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Shun Feng, Aidan J. Campbell, Mauro Brotons-Gisbert, Daniel Andres-Penares, Hyeonjun Baek, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Bernhard Urbaszek, Iann C. Gerber, Brian D. Gerardot

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[Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2](https://mdr.nims.go.jp/datasets/d219e98e-219e-4e7c-9c62-e3cf79563e17)

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Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2Article https://doi.org/10.1038/s41467-024-48476-xHighly tunable ground and excited stateexcitonic dipoles in multilayer 2H-MoSe2Shun Feng 1,6, Aidan J. Campbell1,6, Mauro Brotons-Gisbert 1 ,Daniel Andres-Penares1, Hyeonjun Baek1, Takashi Taniguchi 2,Kenji Watanabe 3, Bernhard Urbaszek4, Iann C. Gerber 5 &Brian D. Gerardot 1The fundamental properties of an exciton are determined by the spin, valley,energy, and spatial wavefunctions of the Coulomb-bound electron and hole. Invan der Waals materials, these attributes can be widely engineered throughlayer stacking configuration to create highly tunable interlayer excitons withstatic out-of-plane electric dipoles, at the expense of the strength of theoscillating in-plane dipole responsible for light-matter coupling. Herewe showthat interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intra-layer A excitons. We demonstrate that the hybrid states of these distinctexciton species provide strong oscillator strength, large permanent dipoles(up to 0.73 ± 0.01 enm), high energy tunability (up to ~200meV), and fullcontrol of the spin and valley characteristics such that the exciton g-factor canbemanipulated over a large range (from −4 to +14). Further, we observe the bi-and tri-layer excited state (2s) interlayer excitons and their coupling with theintralayer excitons states (1s and 2s). Our results, in good agreement with acoupled oscillator model with spin (layer)-selectivity and beyond standarddensity functional theory calculations, promote multilayer 2H-MoSe2 as ahighly tunable platform to explore exciton-exciton interactions with stronglight-matter interactions.A range of exotic collective effects are predicted to arise from dipolarinteractions1,2, which have a quadratic dependence on the magnitudeof the static electric dipoles (p). For example, strong dipolar interac-tions may result in exciton crystals, which exhibit ordering due to abalance between exciton kinetic energy and many-body Coulombinteractions3–7, or lead to nonlinear exciton switches which can reachthe quantum limit when the strength of the interaction is larger thanthe exciton’s radiative linewidth8–10. Hence, in the solid-state, muchemphasis has been placed on engineering interlayer excitons withlarge p in pioneering III–V heterostructures11 and more recently intransition metal dichalcogenide (TMD) heterostructures12–14 whichhost excitons with huge binding energies and thus small Bohr radii15,16that enable high exciton densities17,18. In TMD heterostructure devices,tunable interlayer excitons with large p have been realised inhomobilayers19–29 and heterobilayers30–33, even at the single excitonlevel34–36. However, many of the exotic collective effects underpinnedby strong dipolar interactions remain to be observed, motivating fur-ther exploration of interlayer excitons and ways to manipulate theirspin and optical properties. For example, it is desirable to increase theelectron-hole spatial separation beyond the interlayer distance, butReceived: 28 March 2024Accepted: 29 April 2024Check for updates1Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh, UK. 2International Center for Materials Nanoarchitectonics, NationalInstitute forMaterials Science, Tsukuba, Japan. 3ResearchCenter for FunctionalMaterials, National Institute forMaterialsScience, Tsukuba, Japan. 4InstituteofCondensed Matter Physics, Technische Universität Darmstadt, Darmstadt, Germany. 5INSA-CNRS-UPS LPCNO, Université de Toulouse, Toulouse, France.6These authors contributed equally: Shun Feng, Aidan J. Campbell. e-mail: m.brotons_i_gisbert@hw.ac.uk; B.D.Gerardot@hw.ac.ukNature Communications |         (2024) 15:4377 11234567890():,;1234567890():,;http://orcid.org/0000-0003-1831-8255http://orcid.org/0000-0003-1831-8255http://orcid.org/0000-0003-1831-8255http://orcid.org/0000-0003-1831-8255http://orcid.org/0000-0003-1831-8255http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://orcid.org/0000-0001-7254-8292http://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/0000-0001-5091-2655http://orcid.org/0000-0001-5091-2655http://orcid.org/0000-0001-5091-2655http://orcid.org/0000-0001-5091-2655http://orcid.org/0000-0001-5091-2655http://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://orcid.org/0000-0002-0279-898Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48476-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48476-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48476-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48476-x&domain=pdfmailto:m.brotons_i_gisbert@hw.ac.ukmailto:B.D.Gerardot@hw.ac.uknot at the cost of vanishing oscillator strength. This goal is intrinsicallydifficult for bare interlayer exciton states (e.g. in TMD heterobilayerswith type II interfaces). Recent experimental and theoreticalefforts21,23,37 suggest that each ‘bare exciton’ is actually composed of amixture of other exciton wave functions, and their mixture can betuned by detuning energy between transitions. Here we use the termbare exciton to denote the majority of each transition for simplicity.While previous studies focusedonhybrid interlayer excitons formed inadjacent ‘natural’ homobilayers21–23, an open question remains if largerhybrid interlayer dipoles, with the electron and hole highly confined inseparate layers, can be generally obtained in multilayer TMD plat-forms. Further, due to the decreasing oscillator strengths of excitedRydberg-like states15,16,38, the observation of excited states of interlayerexcitons has proven elusive to date. Characterisation of the excitedstate spectrum of interlayer excitons provides additional informationabout their basic properties and a potential means to further engineerdipolar interactions by taking advantage of their larger Bohr radii,which has been crucial to realise optical nonlinearity39 and excitonicanalogues of spatially ordered structures in ultracold atomic gases40.To address these issues, we take advantage of hybridised excitons inbilayer (2L) and trilayer (3L) 2H-MoSe2 composed of the bare excitonstates of the interlayer excitons (both 1s and 2s) and the ground (1s)and excited (2s) states of the intralayer A-excitons. We simultaneouslydemonstrate strong oscillator strength and wide tunability of thefundamental properties (spin, valley, energy, and spatial wavefunc-tion) of the hybrid exciton species in multilayer MoSe2.Results and discussionDevice structure and introduction to excitons in multilayer2H-MoSe2Figure 1a shows a sketch of our device, which consists of a terraced 2H-MoSe2 flake with 2L and 3L regions encapsulated by hexagonal boronnitride (h-BN) layers with nearly identical thicknesses (~18 nm). Gra-phene layers act as electrical contacts for theMoSe2 crystal and the topand bottom gates (seemethod section for further details of the devicefabrication). In our experiments, the MoSe2 contact is grounded whilewe apply voltages to the top and bottom gates, labelled as VT and VB,respectively. This configuration allows us to apply a vertical electricfield with a magnitude VE (where VE =VB = −VT) while keeping the car-rier concentration in the MoSe2 sample constant at charge neutrality.Similar to other TMDs, each layer in our terraced 2H-MoSe2 flake hoststightly bound intralayer excitonswith both ground (1s) and excited (2s,3s, etc.) states15. Ground and excited intralayer exciton states presentthe same exact spin-valley configuration. In the case of the lowestenergy excitons in MoSe2 (the so-called A excitons, XA), both theground and excited exciton states originate from Coulomb-boundelectron-hole pairs in the lower- (higher-) lying conduction (valence)band at ±K (see Fig. 1b), respectively, which endows them with thesame optical selection rules: excitons at ±K couple to σ±-polarisedlight41. In addition to XA, there are intralayer B excitons (XB) composedof the electron (hole) at the top (bottom) of the conduction (valence)band at ±K, respectively, with a considerable energy difference andopposite spin index compared to XA.Beyond intralayer exciton states, multilayer TMDs also hostinterlayer excitons, in which the layer-localised electron wave func-tions can bind to holes with wave functions confined predominantlywithin adjacent layers or spread across several layers, giving rise toexcitons with spatially extended wave functions19,21–25. Interlayer andintralayer excitons have been shown to coexist in multilayer20 and 2L2H-MoSe224. Figure 1a shows a sketch of the possible intra- and inter-layer exciton spatial configurations in our terraced 2L/3L 2H-MoSe2,wherewe have assumed that, despite the possible spatial spread of thecarrier wave functions, the carriers are predominantly confined to asingle layer. This assumption leads to three different bare excitonspecies: (i) intralayer excitons within each individual layer (i.e. groundand excited states of the A and B exciton series in MoSe242); (ii) inter-layer excitons with the carriers residing in adjacent layers (IX2L), inwhich the electron and hole occupy the upper spin-orbit-split con-duction band and the topmost valenceband of each layer, respectively(see Fig. 1b); and (iii) interlayer excitons in which the carriers reside inthe outermost layers of the 3LMoSe2 region (IX3L), where the electron(hole) occupies the lowermost (topmost) conduction (valence) band(see Fig. 1b). In the 3L MoSe2 region, IX2L can be formed with carriersfrom the middle MoSe2 layer (L2) and carriers from either the bottom(L1) or top (L3) MoSe2 layers. Note that, despite the spatially indirectcharacter of IX2L and IX3L, these interlayer exciton species exhibitmomentum-direct (intravalley) optical transitions within ±K. More-over, the vertical displacement of the electron andholewave functionsof the bare interlayer excitons results in an out-of-plane static electricdipole (negligible for intralayer excitons), with a dipole polarity andmagnitude that depend on the positions and the spatial separation ofthe electron and hole in the multilayer, respectively (see Fig. 1a). Suchout-of-plane permanent electric dipoles of interlayer excitons in otherTMD multilayers, homostructures, and heterostructures have beenshown to lead to large shifts of the exciton transition energies via thequantum confined Stark effect21–23,32,35,43. Finally, the natural 2HaL3L2L1+ ++K -KXACB: L1 (L2, L3)VB: L1 (L2, L3)XBL1 (L2, L3)L1 (L2, L3)+ +Intralayer excitons+IX2LL1 (L3) L2 (L2)Interlayer excitonsbGraphenehBNVTVB- - -- -+K -K+K +K+K -K+K -K+-+IX3LL1 (L3) L3 (L1)+K +K--+Fig. 1 | Intralayer and interlayer excitons in a terraced 2L/3L 2H-MoSe2 sample.a Sketchof the sample anddeviceused in this work: a 2H-MoSe2 crystalwith 2L- and3L-thick terraces in a dual-gated device configuration. Electrons and holes (red andblue circles, respectively) can be localised either in the bottom (L1), middle (L2), ortop (L3) MoSe2 layers, giving rise to different species of strongly bound intralayerand interlayer excitons. The vertical white arrows indicate the direction of thepermanent electric dipoles for the different interlayer excitons. The interlayerstackings are highlighted asRhh between L1 and L3 andHhh between L1 (L2) and L2 (L3),wherehdenotes the hexagon centre in the crystal lattice of each layer.b Spin-valleyconfigurations of the intralayer and interlayer excitons depicted in panel a: intra-layer A and B excitons (purple shaded ovals), and bilayer and trilayer interlayerexcitons (red and grey shaded ovals, respectively). The layer labels (L1–L3) on eachpanel indicate the layer origin of the corresponding electronic states in the con-duction (CB) and valence (VB) bands. The purple (green) bands correspond to spinup (down).Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 2stacking of our terraced 2L/3LMoSe2flake results in a different relativestacking configuration between the different layers. While IX2Linvolves MoSe2 layers with a relative 2H stacking, IX3L originates fromMoSe2 layers with a relative Rhh-type stacking, where h denotes thehexagon centre of the crystal lattice in each layer (see Fig. 1a). Hence,each IX species is endowed with distinct spin-layer-valley configura-tions (see Fig. 1b) that can be optically probed. Finally, we note that therelative Rhh-stacking between L1 and L3 is distinct from 3R-stackedhomobilayers27,44. For 3R-type bilayers the two layers are laterallyshifted so that the hexagon centres in each layer are not verticallyaligned, rendering a different symmetry and resulting in a forbiddenhole tunnelling45.Electric field-dependent excitonic transitions in 2L 2H-MoSe2To investigate the layer-dependent and intra-/interlayer nature of thedifferent exciton species in the terraced 2H-MoSe2 flake, we performdifferential reflection contrast (ΔR/R0) spectroscopy at cryogenictemperature (4 K) as a function of VE at charge neutrality, whereΔR =Rs −R0, andRs (R0) is the intensity of the light reflectedby theflake(substrate). We focus first on the 2L region of our MoSe2 sample.Supplementary Fig. S1 shows a representative reflection contrastspectrum of our 2L 2H-MoSe2 at VE = 0V, where several excitonicresonances with different linewidths and absorption strengths areobserved (see Supplementary Fig. S2. for the extracted exciton line-widths). The strongest exciton resonances at low (~1.63 eV) and highenergy (~1.86 eV) correspond to the ground states of intralayer A (XA1s)and B (XB1s) neutral excitons in 2L MoSe2, respectively. Two additionalweaker exciton resonances, separated only by ~25meV, are alsoobserved in the energy range between the A and B intralayer 1s excitonstates, which can be attributed to IX2L (~1.715 eV) and the first excitedexciton state XA2s of the neutral A exciton (~1.74 eV), in agreement withprevious experimental and theoretical results on bulk20 and 2L 2H-MoSe224. More precisely, we perform GW+BSE calculations (see Sup-plementary Note 2 for computational details) and obtain IX2L and XA2speaks 0.11 and 0.17 eV above the XA1s one, respectively (see Supple-mentary Fig. S3), which qualitatively agrees with our experiment inwhich IX2L and XA2s are 0.07 and 0.11 eV above XA1s. To corroborate theintra-/interlayer character of the IX2L and XA2s states and unravel theirlayer-dependent properties, we show in Fig. 2a a density plot of the VE-dependence of the first derivative of the reflectance contrast spectrawith respect to photon energy (d(ΔR/R0)/dE) in the spectral range1.68–1.78 eV, which helps to visualise these exciton transitions (seeSupplementary Fig. S5 for comparison with bare ΔR/R0 spectra). AtVE =0V, we observe the two excitonic resonances attributed to IX2LandXA2s . The application of aVE lead to a stark contrast in the behaviourof the two resonance peaks. For small positive applied VE, the reso-nance energy of the high energy peak remains almost constant, whilethe low energy peak splits into two exciton branches which shiftsymmetrically towards lower and higher energies with a lineardependence with VE. This phenomenon can be interpreted in terms ofthe DC Stark energy (ΔU) tuning experienced by interlayer excitonsunder applied out-of-plane electric fields:ΔU = −pE, with E the strengthof the vertical electric field and p = ed the out-of-plane electric dipolemoment (where e represents the electron charge and d the electron-hole distance). The absolute values of the energy shifts of the two IX2Lbranches allow us to estimate an average electron-hole spatialseparation of d =0.34 ±0.01 nm for IX2L, which is comparable to thereported values of 0.39–0.47 nm for IXs in other TMD homostructuresca↑/↓IX2LA, L1/L2X2seA, L2X2sIX2L+K+KhX1, hX3++K +K++-A, L1X2s ↑IX2LhX2, hX4VE > 0L1 L2 L1 L2B, L2XB, L1X↓VE < 0+ +--+--4-202461.68 1.70 1.72 1.74 1.76 1.780.000.010.020.030.040.05-0.08 -0.04 0.00 0.04 0.080.00.10.20.30.40.00.40.1 0.20.00.40.00.10.20.30.4IX↑2LXA, L12sXA, L22sIX↓2LhX1, hX3hX2, hX4Electric Field (eV/Å)Energy Shift (eV)Absorption (a.u.)0.03 eV/ÅIX↑2LXA, L22sXA, L12sIX↓2L0 eV/ÅEnergy Shift (eV)IX↑/↓2LXA2sOscillator Strength(a.u.)bdhX2 hX4hX1 hX3Fig. 2 | Layer hybridised excitons in 2L 2H-MoSe2. a VE dependence of the firstderivative of the reflectance contrast spectra with respect to photon energy(d(ΔR/R0)/dE) in our 2L 2H-MoSe2 in the spectral range 1.68–1.78 eV. b Calculatedenergies of the different hybrid IX2L–XA2s exciton states as a functionofVE, whichwelabel as hX1, hX2, hX3, and hX4 from low to high energy atVE >0V, respectively. Thecolour of the solid lines denotes the contribution of the different bare excitonstates to each hybrid exciton. c Schematics of the spin, valley, and layer config-uration of the exciton states responsible for the exciton hybridisation shown inpanel a for negative and positive appliedVE (left and right panels, respectively). Theexciton hybridisation is attributed to a second-order effective coupling betweenIX2L and the intralayer A exciton facilitated via the A and B exciton admixture(depicted by the glowing double arrows).d The energy position of IX2L and XA2s as afunction of the applied electric field, as obtained from GW+BSE calculations. Thelabels identify the simplified bare exciton states. eNormalised theoretical oscillatorstrengths (red vertical line) and absorption spectra (black line) at 0 eV/Å and0.03 eV/Å focusing on the energy range of IX2L and XA2s . The numerical precision ofour calculations is estimated to be of the order of ±5meV, see computationaldetails in Supplementary Note S2.Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 3such as 2L MoS222,23, and 0.63 nm (0.26 nm) for momentum direct(indirect) IXs in twisted 2L MoSe228. This result unambiguouslydemonstrates the presence of a sizeable static electric dipole in theout-of-plane direction and corroborates the interlayer exciton natureof IX2L20,24. Moreover, the symmetrical but opposite energy shifts ofthe two IX2L branches reveal the presence of IX2L excitons with dif-ferent polarities (i.e. with static electric dipoles aligned parallel andanti-parallel to the applied electric field), as sketched in Fig. 1a. Forpositive VE, IX2L excitons shifting to lower (higher) energies originatefrom Coulomb-bound electron-hole pairs in which the hole is spatiallylocated in the top (bottom) layer of the 2L MoSe2, i.e. with staticelectric dipoles pointing up (IX"2L) and down (IX#2L), respectively. Notethat for negative VE, the behaviour of IX"ð#Þ2L is reversed. Therefore, theStark shifts of IX"ð#Þ2L allow us to unravel their layer configuration.Further, the large DC Stark tuning of IX2L allows us to explore thepossible hybridisation between IX2L and the energetically close XA2s byreducing their energy detuning via the applied VE. For ∣VE∣ ≈ 2 V, IX2Land XA2s show an energy anti-crossing characteristic of coupled sys-tems, suggesting the hybridisation of the two exciton species.We notethat this observation is reproduced across the 2L 2H-MoSe2 sample.Supplementary Fig. S6 shows the results for a different spatial locationin the 2L 2H-MoSe2.In order to estimate the magnitude of the coupling between IX2Land XA2s, we employ a phenomenological model in which the hybridi-sation between the exciton states is treated as a coupling betweenoscillators with resonance energies corresponding to the bare excitonstates (see Supplementary SectionS1 for details). In ourmodel,we takeinto account the spin, valley, and layer degrees of freedom of eachexciton species, which leads to eight exciton resonances with differentspin, valley, and layer properties: two IX2L with opposite polarities(IX"ð#Þ2L ) andmomentum-direct transitions at ±K each, and XA2s localisedin the top (XA,L22s ) and bottom (XA,L12s ) MoSe2 layers with momentum-direct optical transitions at ±K each. Regarding the IX2L–XA2s hybridi-sation, we include it in our model as a phenomenological interlayercoupling of holes at ±K, with a magnitude which we assume to beindependent of VE. In our calculations, the energies of the excitonstates at VE =0V and the slope of the DC Stark shift for IX"ð#Þ2L are set tomatch the corresponding experimental values, while the value of thecoupling strength between the exciton states is left as a free parameterthat can be tuned to fit our experimental data. Figure 2b shows thecalculated energies of the resulting hybrid exciton states as a functionof VE, which we label as hX1, hX2, hX3, and hX4 from low to high energyat VE >0V, respectively. The colour of the solid lines in Fig. 2b denotesthe contribution of the different bare exciton states to each hybridexciton. Thephenomenologicalmodel captureswell the hybridisation-induced renormalisation of the exciton resonance energies withincreasing electric field, allowing us to estimate an IX2L–XA2s couplingstrength κ2L−2s ≈ 5.2meV, which is slightly smaller but of the sameorder of magnitude as the linewidths of the exciton states at VE =0V(see Supplementary Fig. S2).The physical origin of the observed hybridisation between aninterlayer exciton and the first excited state of an intralayer exciton isintriguing, and to the best of our knowledge has not been reported inany other homobilayer TMD system.We discard the possibility of spin-conserving electron hopping between the electron states involved inIX2L and XA2s, since such interlayer electron hopping is forbidden in 2L2H-MoSe2 due to theC3 symmetry of the dz2 orbitals of the conductionband states at ±K45,46. However, recent theoretical work has shown thatthe application of a vertical electric field can lead to the hybridisationof IX2L and XB1s in 2L 2H-MoSe2 via spin-conserving interlayer holetunnelling47, in agreement with previous experimental and theoreticalresults for 2L 2H-MoS223,48. Moreover, similar to 2L 2H-MoS249, thetheoretical results in Ref. 47 also suggest a weak admixture betweenthe A and B excitons in 2L 2H-MoSe2, which leads to a non-vanishingsecond-order effective hybridisation of IX2L and the intralayer XA1sexciton. Since XA1s and XA2s have the same nature (i.e. same exact spinand valley configuration), we tentatively attribute the observedIX2L–XA2s hybridisation to a second-order effective coupling betweenIX2L and the intralayer A exciton facilitated by through intravalleyexchange interaction between the A (spin up) and B (spin down)excitons (see Fig. 2c)47–49. This result agrees well conceptually with thetheoretical modelling in ref. 47, and leads to a layer selective couplingbetween IX2L and the intralayer A exciton, as also captured by ourphenomenological model (see Fig. 2b). Our estimated value of thecoupling strength κ2L−2s ≈ 5.2meV is very similar to the couplingstrength reported for IX2L and XA1s excitons in 2H-MoS2, and sig-nificantly smaller than the direct coupling between the IX2L and XB1sexcitons in the same 2H-MoS223,48 and 2H-MoSe2 sample50, which sup-ports our hypothesis.To further corroborate our hypothesis, we calculate GW+BSE-based estimates of the excitonic transition energies and their corre-sponding oscillator strengths at various external electric field values(see Fig. 2d, e). For vertical applied positive electric fields, the IX2Lexcitons experience a significant Stark shift, which supports theirinterlayer nature. The XA,L12s remains relatively unchanged, while theXA,L22s exhibits an energy shift with the applied electric field, indicativeof the layer-selectivemixingwith the IX2L state. In fact, our calculationsreveal a sizeable mixing between IX2L and XA,L22s even at zero appliedelectric field. Table 1 in Supplementary Section S2 summarises theoscillator strengths of the different bare optical transitions con-tributing to each excitonic resonance in Fig. 2d, e, corresponding to0V/Å and 0.03 V/Å applied electricfields, respectively. The conversionfrom VE to electric field is shown in Fig. S4.Electric field-dependent excitonic transitions in 3L 2H-MoSe2To explore the potential for multilayer TMDs to host IX with dipolemoments even larger than IX2L andwith greater tunability, we opticallyprobe the 3L region of our terraced 2H-MoSe2 sample at charge neu-trality as a function of VE. Figure 3a shows the VE-dependence ofd(ΔR/R0)/dE in the spectral range 1.58–1.78 eV (with the values in theenergy range 1.66–1.78–eV multiplied by a factor 4 for visualisationpurposes). The reflectance spectrum at VE = 0V is markedly differentto the one observed in the 2L region (see Fig. 2a). We observe twoexciton transitions in the energy range corresponding to XA1s with anenergy splitting of ~11meV, and two exciton resonances in the energyrange of IX2L with an energy splitting of ~14.5meV. The resonances atlow energy can be attributed to XA1s excitons localised in the differentlayers of our sample, in which the lower average permittivity envir-onment of L1 and L3 (h-BN/L1,(3)/MoSe2) compared to L2 (MoSe2/L2/MoSe2) results in a dielectric-induced energy blue shift for XA1s excitonsin L1 and L3 (XA,L1ðL3Þ1s ) compared to XA1s excitons in L2 (XA,L21s )51, similar towhat has been observed for 3L MoS223.To unravel the nature of the excitons in the energy range corre-sponding to IX2L, we focus on their behaviour as a function of VE. Asshown in Fig. 3a, the applicationof a vertical electric field gives rise to aStark-effect-induced splitting of each resonance into two distinctexciton branches which shift symmetrically towards lower and higherenergies with a linear dependence with VE (see the comparisonbetween ΔR/R0 and d(ΔR/R0)/dE in Supplementary Fig. S7). For thelower exciton resonance, we estimate an average electron-hole spatialseparation of d =0.36 ±0.01 nm, which agrees very well with the valuefound for IX in the 2L region of our sample, confirming its IX2L nature.The energy splitting of the two branches belonging to the higherenergy resonance yields an average electron-hole separation ofd =0.73 ± 0.01 nm, which exceeds the interlayer distance of TMDhomobilayers52 and is approximately twice the IX2L dipole size. Wetherefore identify this resonance as IX3L. Note that the deviationbetween the effective dipole moment and physical interlayer distance(~0.6 nm and 1.4 nm for 2L and 3L, respectively) further indicates thatthese hybrid interlayer excitons are not pure ‘bare excitons as in theArticle https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 4simple cartoon picture, rather, they are composed of a mixture ofintra/interlayer exciton wave functions. The wavefunction admixtureleads to intra/interlayer contributions to the effective dipolemomentsof the hybrid IX2L and IX3L. Using IX2L as an example, it consists of thebare intralayer exciton with negligible vertical dipole moment and thebare interlayer exciton with dipole moment ~0.62 nm. In real space,this is in line with a qualitative description that the electron of the IX isrelatively layer localised while the holes are relatively delocalised inboth layers37, which yields an effective dipole size that is roughly 50%of the physical interlayer distance. The DFT calculations also suggestsimilar exciton admixtures at high field i.e. 52% of intralayer X2s and38% IX2L (Table I in Supplementary Information, XA,L22s list in lowerpanel), qualitatively supporting the experimental results. As a result ofthe complex wave function mixing, the hybrid K-valley IX may havematerial-dependent effective dipole moments. In addition, the choiceof the dielectric constants differs in hybrid IX studies53, which alsointroduces discrepancies in the extracted dipole moments.Furthermore, the larger Stark shift of IX3L allows tuning its energyinto resonance with XA1s (see Fig. 3a). For ∣VE∣ ~ 4 V we observe a clearavoided crossing between IX3L and XA,L1=L31s , indicative of the hybridi-sation between the exciton species with carriers hosted in the outer-most layers of the 3L MoSe2 sample. Supplementary Fig. S8 shows theresults for a different spatial location in the 3L 2H-MoSe2.We note thatcontrary to the results for the 2L region, we observe negligible oscil-lator strength of XA2s in the 3L MoSe2 region, which prevents clearobservation of coupling between this exciton state and the two IXspecies. Therefore, we focus on the clear IX3L–XA1s hybridisation.Similar to the 2L case, we simulate the VE-dependent energy dis-persion of the hybridised excitons in the 3L MoSe2 system using aphenomenological model of coupled oscillators, in which the excitoncoupling is both spin- and layer-selective (see Fig. 3b). In this case, weinclude three different XA1s excitons (i.e. one in each layer) and two IX3Lwith opposite polarities (IX"ð#Þ3L ) and momentum-direct transitions at±K each. Spin-conserving hole tunnelling results in a layer-selectivecoupling between IX3L andXA1s; the polarity of IX3L is locked to the layerdegree of freedom of XA1s (e.g. IX"ð#Þ3L only couples to XA,L1ðL3Þ1s ). However,the energy degeneracy of XA,L11s and XA,L31s prevents clear observation ofsuch layer-selective coupling experimentally. Figure 3b shows theresults of the best fit of themodel to our experimental data. The colourof the solid lines denotes the contribution of the different bare excitonstates to each hybrid exciton. Overall, the phenomenological modelcaptureswell the hybridisation-induced renormalisation of the excitonresonance energies with increasing electric field, allowing us to esti-mate an IX3L–XA1s coupling strength κ3L−1s ≈ 7.5meV, which is slightlylarger but of the same order of magnitude as κ2L−2s in the 2L region.Furthermore, it is worth noting that the R-type relative stacking of thelayers L1 and L3 leads to some differences between the IX3L–XA1s andIX2L–XA2s couplings. The R-type stacking between L1 and L3 results inIX3L with electron-hole pairs with the same spin-valley configurationsas XA (see Fig. 1a), which allows the hybridisation of the two excitonspecies via direct spin-conserving interlayer hole tunnelling in thepresence of an additional layer between L1 and L329,54. For the specificstacking registry of Rhh between L1 and L3, a recent work calculated an11meV tunnel splittingof the valenceband (withmonolayer BNasL2)29,supporting our interpretation. On the contrary, due to the 2H relativestacking between adjacent layers, the direct hole tunnelling betweenthe valence band states in IX2L and XA has to compete with a sizabledetuning equal to the spin splitting at the valencebandedges (150meVin MoSe254), and is thus only facilitated by the admixture of XA and XB.Finally, we note that the energy detuning between IX2L and the energydegenerate XA,L11s and XA,L31s exciton resonances is slightly smaller in the3L region as compared to the 2L one. As a consequence, we are able toobserve experimental signatures of the coupling between these twoexciton species at VE ~ 6 V (see Fig. 3a and Supplementary Informa-tion S4), which corroborate our results for the 2L 2H-MoSe2. Wesummarise the rules for determining which excitons can hybridisebased on our new insight and other references (see SupplementaryInformation S5).Electric-field-dependent magneto-optical properties of hybridexcitons in MoSe2Beyond tuning of the exciton resonance energies, oscillator strengths,and effective permanent electric dipoles, here we explore if theelectric-field-dependent control of the exciton nature enables preci-sion tuning of the effective Landé g-factors. The application of a ver-tical magnetic field B results in the Zeeman splitting of the opticaltransitions of each exciton at ±K, with an energy splitting ΔE(B) = gμ0B,with μ0 the Bohr magneton. Optical transitions at ±K can be inde-pendently probed by σ±-polarised light, respectively, which enables usto perform circularly polarised reflectance contrast measurements toestimate the experimental Zeeman splitting ΔE = Eσ + � Eσ�, with Eσ ±the energy of the σ±-polarised transition. We focus first on the hybridIX2L–XA2s exciton states in our 2L region. Figure 4a shows themeasuredZeeman splittings (blue dots) for hX4 at three different applied VEvalues. Supplementary Fig. S9 shows the linecuts for the σ±-resolvedd(ΔR/R0)/dE at VE = 0V for 5 T. The blue solid lines represent linear fitsof the experimental data, fromwhichwe estimate the effective g-factorat each applied VE. We observe the effective g-factor of hX4 is tunedfrom a negative value (−1.9 ± 0.5) to a relatively large positive value(11.8 ± 0.4). To explore this effect in more detail, we employ the sameexperimental procedure and extract the effective g-factors of hX3 andhX4 in the range of applied VE in which the oscillator strength of eachba c× 4↑/↓IX3LA, L1/L3X1s↑/↓IX2LA, L2X1sA, L1/L3X1sA, L2X1s + +A, L3X1sK+ K+L1 L2-+KL3↓IX3L+ +A, L1X1sK+ K+L1 L2-+KL3↑IX3LVE < 0 VE > 0↑/↓IX3LFig. 3 | Layer hybridised excitons in 3LMoSe2. a VE dependence of d(ΔR/R0)/dE inthe 3L MoSe2 region of our sample. b Energies of the different hybrid IX3L–XA1sexciton states as a function of VE, where the colour of the solid lines denotes thecontribution of the different bare exciton states to each hybrid exciton.c Schematics of the spin, valley, and layer configuration of the exciton statesresponsible for the exciton hybridisation shown in panel (a) for negative andpositive applied VE (left and right panels, respectively). The exciton hybridisation isattributed to direct spin-conserving interlayer hole tunnelling between L1 and L3.Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 5transition and their energy detuning with respect to other transitionsenable a reliable estimate of Eσ ±, i.e. VE <0 for hX3 and VE >0 for hX4(as indicated by the red and blue shaded areas in Fig. 4b). The resultshighlight a continuous and smooth transitionof the g-factor of the twohybrid exciton states from − 1.9 ± 0.5 to 11.8 ± 0.4 by changing VE from0V to±4.5 V. Such evolutionof the effective g-factor arises from theVE-dependent hybridisation between IX2L and XA2s, and can be quantita-tively explained by our phenomenological model of coupled oscilla-tors. In this model, the wave function of each hybrid exciton isexpressed as a superposition of the bare intralayer and interlayerexciton wave functions (see Supplementary Section S1). In the case ofhX3 and hX4, these exciton wave functions are expressed as follows:∣hX3ðVE Þ�= CIX3 ðVE Þ∣IX"2LE+ CX3 ðVE Þ∣XA,L12sEð1Þand∣hX4ðVE Þ�= CIX4 ðVE Þ∣IX#2LE+ CX4 ðVE Þ∣XA,L22sE, ð2Þwhere CIXðXÞi ðVE Þ represents the VE-dependent amplitude of the bareinterlayer (intralayer) exciton state in hybrid exciton state ∣hXi�, withjCIXi ðVE Þj2 + jCXi ðVE Þj2 = 1. Therefore, the effective g-factor of eachhybrid exciton state (ghXi) can be expressed asghXiðVE Þ = jCIXi ðVE Þj2gIX2L+ jCXi ðVE Þj2gX2s, ð3Þwhere gIX2LðX2s Þ represents the g-factor of the bare IX2L (X2s) state. Thesolid line inFig. 4b represents afit of the experimental data to Eq. (3), inwhich we have used the CIXðXÞi ðVE Þ values shown in the top panel ofFig. 4b (obtained from the fits in Fig. 2b), and gIX2Land gX2shave beenleft as free fitting parameters. Our model captures well thehybridisation-induced evolution of the g-factors and allows us toestimate of the effective g-factors of the bare states: gX2s≈� 4 andgIX2L≈12:5.Wenote that, although to thebestof our knowledge gX2shasnot been previously reported for 2LMoSe2, our estimated value of gX2sis in very good agreement with reported experimental (−3.6 ± 0.155)and theoretical (−3.756) values for this excited exciton state inmonolayer MoSe2 and other TMD systems such as bulk WSe2(−3.3 ± 0.620). Regarding gIX2L, the estimated sign and value are alsoin good agreement with the value predicted by a simplistic “atomicpicture”, in which the g-factor of the bands hosting the electron-holepairs are assumed to be equal to the sum of their spin, orbital, andvalley magnetic moments57. Within this model, the spin-valleyconfiguration of IX2L results in a gIX2L= 2ðm0m*c+ m0m*vÞ+4≈9:7, with m0the free electron mass, and m*c and m*v the experimentally reportedelectron and hole effective masses for the bottom conduction bandand top valence band in monolayer MoSe2, respectively58. Therelatively large and positive value of the g-factor estimated with thisatomic picture model provides additional confirmation of the spin-valley configuration and interlayer natureof IX2L. Also,we note that thesmall discrepancy between the experimental and the calculated valuefor gIX2Lmight arise from a combination of several factors, includingthe limitation of this simple model to estimate accurately the g-factorof the relevant bands59 and the absence of experimental values for theelectron effectivemass of the top conduction band in 2LMoSe2, whichtheoretical calculations predict to be slightly smaller than for thebottom conduction band in Mo-based TMDs such as 2H-MoSe260 and2H-MoS261. Nevertheless, we note that the extracted g-factors of thebare IX2L and X2s states allow us to include the effects of the Zeemansplitting in the calculated VE-dependent evolution of the hybridIX2L–X2s states, for which we find a very good agreement with theexperimental results (see Supplementary Note S3 and SupplementaryFig. S14).Finally, we investigate the magneto-optical properties of IX3L inthe 3L region of the sample. Figure 4c shows the experimental Zeemansplitting for this exciton species at VE =0V, from which we estimate ag-factorgIX3L= � 4:9 ± 0:1. The extracted value for gIX3Lis very similarto the experimentally reported g-factor of XA1s in 3L MoSe259, whichconfirms the identical spin-valley configuration of these two excitonspecies and corroborates that the giant dipole IX3L indeed originatesfrom electron and hole in L1 and L3 (or vice versa), respectively. Theidentical spin-valley configuration of XA1s and IX3L has an importantconsequence on themagneto-optical properties of the hybrid XA1s–IX3Lstates: contrary to the hybrid XA2s–IX2L states in 2L MoSe2, hybridXA1s–IX3L do not feature a VE-tunable g-factor (see VE = 3 V Zeemansplitting in Fig. S10), since the two bare exciton states already exhibit asimilar g-factor.Excited state interlayer excitons in multilayer 2H-MoSe2Although excited (Rydberg) exciton states have weaker oscillatorstrength than their corresponding ground states15, in this section, weshow that the hybridisation of interlayer excitons with intralayertransitions leads to clear spectroscopic signatures of excited Rydbergstates for both IX2L and IX3L. Figure 5a,b show d2(ΔR/R0)/dE2 spectra asa function of VE for 2L and 3L 2H-MoSe2 regions, respectively, corre-sponding to spatial locations where the interlayer excited excitonstates present appreciable oscillator strengths. The data shown in thespectral ranges 1.797–1.830 eV and 1.665–1.800 eV in Fig. 5a, b haveca bhX4hX3Fig. 4 | Magneto-optical properties of layer-hybridised excitons in 2L MoSe2and3LMoSe2. aZeemansplittingofhX4 at threedifferent appliedVE. Thebluedotsrepresent the experimental values, while the blue solid lines show linear fits of theexperimental data, from which we are able to estimate the effective g-factor of thishybrid exciton at each appliedVE.bVE-driven evolutionof the g-factor of the hybridexcitons hX3 (−5 V to 0V, red shaded area) and hX4 (0V to 5 V, blue shaded area) inbilayer MoSe2 (bottom panel). The top panel shows the VE-dependent contribu-tions of each bare exciton state jCIX ðX Þ3,4 j2 to the corresponding hybrid excitons.c Zeeman splitting of IX3L atmeasured at VE =0V. Error bars are from uncertaintiesin Lorentz peak fit and linear fit, respectively.Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 6been multiplied by a factor 2 for visualisation purposes. In the 2Lregion (Fig. 5a), for 4≲VE≲ 6V we resolve an additional exciton tran-sition in the energy range ~1.7 eV with a linear Stark shift parallel to theIX"2L. Extrapolation of the linear energy shift to VE =0V gives an esti-mated energy of ~1.77 eV for this excitonic transition with clear inter-layer nature.We note that the relative energy position of this excitonicpeakwith respect to both IX2L and XA2s agrees well with the first excitedRydberg state of IX2L predictedbyourGW+BSE results (see Fig. 2e andSupplementary Fig. S3). This, together with the dipole moment of0.30 ± 0.01 enm estimated from the linear Stark shift (almost identicalto the one for IX2L), allows us to attribute the observed resonance tothe first excited Rydberg state of IX"2L (i.e. IX"2s,2L). Notably, for ∣VE∣ ~ 3 Vand energies ~1.82 eV, we observe two additional resonances withopposite Stark shift slopes that also extrapolate to an energy of~1.77 eV at VE =0V, which we attribute to IX#2s,2L (VE >0V) and IX"2s,2L(VE <0V), corroborating our peak assignment. We note that the IX2s,2Lstate is a general feature rather than a location-dependent feature ofour sample, aswe also observe IX2s,2L in themain locations of 2L and 3LMoSe2 shown in Figs. 2–4, as depicted in Supplementary Fig. S11.Further, we observe a very weak transition near 1.72 eV for 4≲ VE≲ 6Vwith a Stark shift parallel to IX2s,2L, which we tentatively ascribe as the3s Rydberg state of IX2L. Extrapolation to VE =0V gives an estimatedenergy for the 3s state of ~20meV higher than the 2s at zero appliedelectric field (Supplementary Fig. S12).Similar to Fig. 5a, the results in Fig. 5b also display clear excitedRydberg states in the 3L 2H-MoSe2 sample. In addition to the coexistinginterlayer exciton species IX2L and IX3L already shown in Fig. 3, weobserve twoadditional transitionswithStark-induced linear energy shiftsparallel to the IX3L, which we attribute to the two opposite polarities ofthe 2s excited Rydberg state of IX3L (i.e. IX"ð#Þ2s,3L). Extrapolation of themeasured linear energy shifts of IX"ð#Þ2s,3L to VE=0V gives an estimatedenergy ~40meV above the IX3L ground state (near the XA2s transition).We simulate the VE-dependent energy dispersions of the hybri-dised ground and excited exciton Rydberg states using the phenom-enological coupled oscillatormodel previously described.We build onthe models used for Figs. 2b and 3b and add the the observed excitedRydberg states, which we assume to have identical Stark shifts and thesame spin- and layer-selective couplings as their correspondingground states. Figure 5c, d shows the simulated energy dispersionscorresponding to the results in Fig. 5a, b, respectively. As can beobserved in these figures, the simulated energy dispersions capturewell the VE-induced hybridisation and energy dispersion of the differ-ent excitonic transitions (see Supplementary Information Fig. S17 forthe simulated absorption spectrum as a function of VE correspondingto Fig. 5b using this model and Supplementary Information section S1for simulation details), supporting our interpretation of their differentintra-/interlayer origin, ground/excited state character, and spin andvalley configurations. On top of the electric field sweeps, we per-formed additional characterisations on the excited state IXs, whichreveal the doping-dependent energy dispersion and magnetic field-dependentdiamagnetic shift of IX2s,2L andhigher order excited state ofIX3L (Supplementary Information S7 and 8).Finally, we note that the relative energy order of IX2L and IX3L at0 V varies across the sample. Here we summarise our experimentalfindings and provide a qualitative explanation. In the primary 3Llocation (Fig. 3), the IX2L (lower energy) and IX3L (higher energy) areseparated by 12.6meV; in the secondary 3L location (Fig. 5), the IX2Land IX3L energetic ordering is reversed with a 15meV difference(opposite sign to the primary location); in a tertiary location (Fig. S8b),we observe similar trend as the first location, where IX2L can beextrapolated to be around 17meV lower in energy than IX3L at 0 V. Theenergy order is interpreted as a combined effect of interband transi-tion energies (determined by the band gap and binding energy),dielectric screening, local strain, andpossible exciton statemixing (seeSupplementary Information S6 for a more detailed discussion)DiscussionOur work reports the observation of giant Stark splitting of the inter-layer excitons in 2L and 3L 2H-MoSe2. First, we observe hybridisationbetween IX2L and XA2s. In addition to their spectral evolution, aFig. 5 | Observation of excited states of IX2L and IX3L. a VE dependence ofd2(ΔR/R0)/dE2 in a second location of the 2L 2H-MoSe2 sample in the spectral range1.67–1.83 eV. b d2(ΔR/R0)/dE2 in another location of the 3L 2H-MoSe2 sample in thespectral range 1.58–1.8 eV. c Calculated energies of the different exciton states of2L 2H-MoSe2 including IX2s,2L with the same spin and layer configuration as IX2L.d Calculated energies of the different exciton states in 3L 2H-MoSe2 includingIX2s,3L with the same spin and layer configuration as IX3L.Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 7hybridisation-driven g-factor evolution of the coupled excitons isresolved and understood via a unified coupled oscillator model. Theability to drive the exciton Zeeman splitting from negative to positivethrough zero has potential in electrically tunable valleytronics andspin-dependent exciton-exciton interactions. Next, we report the giantexcitonic trilayer dipole IX3L, which exhibits distinct spin-layer selec-tion rules for hybridisation with XA1s. A salient feature of the large IX3Ldipole is that it can be Stark tuned to become the ground state (e.g.lower energy thanXA1s), promising for applications in exciton transport.Finally, by harnessing the exciton hybridisation effects, we successfullyprobe the excited state IX for the first time in a TMD system. Futuretheory and experimental effort is encouraged to better understand theexcited IX states, including comparisons with the hydrogenmodel andthe magnetic field and doping dependence to reveal the g-factor,effective mass58 and Roton-like62 properties of the interlayer Rydbergexcitons. In future work, an external cavity could be used to enhancethe light-matter interaction strength63 and take advantage of the largeenergy tunability. The excited state IX with large spatial extension, aswell as dipolar nature, may further facilitate polariton blockade in realspace that may even lead to quantum nonlinearity64,65. Altogether,these results promote a new TMD homostructure candidate forapplications with enhanced exciton-exciton interactions with stronglight-matter coupling. Beyond 3L 2H-MoSe2, a strategy of furtherengineering IX dipoles by tuning the layer number, including thickermultilayer (>3L) 2H-TMDs or heterostructures with multilayer TMDcomponents and hBN spacers, is encouraged.Following the submission of our manuscript, a related work oninterlayer excitons (similar transition as IX3L in our work) in multilayer2H-WSe2 has been published53.MethodsSample fabricationBulk MoSe2 crystal was exfoliated onto polydimethylsiloxane (PDMS)stamps and aflakewith a terraced 2L and 3L regionwas identifiedusingoptical contrast. Few-layer graphene and hBN layers were also pre-pared and identified on PDMS. The flakes were then stacked sequen-tially onto pre-patterned Au electrodes on SiO2/Si substrates using theall-dry viscoelastic transfer technique in an Ar-filled glove box66.Optical measurementsThe sample was held in a closed-cycle cryostat (Attodry 1000) at 4 K,where a magnetic field can be applied out-of-plane to the sample(Faraday configuration). For the reflectance measurements, thebroadband spectrum from a power-stabilised tungsten lamp was col-lected by a multimode fibre. The light was collimated by a 20×objective and focusedon the samplewith an achromaticobjectivewitha 0.82 numerical aperture. The reflected light was collected with thesame objective and then focused onto a single-mode fibre and detec-ted using a liquid nitrogen-cooled CCD spectrometer. The setup isconfocal in collection due to the small diameter of the core of thecollectionfibre. The incident and collectedpolarisationof the lightwascontrolled using a series of linear polarisers, quarter-wave and half-wave plates.Data availabilityThe dataset generated and analysed during the current study isavailable at https://doi.org/10.17861/5a2ae35f-9787-47bc-bb0e-a0395f064509. Source data are provided with this paper.References1. Butov, L. Condensation and pattern formation in cold exciton gasesin coupledquantumwells. J. Phys.Condens.Matter 16, R1577 (2004).2. Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. Thephysics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72,126401 (2009).3. Astrakharchik, G. E., Boronat, J., Kurbakov, I. L. & Lozovik, Y. E.Quantum phase transition in a two-dimensional system of dipoles.Phys. Rev. Lett. 98, 060405 (2007).4. Capogrosso-Sansone, B., Prokof’ev, N. V. & Svistunov, B. V. Phasediagram and thermodynamics of the three-dimensional bose-hub-bard model. Phys. Rev. B 75, 134302 (2007).5. Slobodkin, Y. et al. 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Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1,011002 (2014).AcknowledgementsThisworkwas supportedby theEPSRC (grant nos. EP/P029892/1 andEP/L015110/1), and the ERC (grant no. 725920). S.F. is supported by a MarieSkłodowska-Curie Individual FellowshipH2020-MSCA-IF-2020SingExTr(no. 101031596). M.B.-G. is supported by the Royal Society UniversityResearch Fellowship. B.D.G. is supportedby aWolfsonMerit Award fromthe Royal Society and a Chair in Emerging Technology from the RoyalAcademy of Engineering. K.W. and T.T. acknowledge support from theElemental Strategy Initiative conducted by the MEXT, Japan (grant no.JPMXP0112101001) and JSPS KAKENHI (grant nos. 19H05790,20H00354, and 21H05233). I.C.G. acknowledges the CALMIP initiativefor the generous allocation of computational time, through project no.p0812, aswell asGENCI-CINES,GENCI-IDRIS, andGENCI-CCRT for grantno. A012096649.Author contributionsS.F. and A.J.C. contributed equally to this work. S.F. and A.J.C. per-formed the optical measurements. H.B. fabricated the sample. D.A.-Pperformed transfer matrix analysis. S.F. and M.B.-G. performed coupledoscillator model simulation. S.F., A.J.C., M.B.-G., B.U., and B.D.G. ana-lysed the data. I.C.G. performed the theoretical calculations. T.T. andK.W. grew the hBN crystals. B.D.G. and M.B.-G. conceived and super-vised the project. S.F., A.C., M.B.-G., and B.D.G. wrote the paper withinput from all authors.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-024-48476-xNature Communications |         (2024) 15:4377 9https://doi.org/10.48550/arXiv.2303.09931https://doi.org/10.48550/arXiv.2303.09931Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-48476-x.Correspondence and requests for materials should be addressed toMauro Brotons-Gisbert or Brian D. Gerardot.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/s41467-024-48476-xNature Communications |         (2024) 15:4377 10https://doi.org/10.1038/s41467-024-48476-xhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2 Results and discussion Device structure and introduction to excitons in multilayer 2H-MoSe2 Electric field-dependent excitonic transitions in 2L 2H-MoSe2 Electric field-dependent excitonic transitions in 3L 2H-MoSe2 Electric-field-dependent magneto-optical properties of hybrid excitons in MoSe2 Excited state interlayer excitons in multilayer 2H-MoSe2 Discussion Methods Sample fabrication Optical measurements Data availability References Acknowledgements Author contributions Competing interests Additional information