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Edoardo Lopriore, Charalambos Louca, Armando Genco, Irantzu Landa, Daniel Erkensten, Charles J. Sayers, Samuel Brem, Raul Perea-Causin, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Christoph Gadermaier, Ermin Malic, Giulio Cerullo, Stefano Dal Conte, Andras Kis

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[Electrically tunable ultrafast dynamics and interactions of hybrid excitons in a 2D semiconductor bilayer](https://mdr.nims.go.jp/datasets/8efdc065-6444-428b-b045-975fa3d189d3)

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Electrically tunable ultrafast dynamics and interactions of hybrid excitons in a 2D semiconductor bilayerArticle https://doi.org/10.1038/s41467-025-65733-9Electrically tunable ultrafast dynamics andinteractions of hybrid excitons in a 2Dsemiconductor bilayerEdoardo Lopriore 1,2,10, Charalambos Louca 3,4,10, Armando Genco 3 ,Irantzu Landa3, Daniel Erkensten5, Charles J. Sayers 3, Samuel Brem 5,Raul Perea-Causin 6, Kenji Watanabe 7, Takashi Taniguchi 8,Christoph Gadermaier 3, Ermin Malic 5 , Giulio Cerullo 3,9,Stefano Dal Conte 3 & Andras Kis 1,2Extended efforts have been devoted to the study of strongly-interacting exci-tons and their dynamics, towards macroscopic quantum states of matter suchas Bose-Einstein condensates of excitons and polaritons. Momentum-directlayer-hybridized excitons in transition metal dichalcogenides have attractedconsiderable attention due to their high oscillator strength and dipolar nature.However, the tunability of their interactions and dynamics remains unexplored.Here, we achieve an unprecedented control over the nonlinear properties ofdipolar layer-hybridized excitons in an electrically gated van der Waals homo-bilayer monitored by transient optical spectroscopy. By applying a verticalelectric field, we reveal strong Coulomb interactions of dipolar hybrid excitons,leading to opposite density-dependent energy shifts of the two main hybridspecies based on their dipolar orientation, together with a strongly enhancedoptical saturation of their absorption. Furthermore, by electrically tuning theinterlayer tunneling between the hybridized carriers, we significantly extend theformation time of hybrid excitons, while simultaneously increasing their decaytimes. Our findings have implications for the search on quantum blockade andcondensation of excitons and dipolaritons in two-dimensional materials.Light-matter interactions in van der Waals heterostructures of two-dimensional materials have been widely investigated for fundamentalstudies as well as optoelectronic device applications1–3. Linear andnonlinear optical properties of excitons in bilayers of transitionmetal dichalcogenides (TMDCs) can be tailored with unprecedentedflexibility, allowing the exploration of macroscopic quantumstates of matter4,5 and novel quantum photonics applications6. Type-IITMDC heterobilayers can be optically excited to form strongly-bound inter-layer excitons with a characteristic out-of-plane staticdipole due to the spatial separation of the electron and hole wave-functions in different constituent layers7–9. Interlayer excitons arecharacterized by the field tunability of their emission energy via thequantum-confined Stark effect10,11, with long lifetimes and diffusionlengths12,13.Received: 7 February 2025Accepted: 22 October 2025Check for updates1Institute of Electrical and Microengineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland. 2Institute of Materials Science andEngineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland. 3Dipartimento di Fisica, Politecnico di Milano, Milano, Italy. 4Nano-PhotonicsCentre, Cavendish Laboratory, University of Cambridge, Cambridge, UK. 5Philipps-UniversitätMarburg,Marburg, Germany. 6StockholmUniversity,Stockholm, Sweden. 7Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 8Research Center forMaterials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. 9CNR-IFN, Milano, Italy. 10These authors contributed equally: EdoardoLopriore, Charalambos Louca. e-mail: armando.genco@polimi.it; ermin.malic@uni-marburg.de; stefano.dalconte@polimi.it; andras.kis@epfl.chNature Communications |        (2025) 16:10710 11234567890():,;1234567890():,;http://orcid.org/0000-0001-8975-413Xhttp://orcid.org/0000-0001-8975-413Xhttp://orcid.org/0000-0001-8975-413Xhttp://orcid.org/0000-0001-8975-413Xhttp://orcid.org/0000-0001-8975-413Xhttp://orcid.org/0000-0002-1122-3133http://orcid.org/0000-0002-1122-3133http://orcid.org/0000-0002-1122-3133http://orcid.org/0000-0002-1122-3133http://orcid.org/0000-0002-1122-3133http://orcid.org/0000-0002-1292-2614http://orcid.org/0000-0002-1292-2614http://orcid.org/0000-0002-1292-2614http://orcid.org/0000-0002-1292-2614http://orcid.org/0000-0002-1292-2614http://orcid.org/0000-0002-3777-5155http://orcid.org/0000-0002-3777-5155http://orcid.org/0000-0002-3777-5155http://orcid.org/0000-0002-3777-5155http://orcid.org/0000-0002-3777-5155http://orcid.org/0000-0001-8823-1302http://orcid.org/0000-0001-8823-1302http://orcid.org/0000-0001-8823-1302http://orcid.org/0000-0001-8823-1302http://orcid.org/0000-0001-8823-1302http://orcid.org/0000-0002-2229-0147http://orcid.org/0000-0002-2229-0147http://orcid.org/0000-0002-2229-0147http://orcid.org/0000-0002-2229-0147http://orcid.org/0000-0002-2229-0147http://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/0000-0001-6613-9644http://orcid.org/0000-0001-6613-9644http://orcid.org/0000-0001-6613-9644http://orcid.org/0000-0001-6613-9644http://orcid.org/0000-0001-6613-9644http://orcid.org/0000-0003-1434-9003http://orcid.org/0000-0003-1434-9003http://orcid.org/0000-0003-1434-9003http://orcid.org/0000-0003-1434-9003http://orcid.org/0000-0003-1434-9003http://orcid.org/0000-0002-9534-2702http://orcid.org/0000-0002-9534-2702http://orcid.org/0000-0002-9534-2702http://orcid.org/0000-0002-9534-2702http://orcid.org/0000-0002-9534-2702http://orcid.org/0000-0001-8582-3185http://orcid.org/0000-0001-8582-3185http://orcid.org/0000-0001-8582-3185http://orcid.org/0000-0001-8582-3185http://orcid.org/0000-0001-8582-3185http://orcid.org/0000-0002-3426-7702http://orcid.org/0000-0002-3426-7702http://orcid.org/0000-0002-3426-7702http://orcid.org/0000-0002-3426-7702http://orcid.org/0000-0002-3426-7702http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65733-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65733-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65733-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65733-9&domain=pdfmailto:armando.genco@polimi.itmailto:ermin.malic@uni-marburg.demailto:stefano.dalconte@polimi.itmailto:andras.kis@epfl.chwww.nature.com/naturecommunicationsEvidence supporting the occurrence of high-temperatureBose–Einstein condensation (BEC) of interlayer excitons in TMDCheterobilayers has been recently reported, although a clear observa-tion of quantum phase transitions in these systems is still missing14. Inthe past, dipolar excitons have been strongly coupled to cavity pho-tons in InGaAs double quantum wells, forming electrically-tunabledipolar polaritons15, with enhanced nonlinear interactions towardshigh-temperaturepolaritonBEC16. However, the lowoscillator strengthof interlayer excitons in type-II van der Waals heterobilayers hindersthe creation of interlayer polariton states17.On the other hand, layer-hybridized excitons (hIXs) in TMDCbilayers are characterized by an electron (or hole) that is delocalizedbetween the two constituent layers through coherent tunneling, thusexhibiting a coexistence of inter- and intra-layer characters18. Theirelectrical tunability19–23, allowing the modulation of their dynamics24,25and interactions, has been recently exploited to achieve anomalousdiffusion regimes of transport with high exciton mobilities24,26. Inparticular, previous works on tunable momentum-indirect hIXs havefocused on their power-independent quantum yield and repulsiveinteractions by their emission via phonon replicas21,24. However, thestudy of their ultrafast formation and interactions, as well as theirstrong coupling with light, is hindered by their momentum-indirectnature. On the other hand, momentum-direct hybrid excitons exhibitlarge oscillator strengths, allowing the observation of dipolar layer-hybridized exciton-polaritons (dipolaritons) with highly nonlineareffects both inhomobilayers27–29 and in heterobilayers30,31.Momentum-direct hIXs in bilayer 2H-MoS2 have been proposed as optical probesfor correlated many-body phases, such as interlayer excitoncoherence32, holding promise for the high-temperature superfluidityof hybrid exciton condensates33. Furthermore, bilayer TMDCs hostinghybrid species have been identified as an ideal platform for the reali-zation of Bose–Einstein condensates of dipolar exciton ensembles34.Combining interlayer charge tunneling with the twist angle degree offreedom has also allowed the realization of moiré-hybridized inter-layer excitonic states, owing to the additional electronic band foldinginduced by themoiré superlattice35,36. Such hybridmoiré excitons haveshown enhanced nonlinear interactions in the few-polaritons regimedue to localization effects in the moiré potential, potentially useful forpolariton quantum blockade28.For these reasons, the control and enhancement of momentum-direct hIX interactions, as well as their dynamics, is crucial to obtainmacroscopic states of matter based on hybrid excitons anddipolaritons37. However, the field-dependent tunability of the interac-tions and the dynamics of momentum-direct hIXs remain unexplored.Moreover, while the formation dynamics of interlayer excitons in type-II heterobilayers have been recently investigated38–40, the electricaltunability of the formation time for any interlayer excitonic species hasnot been reported until now.Here, we optically investigate the density-dependent repulsive andattractive nonlinear interactions between differently oriented dipolarhybrid excitons in a MoS2 homobilayer under an external electric field.We observe opposite energy shifts and a strongly enhanced opticalsaturation of exciton absorption compared to the zero-field case. Usingtransient reflectance spectroscopy, we demonstrate the tunability oflayer-hybridized dipolar exciton interactions on ultrafast timescales.Finally, we electrically modulate the ultrafast formation and relaxationdynamics of momentum-direct hIXs, achieving their strong enhance-ment at a finite electric field. Our experiments are supported by amicroscopic many-particle theory based on an equation-of-motionapproach applied to excitons in TMD bilayers41.ResultsLayer-hybridized exciton species in MoS2 homobilayersOur device consists of a fully hBN-encapsulated naturally stackedMoS2homobilayer with bottom and top graphene gates (Fig. 1a,Supplementary Note 1). The dual-gate configuration allows us toapply a vertical electric field without inducing extrinsic electrostaticdoping11,24. At zero applied vertical electric field, MoS2 homobilayershost A and B excitonic resonances (XA and XB) with predominantlyintra-layer character, and an inter-layer excitonic transition that isstrongly hybridized with XB due to a significant hole tunnelingstrength at the K/K’ valleys (tv � 40 meV)42. This hybrid species(hIXs) is characterized by a layer-localized electron and a delocalizedhole wavefunction that is shared between both constituent MoS2layers.The application of a vertical electric field lifts the degeneracy ofhIXs due to the presence of twodistinct interlayer dipolar orientations.The non-negligible out-of-plane static dipoles cause the two (KK) hIXconfigurations to display progressive shifts of their excitonic transi-tions in opposite energy directions. Here, we label the lower andhigher-energy excitonic species as L-hIX and H-hIX, respectively, withtunneling rates JL and JH (Fig. 1b). Consequently, as the electric fieldincreases, L-hIX becomes more interlayer-like while H-hIX becomesmore intralayer-like, as obtained from microscopic theory in Supple-mentary Fig. 3.To experimentally visualize the Stark effect of hybrid excitons inbilayerMoS2, we illuminate our sample (Fig. 1c) with broadbandwhite-light supercontinuum pulses and measure the reflectance contrast(RC) spectra as described in the Methods section. Figure 1d shows theRC spectra as a function of the applied vertical electric field. Thedipolar nature of layer-hybridized species is evidenced by their Starkeffect22,24. We extract from it an upper-bound estimate of �0.2 nm forthe effective dipole length of both L-hIXs and H-hIXs at near-zeroelectric fields (Supplementary Note 3). The measured field-dependentStark shift magnitude is lower than the value extracted from the cal-culated energy landscape in Supplementary Note 2, but remains ingood qualitative agreement. We attribute this discrepancy to intrinsicdoping in the active area, which affects the field-dependent behaviorof dipolar excitonic species24,43. Evidence of intrinsic doping is alsoprovided by the non-negligible trion peak X *A (Fig. 1e), which becomesvisible at higher electric fields, probably due to electrostatic chargemigration, whose characterization is beyond the scope of this work(Supplementary Note 3).Figure 1e displays two characteristic RC spectra obtained at zeroand high (230mV/nm) electric fields. Evenwith a significant Stark shift,represented by a H-L energy splitting of δEH�L ’ 40 meV, the totaloscillator strength of the two species remains ~20% of that of XA, inagreement with the previous literature22.Strong hIX nonlinearities due to dipolar interactionsTo investigate dipolar interactions (Fig. 2), we illuminate the samplewith single ultrashort (100 fs) white-light supercontinuum pulses ofvarying spectral bandwidths at a fixed vertical electric field (230mV/nm) such that δEH�L ’ 40 meV. With this splitting, the L and H line-shapes can be well distinguished, given their linewidths in the range of15meV, while also being unaffected by the XA and XB tails. We first usea narrowband (NB) excitation configuration, where the pulses arespectrally filtered to excite only the hIX transitions (Methods) with afull-width half-maximum (FWHM) of 100meV. As the pulse fluence isincreased, we observe a progressive bleaching of the hIX peaks,together with a blueshift of the L-hIX peak energy and a redshift of theH-hIX peak energy (Fig. 2a). The hIX density was determined throughan experimental method that takes into account a convolution of theRC spectra and the laser profile (Supplementary Note 5). We note thatthese fluences correspond to hybrid exciton densities (< 1012 cm�2)well below the exciton Mott transition (� 1014 cm�2).To understand the interactions at play, we developed amicroscopic theory based on a hybrid exciton-exciton interactionHamiltonian focusing on the dipolar interactions between hIXs (Sup-plementary Note 4). The density-dependent energy shift of hIXsArticle https://doi.org/10.1038/s41467-025-65733-9Nature Communications |        (2025) 16:10710 2www.nature.com/naturecommunicationsis written as:ΔEi = gi�ix�xni + gi��ix�xn�i ð1Þwhere i=H, L (�i indicates the opposite species, i.e., if i=H, then �i= Land vice versa), ni is the exciton density of a specific population, andgx�x is the dipolar hybrid exciton-exciton interaction. The interactionstrength is determined by the interlayer mixing coefficient CIX , whichis effectively modulated by an applied vertical electric field (Supple-mentary Fig. 3). We refer to gi�ix�x / jCi, IX j2jCi, IX j2dTMD=ϵ? and gi��ix�x /�jCi, IX j2jC�i, IX j2dTMD=ϵ? as the co-hIX and cross-hIX contributions,with repulsive and attractive characters, respectively. Here, dTMD is theTMDC layer thickness, corresponding to the bare dipole, and ϵ? is theout-of-plane component of the dielectric tensor of the TMDC. The H-Lsplitting at a fixed electric field is density dependent, asδE nL,nH� �= δE0 +ΔEL nL� �+ΔEHðnHÞ. At vanishing fields, the inter-layer composition ofH and L is equal to jC0, IX j2 ’ 0:7.We performourcalculations starting from a low-density splitting of δE0 �δEH�LðnL,H < 1010 cm�2Þ ’ 40 meV to best represent our experimen-tal conditions. In this case, the calculated mixing coefficients amountto approximately jCH, IX j2 ’ 0:5 and jCL, IX j2 ’ 0:8, with decreasingand increasing interlayer character, respectively.As a result, ΔEL is dominated by repulsive interactions (gL�Lx�x),giving rise to a density-dependent blueshift (Supplementary Note 2).Instead, given the weaker co-hIX interactions for H-hIXs, the attractiveinteractions between H-hIXs and L-hIXs (gH�Lx�x ) result in a density-dependent ΔEH redshift. In Fig. 2c, we present the measured hIX peakenergy shifts ΔEL,H extracted from the Lorentzian fits to the RCspectra, showing a good agreement with our theoretical calculations(dashed lines in Fig. 2c). The theoretical shifts were taken by assumingnL � 2nH based on a best-fit approach. As discussed in SupplementaryNote 4, the density-dependent L-hIX blue-shift and H-hIX red-shift arequalitatively obtained regardless of the density ratio nL/nH , providedthat nH ≤nL. This is justified by the fact that L-hIX is the lowest excitedstate among the hIX branches, and is aligned with their photo-luminescence reported in the previous literature44.We note thatmany-body effects due to carrier exchange and dynamic screening are notincluded in the calculations, but are expected tomodify quantitativelythe density-dependent energy shifts45,46. In particular, it was shownrecently that ultrafast dynamical screening strongly reduces thedensity-dependent energy shifts of interlayer excitons45. Since themeasured energy shifts for hybrid excitons are larger than those forinterlayer excitons, this may suggest that dynamical screening plays asmaller role in homobilayers. However, further experimental andtheoretical studies are needed to confirm this interpretation.We repeated our experiments in a broadband (BB) configuration,with the white-light supercontinuum pulses filtered to excite hIXs aswell as XA (FWHM ≈ 200meV). In Fig. 2d, e, we show the density-dependent quenching of the integrated RC for L-hIXs andH-hIXs peaksin both configurations. An exponential decrease of integrated RC forboth L and H species is observed in the narrowband case for densitiesnhIX >2 � 1011 cm�2. Supplementary Fig. 6 further shows the bleachingand energy shift of hIXs with respect to illumination fluence in theBB case. Enhanced energy shifts and a stronger density-dependentoptical saturation are found in the BB case due to inter-speciesinteractions involving XA and hIXs. Under BB excitation, both XA andhIX are excited simultaneously, leading to additional interspeciesinteractions, as previously observed in the literature27. Notably, XAand hIX share holes in the same valence band via hole tunneling,enabling a combination of phase space filling and inter-excitonicexchange interactions. Such tunneling-enabled nonlinearity—activatedonly when the common valence band is jointly occupied under BBFig. 1 | Layer-hybridized excitonic transitions in a dual-gated MoS2 homo-bilayer. a Schematic of the device structure, showing the hBN-encapsulated 2H-MoS2 homobilayerwith bottomand topgraphenegates.bBanddiagramof the low-energy (L-hIX, left) and high-energy (H-hIX, right) hybrid excitons in a MoS2homobilayer under an applied electric field EZ≠0. The holes of the interlayer spe-cies are strongly hybridized with the B excitons and delocalized in space betweenthe two layers.With an applied vertical electricfield, the tunnelling strengths JL of L-hIX (JH of H-hIX) are decreased (increased) with respect to the zero-field hIXs (J0).c Optical micrograph of our device, with coloured lines highlighting the MoS2homobilayer (yellow), aswell as the bottomgraphene (black) and the top grapheneflakes (white). Scale bar: 10 μm. d Reflectance contrast spectra as a function of theapplied vertical electric field. The electric field Ez is obtained as described in theMethods section. The hIX degeneracy is lifted upon application of an electric field,showing dipolar hybrid species with opposite orientations, as in (b). e Reflectancecontrast spectra from (d) at electric fields of 0mV/nm (light blue) and 230mV/nm(dark blue) measured with white light continuum pulses and a fluence of0:1 μJ cm�2. All the main excitonic transitions of interest are highlighted at theirrespective energy positions.Article https://doi.org/10.1038/s41467-025-65733-9Nature Communications |        (2025) 16:10710 3www.nature.com/naturecommunicationsillumination—substantially enhances the bleaching of the hIXoscillatorstrength. Thus, in Fig. 2d, eweobserve a strong increase innonlinearityfor both L-hIX and H-hIX under the application of an electric field withBB excitation, as the reduction of their oscillator strengths is evidentfor significantly lower exciton densities (>5-fold) with respect to theNB case.We also performed density-dependent measurements at zeroelectric field, resulting in no sizeable energy shift of the main hIX peakand a less pronounced optical saturation (Supplementary Note 7). Inparticular, we observe bleaching of zero-field hIXs (nhIX > 1012 cm�2 innarrowband) at densities about one order of magnitude higher withrespect to high-field L-hIX and H-hIX. We attribute such stronglyenhanced nonlinear response under a high electric field to theincreased contribution of Coulomb exciton interactions. Thus, with anapplied electric field we uncover strongly-interacting dipolar specieswith highly-nonlinear behavior.Tunable hIX formation and relaxation dynamicsWe have performed ultrafast transient absorption measurements tounveil the time-dependent interactions and dynamics of electrically-tunable dipolar hIXs in our platform. Figure 3a, b shows the 2Dmaps ofthe differential reflectivity (ΔR=R) spectra as a function of pump-probedelay τ and probe photon energy in the cases of zero field and highfield (Ez ’ 230 mV=nm), respectively. In this experiment, ~100 fspump pulses were applied resonantly with XA (FWHM= 10nm). Pre-vious studies on monolayer TMDCs have shown that excitationsresonant with XA induce an instantaneous build-up of the XB transientsignal due to intravalley exchange interactions47,48. Thus, in MoS2bilayers,where the interlayer transition andXB are strongly hybridized,a sizeable hIX population is expected upon resonant photoexcitationofXA.We employ this excitation scheme in order to exclude the roleofexciton cascade effects, allowing us to decouple the excited (XA) andhybridized species (XB and hIX), which remain connected throughintravalley mixing processes. Further discussion on different photo-excitation schemes can be found in Supplementary Note 13.In the 2D map of Fig. 3a, positive and negative signals appearimmediately after time zero (τ =0). Such features can be attributed todifferent pump-induced modifications of the excitonic spectrum (i.e.,reduction of oscillator strength, broadening, and shift in energy).While purely symmetric derivative-shaped signals are a consequenceof exciton line shifts due to exciton-exciton interactions49 or bandgaprenormalization50, prominent positive peaks are mainly related toexciton absorption saturation due to the Pauli blocking effect51.Purely negative signals are generally attributed to photoinducedFig. 2 | Field-tunable interacting dipolar hybrid excitons. a Reflectance contrastspectra as a function of excitation density at a fixed applied vertical electric fieldEz = 230 mV=nm, corresponding to a low-density energy splitting between hIXspecies of approximately 40meV. The sample was excited with ultrashort pulses,filtered inenergy to selectively excite the hIX species in a narrowbandconfiguration(FWHM ≈ 100meV). The excitation fluences range from 0.1 to 14 μJ cm�2 increas-ing magnitude following the black dashed lines. The superimposed fits to the data(smooth lines) are obtained using a Lorentzian model. The energy shift of the twoexciton species is observed upon increasing the pulse fluence. The L-hIX and H-hIXenergy peaks undergo a blueshift and redshift, respectively. A comparable beha-viour is obtained in the broadband configuration (FWHM≈ 200meV), as shown inSupplementary Fig. 6. b Illustration of the dipolar interactions between hIXs in aMoS2 homobilayer with an applied electric field. Same-species interactions (L-L andH-H) result in a density-dependent blueshift, while attractive interactions betweenopposite species (L-H) result in a net density-dependent redshift. c Density-dependent energy shifts for L-hIX (blue) and H-hIX (red) in the narrowband con-figuration, comparedwith the corresponding calculations frommicroscopic theory(dashed lines), with nL � 2nH as a best-fit approach (Supplementary Note 4). Thex-axis is displayed in logarithmic scale to cover the entire range of the appliedpump fluences. The hybrid exciton densities are calculated taking into account thepump fluences and the measured RC spectra, as described in the Methods sectionand SupplementaryNote 5.d, eNormalized integrated reflectance contrast of L-hIX(b) and H-hIX (c) with respect to their corresponding population densities, fornarroband (empty markers) and broadband (full markers) pump configurations. Asubset of the spectra obtained by narrowband excitations is shown in (a), while therespective broadband cases are displayed in Supplementary Fig. 6. All error bars in(c–e) represent the standard deviations of the quantities of interest extracted fromthe double-Lorentzian fits in (a).Article https://doi.org/10.1038/s41467-025-65733-9Nature Communications |        (2025) 16:10710 4www.nature.com/naturecommunicationsabsorption52, while exciton line broadening can lead to more complexshapes in the transient reflectivity spectra, but it becomes significantonly at high pump fluences, since it is mainly caused by excitation-induced dephasing51,53. In our case, positive signals are always domi-nant in the transient reflectivity spectra at all the scanned time delays,pointing at the main role of Pauli blocking of the different excitonicinteractions. We trace the intensity variation of such peaks to monitorthe exciton population dynamics in the system. Supplementary Note 8further expands on the extraction of exciton dynamics from transientabsorption measurements29,49,54.At high Ez , with ~40meV of H-L splitting in equilibrium conditions(Fig. 3b), weobserve positive signals associatedwith the photobleachingof both L-hIX andH-hIX (Fig. 3c). Focusing on the energy range of hybridexcitons (Fig. 3d), we observe a significant shift in the ΔR=R peakpositions for both L and H species as a function of time. We track thetemporal evolution of the photobleaching of the hIX peaks (Methods),revealing the prominent shift of the hIX energies on short timescales(< 0:3 ps), followed by a slower recovery to their unperturbed energieswithin tens of picoseconds (Fig. 3e). In SupplementaryNote 14, by takinginto account the presence of heating effects, causing a linear blueshift atlong timescales, we extract comparable and opposite shifts related toexcitonic interactions for L-hIX and H-hIX at high fields.Figure 4a compares the intensity of the transient signal of theL-hIX and H-hIX peaks with the one of hIX at zero field. The signalsarefittedby anexponential rise (τR) followedby abi-exponential decay(τ1 and τ2), as commonly observed for intralayer exciton dynamics inTMDCs55 (Methods). We note that the energy shifts shown in Fig. 3efollow the timescales of the formation and relaxation dynamicsobserved by the ΔR=R signal presented in Fig. 4a, being caused bydensity-dependent interactions. Upon an external electric field, L-hIXdisplays a clearly delayed formation, as well as an increase in the slowdecay component (Fig. 4a). This is also observed comparing the L-hIXdynamics to the XA and XB ones, taken from the samemeasurement athigh field (Fig. 4b). On the other hand, the transient behavior of H-hIXshows much faster formation and decay times with respect to L-hIX,the former being more similar to the other exciton species.The formation time of purely-interlayer excitons in type-II TMDCheterobilayers is extendedwith respect to intralayer species due to thetype-II band offset ΔE combined with phonon-assisted scatteringmechanisms39,40,56. However, the dependence of the formation time ofan interlayer specieswith respect to a tunable band offset has not beenexperimentally reported. In our case, if we considerMoS2 homobilayerhIXs at the K point, a wider band offsetΔE between the K valleys of thetwo layers due to an external electric field results in a slower and lessefficient momentum transfer (see inset of Fig. 4a). In a single-particlepicture at a specific valley, the interlayer tunneling matrix elementbetween the two layers depends on the spatial overlap between thewavefunctions of the involved states56. In MoS2 bilayers, the measuredStark shift magnitude represents the field-dependent offset betweenthe valence band maxima at the K points in the two layers22,23, asschematically presented in Fig. 1b. With an applied field such thatδEH�L =40 meV, corresponding to a band shift of approximatelyΔE =20 meV, the decrease in spatial overlap between the electron andhole wavefunctions gives rise to a lower momentum transferFig. 3 | Time-domain observation of layer-hybridized exciton interactions.Transient differential reflectance (ΔR=R) spectra as a function of the pump-probedelay τ, obtained by exciting the structurewith a pumppulse (�100 fs) resonant toXA and probing with a broad white-light continuum pulse at electric fieldsEz =0 mV=nm (a) and Ez = 230 mV=nm (b). c ΔR=R traces extracted from (a) and(b) at a pump-probe delay τ = 1 ps. All transitionsof interest are highlighted.dΔR=Rtraces in time in the hIX energy range. From these signals, we observe a change intime of the H-L splitting δEH�L on the picosecond timescale. We note that the fullΔR=R intensity scale from (b) was reduced in (d) in order to visualize the hIXssignals. In order to quantify and understand the observed energy shifts, we fittedthe ΔR=R signals in (e) with a double Lorentzian in order to track the temporalevolution of the L-hIX andH-hIX peaks. We observe two regimes, for τ <0:3 ps andτ >0:3 ps. Right after pump excitation, the build-up of the hIX density results in anincrease of the hybrid exciton dipolar interactions, inducing a transient reductionof δEH�L. This is followed by exciton depopulation processes decreasing the L-hIXandH-hIX densities within tens of picoseconds, leading to an opposite energy shiftfor both peaks. Since the energy shifts are directly proportional to the hybridexciton density nhIX , the energy dependent shifts follow the trend of the corre-sponding ΔR=R intensity traces. Inset: zoom-in on the first 2 ps of the time-dependent L and H energy peak shifts.Article https://doi.org/10.1038/s41467-025-65733-9Nature Communications |        (2025) 16:10710 5www.nature.com/naturecommunicationsefficiency, resulting in a buildup time delay for species with higherinterlayer composition factors (i.e., lower hybridizationwith XB). Thus,the tunneling rate of thehybridizedholes inH-hIXs (L-hIXs) is expectedto increase (decrease) relative to the zero-field hIX tunneling rate (J0).Considering H and L species at non-zero field with rates JH and JL, thisresults in JL < J0 < JH (Fig. 1b). This explains the longer formation ofL-hIX compared to H-hIX and the other exciton species of inter-est (Fig. 4b).Figure 4c compares the fitted formation times of XA, XB L-hIX andH-hIX at high field with those of hIX at zero field. While the zero-fieldhIX formation (τ0�hIXR ) occurs with a slight delay with respect to XBdue to interlayer hybridization, an increase (decrease) in such delayis measured for L-hIX (H-hIX) at a high field. The observed increaseof τL�hIXR with respect to the zero-field case, with a ratioτL�hIXR =τ0�hIXR � 2:6, can be explained by the reduction in the holetunneling rate caused by an increased band offsetΔE under an appliedelectricfield. Furthermore, the number of scattering events needed fora complete exciton thermalization also increases with larger energyoffsets. This leads to an increase in exciton-phonon scatteringrates39,40, and to longer L-hIX formation times, in agreement with ourexperimental findings. Meanwhile, we observe the opposite behaviorfor H-hIX (i.e., lower τH�hIXR due to a decreased band offset), althoughits quantification is limited by our temporal resolution.Regarding the decay dynamics of L-hIX, we observe an increase inboth short (τ1) and long (τ2) decay times of L-hIX at high field. How-ever, the wide uncertainty of τ1 for L-hIX at high field, partially causedby the dominance of the slow component, does not allow us to inferconclusions on the modulation of the fast decay (see SupplementaryNote 8). On the other hand, both short and long decay times of H-hIXare comparable to the zero-field counterpart. Thus, we focus here onthe modulation of the slow decay τ2, occurring in the tens of picose-cond time-scale (Fig. 4d). Based on previous theoretical work on 2L-MoS2, hIXs are expected to have radiative lifetimes on the order ofpicoseconds57, thus contributing to τ2. By employing a formalismbased on an exciton-photon interaction Hamiltonian (SupplementaryNote 9), we find that the radiative decay rate of momentum-direct L-hIX excitons ΓKKrad decreases with respect to interlayer composition asΓKKradðEz Þ / 1� CKKIX ðEzÞ������2. Thus, we estimate afield-dependent increasein radiative lifetime τL�hIXrad ðδE =40 meVÞ=τhIXradð0Þ � 1:7, which is com-patible with the experimentally observed increase in τ2 of about 2. Wenote that a significant contribution to this modulation likely arisesfrom phonon-assisted radiative recombination, which still scales asτrad with respect to the applied electric field.To understand the role of second-order effects in the hybridexciton dynamics, we performed fluence-dependent pump-probeexperiments on the gated MoS2 bilayer, focusing on the dynamics ofthe L-hIX under high electric field. Both the buildup and the long decaytimes are not strongly modulated within our scanned fluence range(Supplementary Note 8). This suggests that the slow buildup time of L-hIX observed under high field is not related to fluence-dependentphonon scattering processes58. Furthermore, exciton-exciton annihi-lation (Auger recombination) canbe neglected in the observed excitonFig. 4 | Electrical control of ultrafast hIX dynamics. a Transient intensity of thehIX peak extracted from theΔR=R spectra at zero electric field (red) comparedwiththat extracted at high field from the L-hIX (yellow) and H-hIX (blue) peaks withδE 0ð Þ=40 meV at a pump fluence of 12:4 μJ cm�2. The transient intensities wereobtained by tracking the peak energy positions based on their time-dependentenergy shifts, asdescribed in theMethods section. The solid lines are fits to the dataobtained using the model described in the Methods section (Eq. 2). b ΔR=Rintensity of XA (red), XB (purple) and L-hIX (yellow) at Ez = 230 mV=nm, withrespectivefits. c,d Formation time τR and longdecay time τ2 extracted from the fitsin (a,b). For hIX at zero field, we obtain τ0�hIXR =48± 20 fs and τ0�hIX2 = 49 ± 3 ps. Athigh field, we extract τAR = 31 ± 8 fs and τA2 = 41± 1 ps for XA, τBR = 26± 12 fs andτB2 = 45± 2 ps for XB, τL�hIXR = 124± 51 fs and τL�hIX2 = 92 ±6 ps for L-hIX, as well asτH�hIXR = 33± 29 fs and τH�hIX2 = 53 ± 14 ps for H-hIX. XA and XB exhibit comparabledynamics at zero field. In Supplementary Note 8, we further compare all shortdecay τ1 values for the excitonic species of interest. All error bars in (c, d) representthe standard deviations of the extracted quantities of interest.Article https://doi.org/10.1038/s41467-025-65733-9Nature Communications |        (2025) 16:10710 6www.nature.com/naturecommunicationsdecaydynamicswithin our rangeoffluences, as recently demonstratedfor MoS2 monolayers59, but previously found in other materialsystems51,60,61. In summary, we mainly attribute the measured field-induced increaseof τL�hIX2 with respect toH-hIX,XA andXB at highfieldand hIX at zero field, to the suppression of the L-hIX (KK) radiativedecay rate with increasing field-dependent interlayer mixing CIX .Recent developments in the literature have revealed that elec-trostatic doping can also induce sizable L-H splitting due to a quasi-static random coupling between L-hIX andH-hIX32. With this regard, inSupplementary Note 12 we further investigate and discuss the doping-dependent dynamics of L-hIX, unveiling an increase in formation andlong decay times for higher δEH�L. Albeit outside the scope of thepresent work, these findings might spark further research on thetunability of many-body electron correlations in TMDCs.DiscussionWe unveiled the strong Coulomb interactions between dipolarmomentum-direct layer-hybridized excitons in a dual-gated van derWaals TMDC homobilayer system using nonlinear reflectivity mea-surements. Opposite energy shifts were observed for the two dipolarexciton species corresponding to their different dipole orientation,together with actively enhanced nonlinearities compared to the zero-field case. We demonstrated electrical control on the hybridized holetunneling rate, resulting in slower hIX formation, as well as on thedecay of hybrid excitons due to the increase in their interlayer char-acter (i.e., decrease in hybridization). The measured density-dependent shifts and the increase of hybrid exciton decay time withelectric field are supported by a microscopic and material-specifictheory with predictive capabilities.Strong nonlinearities and long lifetimes are essential for obser-ving correlated states of interlayer excitons62,63, while a high oscillatorstrength unlocks the potential for polariton condensation15. Our workindicates a route forward to achieve these feats, since unveiling andcharacterizing the electrical tunability of momentum-direct strongly-interacting dipolar species with high nonlinearity represents anessential step towards tunable macroscopic quantum states of matterin TMDC bilayers. Furthermore, electrically-tunable highly nonlinearexciton interactions will be crucial for developing ultrafast electro-optical polariton switches29.MethodsDevice fabricationThe device consists of an hBN-encapsulated MoS2 homobilayer withbottom and top graphene gates over a SiO2/Si substrate with an oxidethickness of 270 nm. The heterostructure was fabricated by a dry-transfer technique using polycarbonate (PC) membranes64. hBN andMoS2 (SPI Supplies) were exfoliated onto SiO2 and PDMS (gelpak)substrates, respectively. The flakes were identified by optical contrast.The heterostack was made by picking up the flakes successively usingthe PC stamp, and then released onto the bottom graphene gate byprogressive adhesion while increasing the temperature above 150 °C.The PC stamp was cleaned by chloroform. The heterostructure wasannealed in high-vacuum (10�6 mbar) for 6 h at a temperature of340 °C. Electrical contacts were fabricated by electron-beam litho-graphy and evaporation of Ti/Au (2 nm/80 nm) layers.Optical measurementsFor all measurements, the sample is maintained in a closed-cyclehelium cryostat at 8 K with electrical feedthrough connections to thegraphene gates and the homobilayer flake. Electrostatic gating isachieved using a two-channel Keithley 2612B.Transient reflectivity measurements. For the transient measure-ments, 100-fs pulses from an amplified Ti:Sapphire laser (800nm) at2 kHz repetition rate are used. The laser output is split into two beams.One beam drives a non-collinear optical parametric amplifier to gen-erate tunable pump pulses. The other beam is focused into a sapphireplate to generate the broadband white light probe pulse. The pulsesare collinearly combined and focused on the sample using anobjectivelens. The two beams are cross polarised and the pump pulse is filteredout in the detection path by a linear polariser. The differential reflec-tivity (ΔR/R) spectra are recorded as a function of time (τ) by con-trolling the delay between pump and probe pulses using a mechanicaldelay line. Specifically, the probe reflectivity spectrum with the pumpon (RPumpOn) at each delay is compared to a reference spectrum takenwithout the pump (RPumpOff ). These are used to calculate.ΔR=R = ðRPumpOn � RPumpOff Þ=RPumpOff . The maps shown in Fig. 3 are theΔR/R values at each delay. The ΔR=R signals of interest in our case arewell described by an exponential rise followed by a bi-exponentialdecay55:ΔRRtð Þ= IRF tð Þ � 1� e�tτR� �� H tð Þ � A1e� tτ1 +A2e� tτ2� �h ið2Þwhere IRF is the Gaussian instrument response function, τR is the risetime, H is a Heaviside function, τ1 and τ2 are the fast and slow decaytimes. The fittingmodel is further discussed in Supplementary Note 11.The evolution of the H and L peaks in time (Fig. 3) is fitted by a double-Lorentzian model.Static reflectivity measurements. For the static reflectivity mea-surements (Fig. 2), only the supercontinuum white light pulses (gen-erated as described above) are used to excite the sample. The incidentpower and bandwidth are chosen with a subsequent use of variablefilters.Microscopic many-particle theoryTo study layer-hybridized exciton states in TMDC bilayers, we deriveda many-body Hamiltonian in a hybrid exciton basis that contained akinetic part, the exciton–photon interaction and the exciton-excitoninteraction relevant at elevated electron-hole densities. By solving thebilayer Wannier equation, we obtained access to pure intra- andinterlayer exciton states. By taking these states together withmaterial-specific tunneling parameters (obtainedbyDFT calculations65) as inputfor a hybrid exciton eigenvalue problem we obtained the hybridexciton landscape of spin- and momentum-bright exciton species. Weincluded an out-of-plane electric field in our calculations by con-sidering the quantum-confined Stark effect leading to energy shifts ofinterlayer resonances42 (Supplementary Note 2). The hybrid excitoneigenstates were used to compute density-dependent energy renor-malizations of hybrid excitons obtained from the Heisenberg equationof motion (Supplementary Note 4), as well as input for the hybridexciton-photon interaction and the electric-field-dependent radiativerecombination rates of hybrid excitons (Supplementary Note 9).Data availabilityThe data that support the findings of this study are available onZenodo at https://doi.org/10.5281/zenodo.17201075.References1. Mueller, T. &Malic, E. Excitonphysics anddevice applicationof two-dimensional transition metal dichalcogenide semiconductors. Npj2D Mater. Appl. 2, 1–12 (2018).2. Wang, G. et al. Colloquium: Excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).3. Perea-Causin, R. et al. Exciton optics, dynamics, and transport inatomically thin semiconductors. APL Mater. 10, 100701 (2022).4. Wilson, N. P., Yao, W., Shan, J. & Xu, X. 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This workreflects only authors’ view and the European Commission is notresponsible for any use that may bemade of the information it contains.AG, SDC, and GC acknowledge financial support by the EuropeanUnion’s NextGenerationEU Programme with the I-PHOQS Infrastructure(IR0000016, ID D2B8D520, CUP B53C22001750006) “Integrated Infra-structure Initiative in Photonic and Quantum Sciences”. The Marburggroup acknowledges funding from the Deutsche For-schungsgemeinschaft (DFG, German Research Foundation) via SFB1083 (project B9) as well as regular DFG project 512604469. K.W. andT.T. acknowledge support from JSPS KAKENHI (Grant Numbers19H05790, 20H00354 and 21H05233).Author contributionsA.K., S.D.C., A.G., and C.G. initiated the project. A.K., S.D.C, A.G., andG.C. supervised the project. E.L. fabricated the device. E.L., C.L., and I.L.performed the optical measurements supervised by A.G. and they allanalysed the data. A.G. and C.J.S. optimized the gate-tunable pump-probe microscopy setup. K.W. and T.T. grew the h-BN crystals. D.E, S.B,R. P-C andE.Mdeveloped themicroscopicmodel. E.L, C.L., A.G. andA.K.wrote the manuscript with contributions from all authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65733-9.Correspondence and requests for materials should be addressed toArmando Genco, Ermin Malic, Stefano Dal Conte or Andras Kis.Peer review information Nature Communications thanks NadineLeisgang, Laurenz Rettig, and the other, anonymous, reviewer(s) fortheir contribution 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/s41467-025-65733-9Nature Communications |        (2025) 16:10710 9https://doi.org/10.1038/s41467-025-65733-9http://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 Electrically tunable ultrafast dynamics and interactions of hybrid excitons in a 2D semiconductor bilayer Results Layer-hybridized exciton species in MoS2 homobilayers Strong hIX nonlinearities due to dipolar interactions Tunable hIX formation and relaxation dynamics Discussion Methods Device fabrication Optical measurements Transient reflectivity measurements Static reflectivity measurements Microscopic many-particle theory Data availability References Acknowledgements Author contributions Competing interests Additional information