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Swarup Deb, Johannes Krause, Paulo E. Faria Junior, Michael Andreas Kempf, Rico Schwartz, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jaroslav Fabian, Tobias Korn

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[Excitonic signatures of ferroelectric order in parallel-stacked MoS2](https://mdr.nims.go.jp/datasets/c53fce43-3d60-42d7-93ae-78f2e9018d99)

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Excitonic signatures of ferroelectric order in parallel-stacked MoS2Article https://doi.org/10.1038/s41467-024-52011-3Excitonic signatures of ferroelectric order inparallel-stacked MoS2Swarup Deb 1 , Johannes Krause1, Paulo E. Faria Junior 2,Michael Andreas Kempf1, Rico Schwartz 1, Kenji Watanabe 3,Takashi Taniguchi 4, Jaroslav Fabian2 & Tobias Korn 1Interfacial ferroelectricity, prevalent in various parallel-stacked layered mate-rials, allows switching of out-of-plane ferroelectric order by in-plane sliding ofadjacent layers. Its resilience against doping potentially enables next-generation storage and logic devices. However, studies have been limited toindirect sensing or visualization of ferroelectricity. For transition metaldichalcogenides, there is little knowledge about the influence of ferroelectricorder on their intrinsic valley and excitonic properties. Here, we report directprobing of ferroelectricity in few-layer 3R-MoS2 using reflectance contrastspectroscopy. Contrary to a simple electrostatic perception, layer-hybridizedexcitons with out-of-plane electric dipole moment remain decoupled fromferroelectric ordering, while intralayer excitons with in-plane dipole orienta-tion are sensitive to it. Ab initio calculations identify stacking-specific inter-layer hybridization leading to this asymmetric response. Exploiting thissensitivity, we demonstrate optical readout and control of multi-state polar-ization with hysteretic switching in a field-effect device. Time-resolved Kerrellipticity reveals direct correspondence between spin-valley dynamics andstacking order.The basic building block for any interfacial ferroelectrics is two layersof certain van der Waals materials aligned parallel to each other1–11. Inthe case of transition metal dichalcogenides (TMDs) like MoS2, layer-asymmetric atomic registry12 along the out-of-plane direction leads tointerlayer hybridization between the valence band of one layer and theconduction band of the other but not vice versa13. Such a preferentialcoupling induces unidirectional charge transfer, leading to the spon-taneous emergence of an electric dipole bound at the interface. Abilayer unit of parallelly-stacked (rhombohedral or so-called 3R)-TMDsthus possesses two equivalent yet opposite ferroelectric orders viz.MX and XM, marking the stacking of metal (M) and chalcogen (X)atoms at the eclipsed sites (Fig. 1).Besides hosting ferroelectricity, parallel stacking of TMDs pre-serves the spin-valley locking, regardedpredominantly as a property ofmonolayers14, even in the multilayer limit due to broken inversion andmirror symmetries15–18. Therefore, the 3R-polymorph of TMDs providemeans for the bottom-up construction of three-dimensional spin-val-leytronic devices on a ferroelectric platform. A visionary goalwould beto engineer the optical response in TMDs by exploiting theferroelectricity-induced interaction, which can be highly localized,non-volatile, and reconfigurable. Despite a tremendous interest in thisemerging phenomenon19,20, so far the field has been limited to indirectsensing or visualizing the ferroelectricity employing surface-sensitiveprobes, such as atomic force microscopy2,4,6,7,11, scanning electronmicroscopy21, or sensing-layer-based approaches2,5 and, therefore,could only provide limited physical insight. In the case of TMDs, thisleaves a void of in-depth knowledge about the influence of ferro-electric order on their intrinsic valley and excitonic properties. To fillthis gap, we exploit hyperspectral reflectivity imaging to discern thecorrespondence between ferroelectric stacking and optical responseReceived: 2 April 2024Accepted: 22 August 2024Check for updates1Institute of Physics, University of Rostock, Albert-Einstein-Str. 23, Rostock 18059, Germany. 2Institute for Theoretical Physics, University of Regensburg,93040 Regensburg, Germany. 3Research Center for Electronic and Optical Materials, NIMS, 1-1 Namiki, Tsukuba 305-0044, Japan. 4Research Center forMaterials Nanoarchitectonics, NIMS, 1-1 Namiki, Tsukuba 305-0044, Japan. e-mail: swarupdeb2580@gmail.com; tobias.korn@uni-rostock.deNature Communications |         (2024) 15:7595 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2919-0608http://orcid.org/0000-0002-2919-0608http://orcid.org/0000-0002-2919-0608http://orcid.org/0000-0002-2919-0608http://orcid.org/0000-0002-2919-0608http://orcid.org/0000-0002-1161-2059http://orcid.org/0000-0002-1161-2059http://orcid.org/0000-0002-1161-2059http://orcid.org/0000-0002-1161-2059http://orcid.org/0000-0002-1161-2059http://orcid.org/0000-0002-7543-0668http://orcid.org/0000-0002-7543-0668http://orcid.org/0000-0002-7543-0668http://orcid.org/0000-0002-7543-0668http://orcid.org/0000-0002-7543-0668http://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/0000-0003-4808-391Xhttp://orcid.org/0000-0003-4808-391Xhttp://orcid.org/0000-0003-4808-391Xhttp://orcid.org/0000-0003-4808-391Xhttp://orcid.org/0000-0003-4808-391Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52011-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52011-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52011-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-52011-3&domain=pdfmailto:swarupdeb2580@gmail.commailto:tobias.korn@uni-rostock.dewww.nature.com/naturecommunicationsin these structures. We demonstrate ferroelectricity-induced controlof spin-valley dynamics by systematically studying the ultrafastresponse of excitons using transient reflection and Kerr ellipticity. As-grown samples are chosen over artificially stacked parallel structures,which provides a moiré-free crystal, enabling us to explore excitonicphenomena of purely ferroelectric origin and to employ far-fieldoptical spectroscopy on mesoscopic domains with well-definedstacking. Clear signatures of stacking-dependent K-valley excitonicresponse and a striking contrast in valley relaxation dynamics areobserved. This presents the prospect of using spin and valley as usefuldegrees of freedom in a robust multilayer platform. It is worth men-tioning that recent experimental efforts22 also underscore the possi-bility of utilizing multilayer 2H-TMDs for valleytronic applicationsdespite their centro-symmetric structure23.ResultsFerroelectric domains in 3R single crystalsWe begin by probing the electric surface potential of deterministicallystamped 3R-MoS2 flakes on non-polar hexagonal boron nitride (hBN)exfoliated on Si/SiO2(-285 nm) substrate (SI. S1). An atomic forcemicroscope operated in side-band Kelvin probe mode (KPFM) (SI. S2)is used to map the surface potential, VKP. Figure 1a shows an opticalmicroscopy image of a representative flake (Sample 1) composed offive and seven layers of MoS2. In a multilayer flake, each of the inter-faces may have either XM (polarization pointing upward) or MX(downward) stacking order creating a potential ladder either goingupwards or downwards, respectively7,13. The difference in the totalnumber of upward- and downward-pointing polarized interfacesdecides the cumulative polarization state, hence the surface potential.Therefore, different ferroelectric domains in a given thickness wouldbe visible in a VKP map. Based on this understanding, the existence oftwo ferroelectric domains, viz. domain I and II in the 5L region of thesample, becomes evident from Fig. 1b. Themeasured surface potentialvariation of ~ 127mV between these domains (SI Fig. S1) correspondsto the sum of effectively two ferroelectric interfaces, consistent withearlier results7,24.The appearance of different domains in a single crystal flake canbe attributed either to inherent stacking faults in the bulk 3R crystal orto the sliding by slip-avalanche of constituting layers from XM to MXstacking order or vice versa. Since the energies of all possible stackingconfigurations are similar (SI Fig. S19), the latter occurs as a result ofinadvertent shear strainduring exfoliation25 or deterministic stamping.To further illustrate the mechanism, we fabricated a sample by inten-tionally applying an in-plane perturbation, achieved by laterally tap-ping the substrate holder during the dry transfer of 3R-MoS2 fromPDMS to the substrate. This horizontal force introduces a shear stressbetween the layers that remain anchored to PDMS and the layersattached to the substrate. This deliberate horizontal force, which issignificantly stronger than the ubiquitously present shear forces dur-ing standard operations, generates smaller and densely packed ferro-electric domains, as identified by KPFM (SI Fig. S2). The ferroelectricdomains, in this case, are of similar dimension as in the artificiallystacked moiré interfacial ferroelectrics. However, achieving precisecontrol over domain formation and their structural organizationremains a challenge.Correspondence of surface potential and exciton fine structureTo check for the ferroelectric-field-induced changes in opticalresponse, we map the exciton transition energies over the entire flake(i.e. Sample 1) using confocal differential reflectance spectroscopy(SI. S3). Typical reflectance contrast (RC) spectra,ΔR/R = (RRef − RFlake)/RFlake26 obtained at different spatial locations of the flake at liquidhelium temperature are presented in Fig. 1d. Here RFlake is the reflec-tion fromMoS2 and RRef is the same from hBN (SI Fig. S3). In the energyrange of interest, the reflectance contrast of the few-layer MoS2 isdominated by three excitonic features, viz. the momentum-indirecttransition at ~1700meV and the well-known A and B excitons atXA ~1900 and XB ~2050meV27–29. Notably, the lowest energy featureFig. 1 | Reflection contrast imaging of ferroelectric domains in few-layer 3R-MoS2. a Optical micrograph of a 3R-MoS2 flake on Si/SiO2/hBN. Topographicalsteps and edges of the bottom hBN have been marked by white dotted lines.b Surface potential mapwithin the area enclosed by the black rectangle in (a). Twodomains, marked by ∘ and □, can be identified by the difference in contrast. c.Integrated intensity map of ΔR/R at the XA spectral region, i.e., from 1906 to1918meV (gray bar in inset of d). d Low-temperature reflectance contrast spectrafrom various spatial locations marked by symbols of corresponding color in c(black - 5L domain I, red - 5L domain II, and blue - 7L). Inset shows high-resolutionspectra collected fromdomain I and II. e, fTwocrystal configurations of 5L3R-MoS2overlayedon layer-projectedKV B andKCBband-edges. Tofirst order, the band edgevariation along Z and the degeneracies, highlighted for the XM-XM-MX-XM stack-ing by dotted lines, result from the ferroelectricity-induced electrostatic con-siderations (SI Figs. S12, 13 for other configurations). Arrows represent polarizationvectors at the interfaces.Article https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 2www.nature.com/naturecommunicationsdespite being a momentum-indirect transition has a prominentappearance. This can be attributed to the favorable thin-film inter-ference condition in the Fabry-Pérot cavity formed by Si/SiO2/hBN/MoS2 in the given energy range (SI Figs. S4, S5 for additional examplesand further discussion). We note that RC spectra, ΔR/R can also becalculated using (RRef − RFlake)/RRef30. We found that both representa-tions, ΔR/RRef and ΔR/RFlake share similar characteristic viz. the pre-sence of three distinct features and their energetic positions (SIFigs. S4, S5, S6, S15). However, the choiceof definitionmodifies the lineshape of each transition and therefore, the overall appearance of thespectra. Evidently, the lowest energy peak appears vividly in ΔR/RFlake(SI Figs. S4–S5, S10). Therefore, in the followingwe refer toΔR/RFlake asRC spectra unless mentioned otherwise.We proceed by constructing RC maps corresponding to differenttransitions by integrating the intensity over selected spectral ranges.The map of the momentum-indirect transition brings out a clearcontrast between the five- and seven-layer regions (SI Figs. S7–S8) dueto the red-shift in its spectral positionwith increasing thickness.On theother hand, the XA intensity map exhibits signatures of two distinctdomains within the topographically smooth 5L area, similar to theKPFM map. The contrast in the intensity map (Fig. 1c) is due to theappearance of higher- and lower-energy sub-features in the spectralregion from 1880 to 1930meV. The energy positions and relativeoscillator strengths of these fine features distinguishably mark theferroelectric stacking configuration, as revealed by the high-resolutionspectra shown in Fig. 1d-inset. In contrast to previous studies on arti-ficial R-stacked TMDs31, these subfeatures are not related to nanoscalereconstruction ofmoiré domains (as confirmedby the complementaryKPFM measurements). A similar spatial map is obtained from roomtemperature spectroscopymeasurements (SI Fig. S9); however, due tothermal broadening, spectral features can not be fully resolved. Cor-respondence between RC maps and KPFM images has been observedin several samples of different thicknesses, see Fig. S10 for example.Upon closer inspection, it becomes evident that XB exhibits a similartrait (SI Figs. S7, S8). To improve the signal-to-noise ratio of the RCspectra around the XB transition, we exploit the cavity effect by care-fully choosing the bottom hBN of our stack. SI Fig. S11 shows an RCspectrum of a trilayer-MoS2 flake on a 95 nm-hBN/285 nm-SiO2/Sisubstrate, where the splitting in theXBbecomes apparent. In a nutshell,momentum-direct excitons at the K points in the Brillouin zone revealthe stacking order, while the spectral feature related to themomentum-indirect transition remains insensitive to it. Based on thetrend of red-shift32 with increasing layer number, as shown in Fig. S4and previous studied on similar systems29,33, one can tentatively assignthe low-energy peak either to the Γ-Q or to K-Q hybrid-excitonic34transition.To explain the asymmetric response of different exciton speciesto ferroelectric ordering,we consider the band structure of 3R-MoS2. Ithas been shown that in bilayer 3R-TMDs, states at the Γ point of thevalence band (VB) or Q point of conduction band (CB) are fully delo-calized due to strong interlayer hybridization7,13,16. In contrast, thewavefunctions at the K points are almost entirely layer-localized. Theferroelectricity-induced built-in potential manifests as a local electro-static perturbation and introduces a shift between the layer-projectedenergy levels at K points, leading to a type-II band alignment at theinterfaces16, with the energies decreasing from layer X to layer M. Bythe same token, in a multilayer sample, the spatial profile of K-pointband extrema along the out-of-plane direction follows the underlyingferroelectric potential and is, therefore, susceptible to the stackingorder, as depicted schematically in Fig. 1e–f and SI Figs. S12, S13.Neglecting interlayer coupling through hybridization, a built-inelectric field should shift the conduction and valence bands by thesame amount, leaving the transition energies unchanged. Clearly, thisalone is insufficient for interpreting the experimentally observedemergingmultiplicity of transition energies. Therefore, to this end, weinspect the stacking-dependent strength of K states delocalizationbased on our band structure calculations depicted in Fig. 2a–c.Figure 2d–f, g–i presents the five lowest energy conduction-band andhighest-energy valence-band spin-up electron wavefunctions at the Kpoint, sorted according to their energy eigenvalues (for the followingsections, we have dropped the term ‘K point’ while referring to bandsand wavefunctions unless stated otherwise). For the fully polarized,XM-XM-XM-XM case (Fig. 2a, d, g), the individual wave functions bothat the valence and conduction band remain layer-localized with theirenergy levels corresponding to the ferroelectric potential ascendingwith each additional layer. However, for other variants, interlayerhybridization is evident (e.g., Fig. 2b, e, h, c, f, i). This dependence ofhybridization on ferroelectric ordering is the underlying mechanismfor the observed contrast in optical spectra. Before proceeding fur-ther, we note that a five-layer 3R-MoS2 crystal can have sixteen (2N−1,N = 5) stacking configurations, out of which KPFM can distinguishamong five combinations based on their surface potential (SI Fig. S12).At this stage, therefore, instead of attempting a one-to-one quantita-tive description of the stacking-dependent excitonic response, wefocus on the qualitative generic trend with three specific cases asexamples (all the studied systems are shown in the SI Figs. S20–S27).In the fully co-polarized XM-XM-XM-XM stacking, the potentialvariesmonotonically from layer to layer7. Thus, the three central layersexperience a similar ferroelectric field - preserving the energy degen-eracy of their intralayer excitonic transitions, appearing as a singlevertical line in the dipole matrix element plot (Fig. 2j). However, thetop and bottom layers show energetically distinct transitions due tobroken translational symmetry at the surfaces. The scenario changes inpartially polarized stacking due to selective interlayer couplingbetween specific layers. The mechanism described below is similar tothe quantum correction that leads to level anti-crossing by lifting theenergy degeneracy of coupled quantum systems. For instance, in theXM-XM-MX-XM configuration, electrostatic degeneracy (cf. Fig. 1f)leads to layer-specific resonant hybridization35 of KVB states, which isparticularly strong between the second and fourth layers. Pronouncedhybridization also occurs in the XM-XM-MX-MX case between themirror-symmetric layers, namely the first and fifth, as well as the sec-ond and fourth. In contrast to the valence band states, the KCB stateslargely retain their layer-localized nature in almost all cases exceptmirror-symmetric stacking orders. This layer- and band-specificstrength of interlayer hybridization leads to unequal shifts of layer-projected conduction and valence bands, lifting the intralayer transi-tion degeneracy even for the center layers and increasing the max-imum spread of energies, clearly visible in Fig. 2j–l. These findings areof a general nature for any parallel-stacked multilayer TMDs. Thisstacking-specific resonant hybridization is not relevant for the Γ and Qstates, which have a significant degree of hybridization irrespective ofstacking.In addition to the corrections to the electronic band structurearising from hybridization, changes in the exciton binding energy dueto asymmetric dielectric surroundings also play a role in determiningthe energetic position of individual transitions36. In order to provide aqualitative comparison to the experimental reflectance contrastspectra, we calculate the absorption spectra based on the intralayerdipole matrix elements and exciton binding energy (SI. S5, S6), con-sidering a phenomenological Lorentzian broadening with a full-width-half-maximum of 20 meV. These results are depicted in Fig. 2m. Evi-dently, the general shape with multiple sub-features, which stronglydepend on the individual stacking, closely mimics the experimentalobservations. However, it is important to note that DFT typicallyunderestimates the band gap of semiconductors due to the unac-counted derivative discontinuity of the typical exchange-correlationfunctionals37 and, therefore, the calculated absorption spectra are red-shiftedby about 480meV incomparisonwith the experimental results.By applying a rigid energy shift to the band gap, estimated from GWArticle https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 3www.nature.com/naturecommunicationscalculations, one can achieve transition energies that are more con-sistent with experimental data. For MoS2, this estimate yields a bandgap increase of about 530 meV38, which nearly matches the experi-mentally observed energies.Theseobservations provide an alternative experimental approachto identify local changes in ferroelectric ordering in 3R-TMD flakeswithout resorting to surface-sensitive5–7,39 measurements, whichbecome a challenge for heterostructures. In contrast to other opticalmeasurement schemes relying on a sensing layer40, the TMD itselfreveals its ferroelectric order in optical spectra. This allows for iden-tifying local domains, even in ‘buried’ layers, as required for integratingmore complex, functional heterostructures based on ferro-electric TMDs.Non-volatile electrical control and optical readout ofmulti-statepolarizationOur findings, therefore, present an unprecedented opportunity ofexploiting ferroelectric fields to gain non-volatile control over exci-tonic transitions in a field effect transistor architecture- a crucial stepforward for applications.We prepare devices on a conducting Si/SiO2(-90 nm) substrate, which acts as the gate electrode, and use few-layergraphite flakes tomake electrical contactwith 3R-MoS2 (viz. Sample 4).We use fully hBN-encapsulated structures for these measurements(therefore, RFlake is the reflection from hBN/MoS2/hBNheterostructureand RRef is the same from hBN/hBN). Here, we present results obtainedon a trilayer sample at room temperature. First, we map the ferro-electric domains at a few different gate voltages. Two differentdomains are visible in the false color map as blue and orange regions.Application of positive gate voltage results in an expansion of the bluedomains at the cost of the orange domains. An opposite change isobserved for negative gate voltage. Next, we measure the reflectioncontrast close to a domain boundary as a function of gate voltage. TheXA and XB transitions becomes weaker as the gate voltage is sweptforward from -18 V to 18 V, corresponding to increasing electrondoping. This reduction is due to a combined effect of Pauli blockingand reduced oscillator strength with state filling - typical of n-typeTMDs41–43. Notably, the reduction of intensity from the highest tolowest occurs through two distinct steps during the sweeping process(Fig. 3e). Furthermore, a prominent hysteretic behavior in the intensityof XA and XB transitions is observed as the gate voltage decreasesduring a backward sweep, for which the intensity rises again andsaturates (Fig. 3b–e and SI Fig. S16). We also examine the standarddeviation, which correlates with the full-width halfmaximumof XA andXB. Evidently, the resulting plots exhibit the same features (SI Fig. S17).The step-like features indicate discrete changes in opticalresponse due to ferroelectric switching through a mechanism knownas slidetronics, where the out-of-plane electricfield induces an in-planeslidingof adjacent layers4,21,44–46. At high electricfields, all the interfacesalign to achieve an energetically favorable configuration, viz. MX-MXor XM-XM, as indicated in Fig. 3e. Therefore, the hysteretic occurrenceof the discrete switching events in response to the external fielddirectly results from a finite coercive field - a hallmark of ferroelectricmaterials. The two distinctive steps observed for the trilayer samplereveal that switching between the multiple ferroelectric states of amultilayer is feasible and controllable via external voltages - a pivotalinsight for scalability.Our study yields an average coercive field of 0.03–0.035 Vnm−1 fordomain wall motion. Moreover, the hysteretic behavior of the mono-tonous intensity variation with gate voltage indicates a stacking-dependent change in average carrier concentration, observed earlierin transport measurements6,47. We note that a complete ferroelectricswitching is not achieved throughout the whole crystal within theexperimentally accessible gate voltage. This can be attributed to theincreasing domain boundary deformation energy48 and domain wallpinning at localized stacking faults as well as surface contaminants21.1 2 3 4 5K CB WFLy. No.XM-XM-MX-MXKM-1.2-1.1-1.00.50.6KM)Ve(ygrenEXM-XM-XM-XM XM-XM-MX-XMKMa b cLayer. No.Spin UpDown1 2 3 4 5Ly. No.d e fygrenE1 2 3 4 5Ly. No.1+52+41350 1370 1390 1410 1430 1450 1470 14900.00.51.0).mroN(noitprosbAEnergy (meV) XM-XM-XM-XM XM-XM-MX-XM XM-XM-MX-MX1880 1900 1920 1940 1960 1980 2000 2020Energy (band gap with scissor shift)(meV)m1554 1560 156601428|pcv|2Ve(Å)2Energy (meV)1554 1560 1566Energy (meV)1554 1560 1566Energy (meV)1 2 3 4 51 2 3 4 5K VB WFLy. No.1 2 3 4 5Ly. No.g hygrenE1 2 3 4 5Ly. No.1+52+4ij k lFig. 2 | Ab initio calculation of stacking-dependent band structure, wave-functions and optical response. a–c Band structure for different stacking orders.Spin orientation (∥ Z) of the individual bands is indicated by solid (spin up) anddashed (spindown) lines, respectively. The bands are colored corresponding to thedominant contribution of specific layers. The stacking of the band extrema at Kfollows the underlying ferroelectric potential. Due to mirror symmetry for the XM-XM-MX-MX case, some bands are (nearly) degenerate and cannot be attributed toan individual layer (indicated by different colors in f, i). d–i Absolute value of thelowest-energy spin-up conduction band (d–f) and highest-energy valence band(g–i) wavefunctions sorted according to their energies superimposed over thecrystal structure. Colors indicate the dominant layer(s) for each wavefunction.Ellipses are used to indicate (near-)degenerate states. The wave functions are layer-localized for the fully polarized case (d, g). For XM-XM-MX-MX (f, i), the lowest-energywave function is localized in the center layer, while the other wave functionshave equal weight in the mirror-symmetric layers. j–l Oscillator strength for tran-sitions from all spin-up KV B to all KCB with s+ polarization. The magnitude of theseintralayer transitions is in good agreement with values for pristine monolayerMoS256,57. m Calculated absorption spectra in the A excitonic region based onintralayer dipole matrix elements and layer-specific exciton binding energy,including a phenomenological Lorentzian line width of 20meV.Article https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 4www.nature.com/naturecommunicationsDomain-resolved exciton population and spin-valley dynamicsBesides gaining control over the excitonic oscillator strength, a meti-culous understanding of excitonic lifetime is essential in the pursuit ofrealizing exciton-based circuits. To this end, we focus on probing thestacking-order-dominated exciton dynamics and spin relaxation usingtwo-color pump-probe Kerr microscopy. Figure 4a illustrates themeasurement scheme. We use a circularly polarized pump pulse,slightly blue detuned to XA, to induce a spin polarization of chosenhelicity. The photo-generated excitons lead to photo-bleaching of agiven valley, resulting in helicity-dependent reflectivity. Therefore, thetransient exciton population and its spin-valley polarization can beprobed by recording the intensity and induced ellipticity of a time-delayed linearly polarized probe pulse after reflection49,50. A series ofsimultaneous transient reflectivity (TRΔR) and transient ellipticity(TRKE) measurements are performed in which the probe laser wave-length is tuned across the energy range ofXAwith the pumpenergy setat 1958meV. Figure 4b, c are false-color representations of TRΔRobtained from domain I and II of Sample 1 (cf. Fig. 1), respectively, as afunction of pump-probe delay. The energy-dependent temporal evo-lution of reflectivity in individual domains clearly corresponds to theirrespective steady-state response (superimposed white lines). For boththe domains, TRΔR traces at the higher resonance (marked by bluearrows) evolve similarly viz. an ultrafast decay component followed byrelatively slower dynamics, as depicted by the blue colored traces inFig. 4d, e. The response at the lower resonance energy has differentcharacters for different domains. For instance, in domain I, we observea monotonous decrease in the signal from t=0. Remarkably, fordomain II, during the initial five ps, the reflectivity of the probe pulseincreases with time, followed by a slower decay. The initial increaselikely stems from slow state filling at the probe energy during relaxa-tion, possibly suggesting interlayer charge transfer prompted byinterlayer hybridization. These observations, therefore, further sub-stantiate the theoretical understanding developed in the context ofsteady-state optical response.Unlike the transient reflection, the ellipticity signal manifests noprominent energy dependence. Instead, it is remarkably sensitive tothe ferroelectric stacking configuration and exhibits entirely differenttraits for the two domains investigated. Figure 4f and g portrays theTRKE results for domain I and II probed at higher and lower resonanceenergies (SI Fig. S28 for the complete spectrum). In domain I, the TRKEdecay is relatively slow, albeit faster than the decay of the transientreflectivity traces, indicating that it is not predominantly driven byexciton recombination but by a spin dephasing mechanism on asimilar timescale as observed in MoS2 monolayers51,52. By contrast, indomain II, the excitons lose their spin polarization almost instantly.The microscopic mechanism for this striking dependence of excitonlifetimes and spin-valley dynamics on ferroelectric order remains anopen question. However, recent calculations53,54 show that in parallel-stacked TMDs, dependent on the symmetry of the stacking order, in-plane spin-orbit coupling terms can arise that lead to spin mixing of Kstates. In this way, specific stacking orders may facilitate spindephasing, while others protect spin orientation, yielding prolongedspin-valley lifetimes comparable to TMD monolayers. This opens upthe use of spin and valley as useful degrees of freedom in 3R-stackedmultilayers, which have so far been limited predominantly to mono-layer TMDs.To conclude,wedemonstrate the direct correspondencebetweenferroelectric order and intralayer excitons in 3R-stacked MoS2 multi-layers, allowing us tomap ferroelectric domains directly using far-fieldoptical spectroscopy. Ab initio theory provides a comprehensiveexplanation of themicroscopic mechanism. In a field-effect device, weare able to control and map domain wall motion at room temperatureand observe clear hysteretic features with a coercive field of roughly0.03–0.035 V nm−1. The relatively small switching field of ferroelec-tricity by domain wall sliding could facilitate efficient electrical controlof various optical properties of 2D materials55. Addressing individualdomains in time-resolved experiments, we find that depending onferroelectric order, 3R-stacked MoS2 multilayers can show spin-valleydynamics on timescales comparable to TMD monolayers or near-instantaneous loss of valley polarization. Our study paves the way forutilizing ferroelectric order in few-layer TMDs embedded withinfunctional van der Waals heterostructures as a local, nonvolatile con-trol lever for excitonic and valleytronic properties. Theses findingsintroduce a distinctive perspective to the field of quantum optoelec-tronics with van der Waals materials and will enable novel optoelec-tronic device architectures that rely on efficient electricalmanipulation of excitons or the optical response in general.MethodsDevice fabrication3R-MoS2, obtained from HQ Graphene, were exfoliated onto poly-dimethylsiloxane (PDMS).MoS2flakeswere selected according to theiroptical contrast. Chosen TMD flakes were stamped on pre-exfoliatedhBN flakes. We use a polycarbonate (PC)/PDMS-based hot pickupFig. 3 | Hysteretic reflectance contrast as a functionof gate voltage. a Integratedamplitude false color map of the numerically calculated first derivative of RCspectra at different gate voltages to visualize domain switching. All measurementswere performed at room temperature. Evidently, the out-of-plane electric fielddrives the blue-colored region to grow in area coverage with increasing gate vol-tage at the expense of the orange-colored region. b, c False color map of A and Bexciton intensity as a function of gate voltage during forward and backward sweep.They share the same y-axis, given on the left. d Two representative room tem-perature reflectance contrast spectra at opposite gate voltages. Inset- schematicillustration of the field effect device. e Integrated intensity profile ( ≡ vertical linecuts from b) at 1852 ± 2meV. The vertical arrows represent the ferroelectricordering of each interface.Article https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 5www.nature.com/naturecommunicationsmethod to transfer hBN flakes from bare Si/SiO2 substrate to encap-sulatehBN/TMDstack. A few layer thickgraphiteflakes (procured fromNGSNaturgraphit), exfoliated on PDMS, are deterministically stampedto make external contact to the sample.KPFM measurementsKPFM measurements were performed using Park System NX20. Theelectrostatic signal was measured at side-band frequencies using twobuilt-in lock-in amplifiers. We used PointProbe Plus Electrostatic ForceMicroscopy (PPP-EFM) n-doped tips. For the unencapsulated sample(Sample 1 c.f. Fig. 1) we used non-contact mode of operation. Theaverage height above the surface was controlled via a two-pass mea-surement. The first pass records the topography, whereas, in the sec-ond pass, the tip follows the same scan line with a predefined lift(typically 4–5 nm) and measures the KPFM signal. In case of Sample 4c.f. Fig. 3 where we used a ~ 85 nm hBN for top encapsulation, weoperated the AFM in tappingmode and the KPFMmeasurements weredone in a single pass.Reflectance measurements and Spatial filteringFor reflectance measurements, the samples were illuminated with aquartz tungsten halogen lamp. The collimated beam was focused onthe sample using an 80X objective (NA=0.50, f=200). The reflectedlight from the sample was collected using the same objective andspectrally resolved using a spectrometer and a charge-coupleddetector. In the detection path, before the spectrograph, we intro-duce a home-built Spatial-Filtering module to enhance the spatialresolution. The input side of the spatial filter consists of an asphericlens mounted on a Z-translator. It focuses the reflected beam onto apinhole. The pinhole was carefully aligned to the beam path with thehelp of an XY translator. A fraction of the focused light passes throughthe pinhole aperture. Another aspheric lens was used to collect thebeam from the pinhole and collimate along the detection path.Time resolved reflectivity and Kerr ellipticityIn the pump-probe setup, two separately tunable pulsed lasers (Top-tica: femtoFiberPro) were used. Each system emitted with a pulserepetition rate of 80MHz, a spectral width of 6 meV, a pulse durationof about ~ 200 fs. Probe and pump pulses were electronically time-synchronized with aa auto- and cross-correlation width of ~ 300 and700 fs, respectively. The cross-correlation time of ~ 700 fs markstemporal resolution of our measurement. The pump beam was circu-larly polarized through an achromatic λ/4 plate. The pump beam wasset to a power of 30 μWand the probebeamwas set to 20 μW.Both thebeams were focused with an 80X (NA=0.50, f=200) objective onto thesample. Therefore, thepumpandprobefluence roughly correspond toa maximum of 1.7 and 1.1 KW/cm2, respectively. After reflection thepump beam was filtered out by a long-pass filter. The polarization ofthe probe beamwas analyzed for its ellipticity by a combination of a λ/4 plate, a Wollaston prism, and two photodiodes (ThorLabs PDB210ASi Photodetector). The difference signal of the two diodes was fed intoa lock-in amplifier, yielding a TRKE signal. The sum signal of the diodeswas fed into a second lock-in amplifier, yielding the TRΔR signal.Data availabilityThe data generated in this study have been deposited in the FigSharedatabase under accession code https://figshare.com/projects/ExcitonicSignaturesOfFerroelectricOrderInParallel-stackedMoS2/217963.Fig. 4 | Exciton population and spin dynamics. a Schematic of pump-probe Kerrmeasurement. A blue detuned (to XA) circularly polarized light pulse for the pumpand linearly polarized pulse for the probe were used. Upon reflection, the linearlypolarized pulses turn elliptically polarized. By projecting the reflected elliptic pulseon a quarter waveplate and a Wollaston prism, we can separate out the relativestrength of right and left circular components. The total probe intensity change isequivalent to net exciton density, and the intensity difference between left andright circular components gives the net spin-valley polarization. All the pump-probe measurements were done at 4 K. b, c False color map of transient reflectionasa functionofprobe energy fromdomain I and II.White contours (without y-scale)are copied from Fig. 1d-inset for comparison. d, e Transient reflection at selectedenergies,markedbycolored arrows in (b, c). Theopposite trend in the amplitudeofthe TRΔR signal at the lower and higher energy states from the two domains is adirect consequence of opposite relative strength of these sub-features in thesteady-state spectroscopic signal. f, g Traces of transient ellipticity at resonantenergies in respective domains. The spin-valley lifetime in domain I is on the orderof 10-15 ps,while in domain II the signaldecaysdown to thedetectionnoise-flooronsub-ps timescales.Article https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 6https://figshare.com/projects/ExcitonicSignaturesOfFerroelectricOrderInParallel-stackedMoS2/217963https://figshare.com/projects/ExcitonicSignaturesOfFerroelectricOrderInParallel-stackedMoS2/217963https://figshare.com/projects/ExcitonicSignaturesOfFerroelectricOrderInParallel-stackedMoS2/217963www.nature.com/naturecommunicationsReferences1. Li, L. &Wu, M. Binary compound bilayer andmultilayer with verticalpolarizations: two-dimensional ferroelectrics, multiferroics, andnanogenerators. ACS Nano 11, 6382–6388 (2017).2. Woods, C. R. et al. Charge-polarized interfacial superlattices inmarginally twisted hexagonal boron nitride. Nat. Commun. 12, 1–7(2021).3. Yasuda, K., Wang, X., Watanabe, K., Taniguchi, T. & Jarillo-Herrero,P. 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K.W. and T.T. acknowledge support from the JSPSKAKENHI (grant numbers 21H05233 and 23H02052) and World PremierInternational Research Center Initiative (WPI), MEXT, Japan.Author contributionsS.D. and T.K. conceived the idea for the study. S.D. performed theexperiments, prepared the samples togetherwith J.K., analyzed the datatogether with T.K. and P.F.J. and wrote the manuscript in close interac-tionwith all other authors. M.K., R.S., and T.K. designed, built, and testedthe setup for the time-resolved Kerr experiments. S.D. upgraded thesetup for simultaneous time-resolved reflectivity measurements. K.W.and T.T. providedhigh-qualityhBNcrystals for sample preparation. P.F.J.and J.F. performed the DFT calculations and analyzed the results toge-ther with S.D. and T.K.FundingOpen Access funding enabled and organized by Projekt DEAL.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-52011-3.Correspondence and requests for materials should be addressed toSwarup Deb or Tobias Korn.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-52011-3Nature Communications |         (2024) 15:7595 8https://doi.org/10.1038/s41467-024-52011-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Excitonic signatures of ferroelectric order in parallel-stacked MoS2 Results Ferroelectric domains in 3R single crystals Correspondence of surface potential and exciton fine structure Non-volatile electrical control and optical readout of multi-state polarization Domain-resolved exciton population and spin-valley dynamics Methods Device fabrication KPFM measurements Reflectance measurements and Spatial filtering Time resolved reflectivity and Kerr ellipticity Data availability References Acknowledgements Author contributions Funding Competing interests Additional information