -off spectra at varying Δt are then used to calculate thetransient reflectance signal (ΔR/R) where ΔR =Ron – Roff with the sub-script indicates either pump-on or -off spectra.Assignment of filling factorsThe charge density, n, in the WSe2/WS2 heterostructure, controlled bythe applied gate voltages (Vt and Vb for the top and bottom gates,respectively), is determined using the parallel-plate capacitor model:n= εε0ΔVtdt+ εε0ΔVbdb, where ε � 3 is the out-of-plane dielectric constant ofhBN, ε0 is the permittivity of free space, ΔVi is the applied gate voltagerelative to the valence/conduction band edge, and di is the thicknessof the hBN spacer. The moiré density, n0, is determined based on themoiré lattice constant, aM, and is given by n0 =2ffiffi3pa2M. The filling factor,v, estimated as the ratio between the charge doping and moiré den-sities, is fit based on the experimental gate-dependent steady-statereflectance and photoluminescence measurements (Fig. 1b and Sup-plementary Fig. 1b). For the 60° device, the thickness of the top andbottom hBN spacers is determined to be dt � 36:4 and db � 39:6nm, respectively. The twist angle is determined to be ~0.8°.Data analysisIn the following we describe the data processing involved in analyzingboth the overall transient signal and the disordering/recoverydynamics. The data is first collected as a function of probe energy andpump-probe delay, Δt, at varying Vg and pump fluence. To generateSupplementary Fig. 2–3, pump-probe spectra are collected at a seriesof Δt at varying Vg and pump fluence. At each Δt and for each fluence,the Vg-dependent spectra are then combined as a function of probeenergy versus Vg to generate two-dimensional pseudo-color plots. Wetake Vg = Vt = Vb unless otherwise specified. The data from these plotsare then integrated in the range 1.67–1.69 eV about the maximum ofthe lowest energy WSe2 moiré sensor, normalized, offset, and multi-plied by -1 to generate Fig. 1c–e.To analyze the time traces, the signal in a ~0.01 eV window aboutthe maximum of the lowest energy moiré band of WSe2 is averaged(e.g., Fig. 2a, b, Supplementary Figs. 7 and 8a). For Fig. 2a, b, thesetraces are then normalized for better comparison of the dynamicsspecifically. The overall |ΔR/R| trend (Supplementary Fig. 5) is analyzedby averaging the rectangular region about the maximum signal alongboth the probe energy axis (in a ~0.01 eV window about the maximumof the lowest energymoiré band ofWSe2) and temporal dimensions (inthe Δt window from 7.5 to 8.5 ps).To isolate thedynamics from the abovementioned time traces,fitsareperformed. For ν = −1 and−2, the normalizedfits compareddirectlyto the data are shown in Fig. 2a, b (black lines) as well as separately inFig. 2c, d. The corresponding normalized residuals are shown in Sup-plementary Fig. 6. A comparison between the unnormalized fits anddata for both states is shown in Supplementary Fig. 7. For ν = 0, Sup-plementary Fig. 8a shows the fits (where applicable) in red where thecorresponding residuals are shown in Supplementary Fig. 8b, c. For allfits, the coherent artifact region arising from pump-probe overlap isomitted. All errors are given by 99% confidence intervals.The ν = −1 data for pumpfluence f = 3, 7, 10, and 14 µJ/cm2 arefit bya biexponential function with disordering captured by the functionalformAd exp[t/τd] and recovery byAr exp[t/τr]. The ν = −1 data for pumpfluence f = 28, 56, and 85 µJ/cm2 are fit using the aforementioned formwith the inclusion of an additional term, A∞ exp[t/τ∞], to account forthe additional component relating to thermionic emission (discussedfurther below). Here, τ∞= 500ps is fixed as the timescale for thisprocess is beyond the duration of the present experiment and istherefore unresolvable. Figures 3–4 show the obtained time constantsfor disordering, τd, and recovery, τr, as a function of fluence. Supple-mentary Fig. 10 shows the corresponding rate of recovery, kr = 1/τr, as afunction of fluence.The ν=−2data forpumpfluence f=3, 7, 10, 14, 28, and56 µJ/cm2 arefit using a function with disordering captured by the functional form Adexp [t/τd] and recovery by Ar /(1+Ar∙t/τr, eff). As explained in the text andsupported by Fig. 4 (τr/τr, eff as a function of fluence) and SupplementaryFig. 10 (kr/kr, eff as a function of fluence), the recovery for ν= −2 is bestrepresented by a second order process as captured by the employedfunctional form for recovery. Figure 3 shows the corresponding τd as afunction of fluence. The ν= −2 data for pump fluence f=85 µJ/cm2 is fitusing the above form with the inclusion of an additional term, A∞ exp[t/τ∞], to account for the additional component relating to thermionicemission (discussed further below). Here, τ∞= 500ps is fixed as thetimescale for this process is beyond the duration of the presentexperiment. We note that unlike ν=−1, this term was not necessary forfitting the f=28 and 56 µJ/cm2 data. This is likely because the overallincreased signal strength for ν=−2 versus ν=−1 obscures contributionsfrom this component at f=28 and 56 µJ/cm2 in the former.Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 6www.nature.com/naturecommunicationsThe ν = 0data for pumpfluence f = 28, 56, and 85 µJ/cm2 is fit usinga function with rise captured by the functional form Arise exp[t/τrise]and an additional long-lived component by A∞ exp[t/τ∞]. Here,τ∞= 500ps is againfixed as the timescale for this process is beyond theduration of the present experiment. The average τrise = 1.4 ± 0.4 ps (seeSupplementary Fig. 8d). Meaningful fits were unable to be attained forf < 28 µJ/cm2.We attribute the observed dynamics for ν =0 with f > 14 µJ/cm2 (aswell as the presence of the additional long-lived component, τ∞, forν = −1, −2) to hot hole injection (into the WSe2/WS2 bilayer) via ther-mionic emission following unavoidable photo-excitation of the Grelectrodes at sufficiently high excitation densities (schematicallydepicted in Supplementary Fig. 9)40,41. We note that in SupplementaryFig. 9, the shown Gr and h-BN band alignment is based on ref. 41, whilethe WSe2 and WS2 band alignment is based on ref. 49. As described inrefs. 40,41, photoexcited carriers in the Gr can rapidly thermalize viascattering (e.g., Auger-like process). Following this, ‘hot’ carriers(specifically holes) in the tail of the resulting thermal distribution havesufficient energy to overcome the Gr/h-BN/WSe2 (or Gr/h-BN/WS2)energetic barrier (i.e., valence band offset) and to undergo interlayertransfer. Further, this process is highly pump fluence-dependent, asalso captured clearly in the time traces of the ν =0where dynamics areonly observed for f > 14 µJ/cm2. This is consistent with the additionallong-lived component only being necessary in this same high fluenceregime for proper fitting of the correlated state dynamics. Interlayercharge transfer ultimately driven via thermionic emission is linked to amulti-component timescale with a faster (<90 fs) and a slower (~1 ps)contribution41. While the former is unresolvable within our instrumentresponse function (and is mainly related to the thermalization ratherthan the transfer process), the latter agrees well with the fit τrise forν =0 as expected (and is mainly related to interlayer transfer). Thelong-lived component (τ∞) in our measurement (for ν = 0, −1, −2) mayresult from, in addition to this thermionic hole transfer and charging,transient lattice heating. This process does not interfere with theobserved disordering/reordering of the ν = −1, −2 states.Data availabilityThe data within this paper are available upon request.References1. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).2. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2moiré superlattices. Nature 579, 353–358 (2020).3. Regan, E. C. et al. Mott and generalized Wigner crystal states inWSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).4. Wang, L. et al. Correlated electronic phases in twisted bilayertransition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).5. Shimazaki, Y. et al. Strongly correlated electrons and hybrid exci-tons in a moiré heterostructure. Nature 580, 472–477 (2020).6. Xu, Y. et al. Correlated insulating states at fractional fillings ofmoirésuperlattices. Nature 587, 214–218 (2020).7. Li, H. et al. 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XYZ acknowledges support for data analysis and modeldevelopment by Programmable Quantum Materials, an Energy FrontierResearch Center funded by the U.S. Department of Energy (DOE), Officeof Science, Basic Energy Sciences (BES), under award DE-SC0019443.E.A.A. gratefully acknowledges support from the Simons Foundation asa Junior Fellow in the Simons Society of Fellows (965526). K.W. and T.T.acknowledge support from the JSPS KAKENHI (Grant Numbers21H05233 and 23H02052) and World Premier International ResearchCenter Initiative (WPI), MEXT, Japan. We thank Yinjie Guo for assistancewith sample mounting and Dipti Jasrasaria and Timothy Berkelbach forhelpful discussions.Author contributionsE.A.A., Y.L., and X.Y.Z. conceived this work. E.A.A. and Y.L. carried out allspectroscopic measurements. B.Y. was responsible for sample fabrica-tion and characterization, under the supervision of C.R.D. T.T. and K.W.provided the h-BN crystal. J.C.H. provided the WSe2 crystal. E.A.A. andX.Y.Z. interpreted the results, with input from X.X. The manuscript wasprepared by E.A.A. and X.Y.Z. in consultation with all other authors.X.Y.Z. supervised the project. All authors read and commented on themanuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-54886-8.Correspondence and requests for materials should be addressed toX.-Y. Zhu.Peer review information Nature Communications thanks JacekMajewski, Su-Fei Shi, and the other, anonymous, reviewer for theircontribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-024-54886-8Nature Communications |          (2025) 16:549 8https://doi.org/10.1038/s41467-024-54886-8http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Time-domain signatures of distinct correlated insulators in a moiré superlattice Results and discussion Steady-state and transient correlated state sensing Distinct temporal responses of correlated insulator states Methods 60° device fabrication and gating Spectroscopic measurements Assignment of filling factors Data analysis Data availability References Acknowledgements Author contributions Competing interests Additional information