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Roberto Rosati, Ioannis Paradisanos, Libai Huang, Ziyang Gan, Antony George, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Laurent Lombez, Pierre Renucci, Andrey Turchanin, Bernhard Urbaszek, Ermin Malic

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[Interface engineering of charge-transfer excitons in 2D lateral heterostructures](https://mdr.nims.go.jp/datasets/f6cae166-7d1b-4b91-ada0-b89a5fc6009a)

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Interface engineering of charge-transfer excitons in 2D lateral heterostructuresArticle https://doi.org/10.1038/s41467-023-37889-9Interface engineering of charge-transferexcitons in 2D lateral heterostructuresRoberto Rosati 1 , Ioannis Paradisanos 2, Libai Huang 3, Ziyang Gan4,5,AntonyGeorge 4,5, Kenji Watanabe 6, Takashi Taniguchi 7, Laurent Lombez2,Pierre Renucci2, Andrey Turchanin 4,5, Bernhard Urbaszek2,8 & Ermin Malic1The existence of bound charge transfer (CT) excitons at the interface ofmonolayer lateral heterojunctions has been debated in literature, but contraryto the case of interlayer excitons in vertical heterostructure their observationstill has to be confirmed. Here, we present a microscopic study investigatingsignatures of boundCTexcitons in photoluminescence spectra at the interfaceof hBN-encapsulated lateral MoSe2-WSe2 heterostructures. Based on a fullymicroscopic and material-specific theory, we reveal the many-particle pro-cesses behind the formation of CT excitons and how they can be tuned viainterface- and dielectric engineering. For junction widths smaller than theCoulomb-induced Bohr radius we predict the appearance of a low-energy CTexciton. The theoretical prediction is compared with experimental low-temperature photoluminescence measurements showing emission in thebound CT excitons energy range. We show that for hBN-encapsulated het-erostructures, CT excitons exhibit small binding energies of just a few tensmeV and at the same time large dipole moments, making them promisingmaterials for optoelectronic applications (benefiting from an efficient excitondissociation and fast dipole-driven exciton propagation). Our joint theory-experiment study presents a significant step towards a microscopic under-standing of optical properties of technologically promising 2D lateralheterostructures.Monolayers of transition metal dichalcogenides (TMD) have attrac-ted much attention due to their remarkable excitonic and opticalproperties1,2. So far the research has focused on vertical TMD het-erostructures obtained by stacking TMD monolayers on top of eachother3. These are characterized by spatially separated interlayerexcitons forming an out-of-plane dipole and thus allowing, e.g., agate-controllable exciton transport4,5. In comparison, much less isknown about lateral TMD heterostructures6–14, where two differentTMD monolayer materials are grown sequentially and covalentlybond in the plane6–12 (Fig. 1a). These structures show regular mono-layer optics and transport features when optically excited far fromthe interface12,13. At the interface, however, bound charge transfer(CT) excitons have been theoretically predicted15. Here, the Coulombinteraction binds together electrons and holes that are spatiallyseparated at opposite sides of the junction (cf. Fig. 1a, b). This spatialseparation results in an in-plane dipole that is typically larger than inReceived: 14 December 2022Accepted: 4 April 2023Check for updates1Department of Physics, Philipps-Universität Marburg, Renthof 7, D-35032Marburg, Germany. 2Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 AvenueRangueil, 31077 Toulouse, France. 3Department of Chemistry, Purdue University, West Lafayette, IN, USA. 4Friedrich Schiller University Jena, Institute ofPhysical Chemistry, 07743 Jena, Germany. 5AbbeCentre of Photonics, 07745 Jena, Germany. 6ResearchCenter for FunctionalMaterials, National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 7International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1Namiki, Tsukuba 305-0044, Japan. 8Institute of Condensed Matter Physics, Technische Universität Darmstadt, 64289 Darmstadt, Germany.e-mail: rosatir@staff.uni-marburg.deNature Communications |         (2023) 14:2438 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2514-3425http://orcid.org/0000-0002-2514-3425http://orcid.org/0000-0002-2514-3425http://orcid.org/0000-0002-2514-3425http://orcid.org/0000-0002-2514-3425http://orcid.org/0000-0001-8310-710Xhttp://orcid.org/0000-0001-8310-710Xhttp://orcid.org/0000-0001-8310-710Xhttp://orcid.org/0000-0001-8310-710Xhttp://orcid.org/0000-0001-8310-710Xhttp://orcid.org/0000-0001-9975-3624http://orcid.org/0000-0001-9975-3624http://orcid.org/0000-0001-9975-3624http://orcid.org/0000-0001-9975-3624http://orcid.org/0000-0001-9975-3624http://orcid.org/0000-0002-9317-5920http://orcid.org/0000-0002-9317-5920http://orcid.org/0000-0002-9317-5920http://orcid.org/0000-0002-9317-5920http://orcid.org/0000-0002-9317-5920http://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/0000-0003-2388-1042http://orcid.org/0000-0003-2388-1042http://orcid.org/0000-0003-2388-1042http://orcid.org/0000-0003-2388-1042http://orcid.org/0000-0003-2388-1042http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37889-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37889-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37889-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-37889-9&domain=pdfmailto:rosatir@staff.uni-marburg.devertical heterostructures15, where the dipole is limited by layerseparation. Therefore, the CT exciton binding energy is expected tobe smaller compared to interlayer excitons15–17. Furthermore, smallerband offsets have been predicted for lateral heterostructures18,suggesting that CT excitons are expected to be energetically closeto the intralayer excitons. This reduced energy separation fromthe bright-exciton energy makes their detection challenging andcould explain that so far there have been no clear experimentalsignatures for the existence of bound CT excitons in lateralTMD heterostructures - in contrast to interlayer excitons in verticalheterostructures3.In this work, we develop a fully microscopic and material-specificmany-particle theory to shed light on the existence of CT excitons inlateral TMD heterostructures. We also perform cryogenic photo-luminescence (PL) measurements to directly check the theoreticalpredictions. Motivated by the recent progress in the growth of lateralheterostructures with atomically sharp interfaces9,14,19–21, we theoreti-cally investigate optimal conditions to find CT excitons (i) via interfaceengineering (interface widths, band offsets) and (ii) dielectric engi-neering (surrounding substrates). In particular, we address the com-petition between Coulomb-induced spatial confinement of excitons(Bohr radius) and interface widths. Considering the exemplary case ofhBN-encapsulated MoSe2–WSe2 lateral heterostructures14,20, we pre-dict for small junction widths and low temperatures the appearance ofan additional low-energy resonance in PL spectra that we assign to abound CT exciton. To test this, we perform cryogenic PL measure-ments in hBN-encapsulatedMoSe2–WSe2 lateral heterostructures witha high-quality, very narrow junction width of ~2–3 nm14. We find PLemission peaks at the heterojunction in the high-quality samples thatare below the MoSe2 and WSe2 intralayer excitons and that presenta strong indication for the bound CT excitons predicted by ourmicroscopic theory. Our joint theory–experiment study presents animportant advance for a microscopic understanding of lateral TMDheterostructures, as we identify key conditions for the observation ofCT excitons in terms of interface and dielectric engineering. Further-more, we predict CT exciton binding energies of just a few tens ofmeVas well as extraordinarily large dipole moments for hBN-encapsulatedmaterials. This indicates that lateral heterostructures with ultrathinjunctions and weakly bound CT excitons to have also technologicalrelevance for optoelectronic devices due to the expected high excitonmobility13, efficient exciton dissociation, and diode-like exciton trans-port across the interface14.ResultsWe investigate the exemplary case of an hBN-encapsulatedMoSe2–WSe2 lateral heterostructure. We start with our microscopictheory and compare then with our cryogenic PL measurements.Figure 1b schematically shows the spatial variation of single-particleenergies E0Mo=WðxÞ in the considered lateral heterostructure. The con-duction and valence bands form offsets ΔEc,ΔEv at the interface,typically inducing a type II alignment12,20,22–24 with the conduction bandminimum located in the MoSe2 layer18. Note that for gate-inducedhomojunctions25–27, the band offsets are the same, i.e. ΔEc =ΔEv,potentially leading to bound excitons for p–i–n junctions confinedto a few tens of nanometers28. At the interface, CT excitons canbe built (purple oval) with the minimum continuum energyE0CT = E0Mo � ΔEv = E0W � ΔEc. Here, we focus on bright CT excitons withthe hole located at the K valley in the WSe2 layer and the electronlocated at the K valley in the MoSe2 layer, as this is the energeticallylowest CT configuration, cf. the Supplementary material. Dark CTexcitons could be important e.g. in lateralWSe2–WS2heterostructures,where the minimum of the conduction band is located in the WS2layer18. Importantly, this CT continuum is lower in energy thanmonolayer bandgaps suggesting a high occupation of these states.To obtain the energy of bound CT excitons, Coulomb interactionneeds to be included resulting in excitonic energies (cf. Fig. 1c, d).The two-dimensional nature of TMD monolayers induces a reducedscreening of the Coulomb interaction. The weakly screened Coulombattraction leads in monolayers to quantization in the relative coordi-nate resulting in the formation of Coulomb-bound electron–hole pairs(excitons) XMo=W = E0Mo=W � XbMo=W with large exciton binding energiesXbMo=W. The lowest 1s excitons are characterized by a Bohr radius in therange of one nanometer for hBN-encapsulated TMD monolayers29. Atthe interface of a lateral heterostructure an additional quantization ofthe center-of-mass motion can occur. The Coulomb-induced bindingof spatially separated electrons and holes can form bound CT excitonsthat are localized at the interface with the energy XCT = E0CT � XbCT.However, their binding energies XbCT are expected to be smaller thanin the intralayer case due to the spatial separation between electronsand holes. This reduced binding energy for spatially-separated exci-tons is qualitatively similar to interlayer excitons in verticalTMD heterostructures16,17, however, the separation of the latter islimited to the interlayer distance of the two TMD layers (althoughextendable via spacers5). In contrast, the separation of electrons andholes in a CT exciton is not limited by any geometrical constraint andcan be principally much larger13,15. As a direct consequence, CTexcitons are expected to have smaller binding energies comparedto interlayer excitons, but exhibiting a large static electric dipole(cf. the Supplementary Materials). One important goal of this work isto study under what conditions these bound CT excitons XCT can beobserved, i.e. when are they clearly below the XMo exciton and havea sufficiently large oscillator strength. To reach this goal weperform interface and dielectric engineering in our calculations,allowing us to shift the relative position of intralayer and CT excitons(cf. Fig. 1c, d).Fig. 1 | Lateral heterostructures. a Two TMD monolayers (e.g. MoSe2 and WSe2)are stitched laterally. b They have intrinsic bandgaps E0Mo and E0W while formingconduction and valence band offsets ΔEc,ΔEv around the junction. Spatially sepa-rated electrons and holes across the interface form charge-transfer (CT) excitonswith the corresponding continuumenergy E0CT = E0Mo � ΔEv. c, dBoundCT excitonsXCT (red flat line) appear below the energy of intralayer MoSe2 exciton XMo (orangeline) for either large band offsets ΔEv (interface engineering) or large dielectricconstants ε (dielectric engineering).Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 2Methodology and key quantitiesTo describe the spatially dependent energy landscape in a lateralheterostructure, it is crucial to include both the material-specific sin-gle-particle energies (Fig. 1b) as well as the Coulomb interaction thatformsexcitons (Fig. 1c, d). To this purpose,we investigate the excitoniceigenstates Ψn�� �with eigenenergies En of the Schrödinger equationH∣Ψn�= En∣Ψn�with the Hamilton operator H including both the spa-tially dependent single-particle energies Eλ(x) (with the band indexλ = c, v) and the Coulomb interaction between electrons and holes byusing a generalized Keldysh potential VC(r)30,31. Here r is the in-planeposition vector, with x and y denoting the component perpendicularand parallel to the interface, respectively. Exploiting the symmetryalong the y direction parallel to the interface and the fact that the totalexciton mass M =me +mh is much larger than the reduced massμ =memh/(me +mh), we can separate the eigenstates in a center-of-mass and a relative part withΨnðR,rÞ=ψnðRxÞe{QyRyϕRx ðrÞ with r as therelative coordinate and R and Q as the center-of-mass coordinate andmomentum, respectively15. Here,ϕRx ðrÞ and ψn(Rx) are the solutions ofthe corresponding Schrödinger equations for the relative and thecenter-of-mass motion:�_2∇2r2μ+ VCðrÞ + VRx ðrÞ" #ϕRxi ðrÞ = ~EiðRxÞϕRxi ðrÞ , ð1Þ� _22M∂2Rx+ ~EiðRxÞ" #ψn,iðRxÞ= En,iψn,iðRxÞ , ð2Þwhere VRx ðrÞ= E0c ðr,RxÞ � E0v ðr,RxÞ acts as an interface potential givenby the space-dependent band edges E0c,v. Note that the quantumnumbers n and i describe the quantization in the center-of-mass andrelativemotion, respectively. In this work, we focus on the energeticallylowest excitons corresponding to the i= 1s states. In the case without ajunction, there are no band offsets, i.e. ΔEc/v = 0 in Fig. 1b, and Eq. (1)becomes the well-known Wannier equation with a space-independentpotential and ~EiðRxÞ � Xi. In this limit, the center-of-mass equation(Eq. (2)) becomes trivial corresponding to fully delocalized plane wavesψnðRxÞ � e{QxRx and resulting in En,i � EQx ,i=Xi + _2Q2x=2M. This impliesthat the center-of-mass motion of excitons is free and there is noquantization.Solving Eqs. (1) and (2), two distinct situations can occur for theground-state energy E0, i.e. either (i) E0 = XMo or (ii) E0 < XMo. In the firstcase, the regularMoSe2 1s exciton is the lowest state and is expected todominate the optical response. In the latter case, the CT excitonE0 ≡ XCT is the lowest state and could be principally observed in opticalspectra. These CT states can be both bound or unbound and they areseparated by the corresponding exciton binding energy XbCT, cf. thered and purple lines in Fig. 1c. The conditions for the visibility of thebound CT excitons are a relatively large binding energy (higher thanthermal energy to prevent thermal dissociation into unbound states)and that the state is located clearly below the lowest intralayer exciton(XMo for the investigated structure) and thus carrying a sufficientlylarge occupation.To optimize the visibility of CT excitons in experiments we needto meet two conditions: (i) sufficiently low temperatures to avoidthermal dissociation of CT excitons and (ii) high sample quality so thatthe XMo−XCT energy separation is larger than the optical transitionlinewidth. Note that we recently reported high structural (electronmicroscopy) and optical quality (exciton transport) at the junction inCVD-grown MoSe2–WSe214. The MoSe2–WSe2 lateral heterostructureoffers a small lattice mismatch between MoSe2 and WSe2, whileencapsulation of the samples with hBN minimizes the dielectricdisorder32 and promotes the intrinsic optical properties of thematerialin experiments performed at a temperature of T = 4K. In addition, wewill show below that hBN-encapsulation plays an important role for CTexciton optics.Charge-transfer excitonsTo determine the exciton energy landscape, we solve the Schrödingerequation (Eqs. (1) and (2)).We consider hBN-encapsulated samples andstart with studying the limit of a relatively small band offset ofΔEv = 100meV. Here, the energetically deepest excitons are found tobe XMo states (cf. Fig. 2a). Momentum-dark exciton states have beenneglected, as they are energetically higher than themonolayer excitonXMo (cf. the Supplementarymaterial). The corresponding XW states arelocated 70meVabove, reflecting thebandgapdifferenceofMoSe2 andWSe2 (Fig. 2a). The center-of-mass dispersion is characterized by aparabola, and their wavefunctions ψ(Rx) are confined either on theright- or on the left-hand side of the interface. For small band offsets,the binding energy of monolayer excitons is stronger than the bandoffset. As a result, we find no bound CT excitons as the energy of theCT continuum is much higher than the intralayer exciton energy XMo(cf. Fig. 1).The energy landscape changes significantly, whenwe increase theband offset to ΔEv = 215meV, which is a realistic value for lateral TMDheterostructures13,18. Interestingly, we find bound CT excitons to bethe lowest states (cf. Fig. 2b). They have a flat dispersion indicatinglocalization of excitons, or to put it in other words, there is a quanti-zation of the center-of-mass motion across the junction. These CTexciton states are unquantized along the interface, i.e. forming a one-dimensional CT-exciton channel. We predict two bound CT states andplot their center-of-mass wave functions in Fig. 2c. These are broad inmomentum space reflecting a localization in real space around theinterface and induced by the Coulomb attraction between the spatiallyseparated electrons and holes. This is in strong contrast to the case of aregular monolayer without a junction, where the center of massmotion is free and the wave functions are very narrow in momentumspace and fully delocalized in real space.Fig. 2 | Interface engineering. a and bDispersion relation of an hBN-encapsulatedMoSe2-WSe2 lateral heterostructure forΔEv = 100and215meV, respectively. cWavefunction of the two lowest bound CT excitons for ΔEv = 215meV. d The energy ofthe lowest CT exciton (relative to XMo) and e its in-plane dipole de−h revealing theappearance of bound CT excitons for band offsets larger than ~100meV. f CTexciton binding energy as a function of junction width w for three different bandoffset values, revealing that sharp interfaces allow deeply bound CT excitons withXbCT ≈ 30meV.Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 3We find that the bound states have typically an alternating sym-metry, resulting in states with a finite and a negligible component inQx =0, respectively (Fig. 2c). The vanishing Qx =0 component has adirect consequence for their oscillator strength so that only evenstates can emit light. The oscillator strength is also affected by therelative wavefunction, as the radiative recombination rate is propor-tional to the probability ∣ϕ(r = 0)∣2 of finding electrons and holes in thesame position15 (cf. “Methods” section). Due to the large spatialseparation, this is smaller by a factor of almost 35 for CT excitonscompared to intralayer states in the situation studied in Fig. 2b.However, being the energetically lowest states, their higher occupa-tion, in particular at low temperatures, could still compensate theirsmaller oscillator strength andmake them visible in optical spectra. Inaddition, relatively large binding energies are important because theygive rise to a larger oscillator strength by increasing ∣ϕ(r =0)∣2 as theelectron–hole separation is reduced.To sum up, the crucial conditions for the visibility of bound CTstates are that they have a relatively large oscillator strength and thatthey are considerably deeper in energy than the lowest intralayerexciton state. In the following, we investigate interface engineering(variationof bandoffset and junctionwidth) anddielectric engineering(variation of substrates) to predict optimal conditions for experi-mental observation of bound CT excitons that have not beendemonstrated so far.Interface engineeringHere, we investigate how the CT exciton energy, its in-plane dipole,and the binding energy depend on the band offset ΔEv and the inter-face widthw (Fig. 1). Note that varying ΔEc gives qualitatively the sameresults. The band offset can be engineered by growing lateral hetero-junctions of different TMDmonolayers. The junction widthw dependson the exact growth technique and conditions. Recently, there hasbeen an impressive technological development in lateral hetero-structures allowing the realization of atomically narrow junctions ofjust a few nanometers13,14,20,23,24,33,34. In Fig. 2d, e we show the energeti-cally lowest exciton state E0 and its in-plane dipole de−h, respectively.To this end, we solve the Schrödinger equation (Eqs. (1) and (2)) as afunction of the band offset ΔEv for three different junction widthsw = 2.4, 5, and 12 nm. The lower values correspond to recent experi-mentally realized sharp interfaces13,14,20,24. Importantly, our calculationsshow that for band offsets smaller than a critical value of about 100meV, there are no bound CT excitons, but rather the regular MoSe2excitonXMo is the lowest state (orange line). IncreasingΔEv, weobservethat after a width-dependent critical value (defined as ΔEcv) boundCT excitons become the lowest states with linearly increasing separa-tion from XMo as ΔEv becomes larger. A similar behaviour is predictedfor the free-standing case, but with a much larger ΔEcv ≈ 200 meV(cf. the Supplementary material). The binding energy XbCT is enhancedfor smaller junction widths w (i.e. the red curve is further away fromthe purple curve in Fig. 2d).To understand this, we plot the CTbinding energy as a function ofthe junction width (Fig. 2f) for three different values of ΔEv>ΔEcv. Wefind that forΔEv = 165meV the binding energy decreases by a factor of3 when going from w = 2.4 to w = 12 nm (XbCT ≈ 23 and 7meV, respec-tively). Importantly, only for narrow junction widths, we predictbinding energies of the order of the thermal energy also at roomtemperature. CT excitons with lower binding energy are thermallyunstable and are expected to quickly dissociate into continuumstates35. In addition, lower binding energies result in a smaller oscillatorstrength via a reduction of ∣ϕ(r =0)∣2. We also observe that the bindingenergy is nearly independent of the band offset (almost overlappinglines in Fig. 2f), in particular for offsetsΔEvmuch larger than the criticalone. For offsets just larger than ΔEcv, we predict a monotonic decreaseof XbCT with increasing ΔEv15 (cf. the Supplementary material). As aconsequence, the energy of the boundCT excitons XCT directly followsthe linear decrease of the CT continuum energy (purple line in Fig. 2d)as a function of the band offset.The abrupt reduction of the CT exciton binding energy forincreasing the junction width w (Fig. 2f) induces an increase of thecritical band offset ΔEcv from approximately 110–140meV for junctionwidthsw going from 2.4 to 12 nm (cf. the critical values in Fig. 2d). Forthe case of ΔEv =XbMo the energy of the MoSe2 exciton XMo exactlycoincides with the energy of continuum states E0CT (cf. Fig. 1). For thegeneral case, the critical band offset has to be defined asΔEcv =XbMo � XbCT, such that the bound CT exciton becomes the ener-getically lowest state. As the binding energy of the monolayer excitonXbMo does not dependon the junctionwidth, XbCT is the crucial quantity.The latter has been shown to be very sensitive to the junction width(Fig. 2f). This explains why the critical band offset is increased forhigher junction widths (i.e. smaller XbCT). This crucial dependence ofXbCT as a function of the junction width stems from the competitionbetween the junction width w and the Bohr radius rB. The latter pro-vides the spatial scale at which Coulomb-bound electrons and holescan redistribute around a center-of-mass position29. When w≫ rB,excitons need huge dipoles de−h for their electron/hole constituents toreach the energetically favourable spatial positions. As a result, boundCT excitons show very small binding energy. In the opposite case ofw≲ rB, the CT exciton experiences the maximum band offset alreadyfor small spatial separations resulting in large binding energies.We now investigate the CT-exciton in-plane dipole de−h as afunction of the band offset (Fig. 2e). Similarly to the case of CT excitonenergy in Fig. 2d, the dipole abruptly increases when the critical bandoffset ΔEcv is reached, i.e. when bound CT excitons are formed. Forlarger band offsets, the dipole only weakly increases. The dipole cru-cially depends on the binding energy of CT excitons: For larger XbCTelectrons and holes are bound close to the interface, i.e. they have asmaller in-plane distance and thus a smaller dipole. Since XbCT dependsstrongly onw andweakly onΔEv (Fig. 2f), there is only a small variationof de−h with the band offset (above the critical value ΔEcv), while de−hincreases by a factor of three for w going from 2.4 to 12 nm (de−h ≈ 8and 27 nm, respectively, cf. red and green lines in Fig. 2e). The pre-dicted dipoles are in the range of several nanometers, which is in goodagreement with previous studies13,15. The values are much larger thanfor interlayer excitons in vertical heterostructures, where theelectron–hole separation is limited by the layer distance4. The com-bination of small binding energies and large dipoles is attractive foroptoelectronic applications due to efficient exciton dissociation andquick exciton propagation13. From the perspective of exciton optics,this can bring two limitations: First the larger de−h, the smaller is thebinding energy XbCT (Fig. 2e, f) and the less stable CT excitons are.Second, the increase of the dipole leads to a decrease of ∣ϕ(r =0)∣2resulting in a lowering of the oscillator strength with crucial implica-tions for the visibility of CT excitons in experiments.In a nutshell, by performing interface engineering one can achievethermally stable bound CT excitons for atomically sharp interfaces. Inparticular, for the case of hBN-encapsulated MoSe2–WSe2, we predictbinding energies of XbCT ≈ 20�30 meV.Dielectric engineeringBesides interface engineering, Coulomb interaction can be changed byvarying the dielectric environment determined by the substrate. Wefocus again on the lateral MoSe2-WSe2 heterostructure with a narrowjunction width of w = 2.4 nm and a band offset of Δv = 215meV (i.e.above the critical value discussed in Fig. 2). These values are realisticaccording to the previous studies on lateral heterostructures13,18. Notethat inour studywe consider the bandoffset and the interfacewidth tobe robust with respect to the change in the dielectric environment.In Fig. 3a we show the bound and unbound CT energies XCT andE0CT as a function of the dielectric constant ε of the substrate. We focuson CT energies relative to the intralayer MoSe2 exciton XMo, as theArticle https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 4occupation of CT excitons is determined by their relative spectraldistance to the monolayer exciton. We find a considerable shift tolower energies for increasing ε. The energy separation from XMo of thebound CT exciton XCT is reduced from approximately 6meV in thefree-standing case (ε = 1) to 88meV for hBN-encapsulated samples.A similar decrease is also found for theunboundCTstate E0CT. Aswe areconsidering only relative energies (with respect to XMo), the depen-dence of the band gap energy E0Mo on the dielectric screening is can-celled out. Thus the crucial quantities here are the binding energiesXbMo and XbCT of themonolayer and the boundCT excitons. The latter isvery sensitive to the dielectric environment, as shown in Fig. 3b. Inparticular, the decrease ofXbMo (orange in Fig. 3b) is responsible for thebehaviour found for the energy of unbound CT excitons E0CT (purple inFig. 3a). Note that for ε ≈ 3, the MoSe2 exciton XMo is shifted abovethe unbound CT energy resulting in a sign change in the purple linein Fig. 3a.Interestingly, we predict a drastic decrease of XbCT resulting in XbCTbeing much smaller than XbMo (by approximately a factor of 4 and 7 inthe case of SiO2-air and hBN-encapsulation, respectively). This drasticdecrease is in contrast to the situation in vertical heterostructures,where the binding energies are comparable for intra- and interlayerexcitons16,17. This difference between vertical and lateral hetero-structures can be ascribed to the much larger spatial electron-holeseparations in CT excitons compared to interlayer excitons, where theseparation is limited by the interlayer distance in vertical hetero-structures. TheCTbinding energydecreaseswith the increasing dipole(cf. the Supplementary material), similar to the behaviour of interlayerexcitons with increasing interlayer spacing16. Only for free-standinglateral heterostructures, we predict that CT excitons have dipolesde−h ≈ 1 nm comparable with vertical heterostructures, resulting incomparable binding energies. In contrast, for substrates with anincreasing dielectric constant, we find significantly enhanced in-planedipolemoments, e.g. de−h ≈ 5 nm for the SiO2 substrate orde−h ≈ 9.6 nmfor hBN-encapsulated samples. The increase inde−h leads to a decreasein the CT binding energy as well as of the radiative recombination rateby one order of magnitude compared to the free-standing case.The behaviour of XCT in Fig. 3a results from the non-trivial inter-play of XbCT and XbMo. The CT exciton binding energy XbCT decreasesfrom about 200meV in the free-standing case (ε = 1) to just a few meVin the presence of high-dielectric substrates (Fig. 3b). As a con-sequence, bound and unboundCT energies almost coincide for large ε(red and purple line in Fig. 3a). Furthermore, they shift well below theintralayer MoSe2 energy XMo. In the limiting case of very large ε, theseparation between XCT and XMo tends toward the value of the bandoffset due to thenegligible excitonicbinding energies, (cf. Fig. 1). In thefree-standing limit, we find XCT ≈ XMo, despite the large CT excitonbinding energy. This occurs since for ε→ 1 also the unboundCT energyis shifted up relative to XMo (purple line in Fig. 3a) and cancels out thechange in XbCT, such that XCT = E0CT � XbCT ≈XMo. In this regime, theboundCT excitons are thermally stable thanks to binding energies of afewhundredmeV (Fig. 3b), but they are locatedonly slightly belowXMo(Fig. 3a). Thus, they are weakly populated and not visible in PL spectra,cf. the supplementary material. It is, however, in the intermediaterange of 2 < ε < 5 that one finds the optimal situation where we have aconsiderably large CT binding energy and at the same time theCT exciton is located well below the MoSe2 exciton. For a SiO2-airenvironment (ε ≈ 2.4), we predict the CT exciton to be ~35meV belowXMo with a binding energy of XbCT ≈63meV. The energy separationbetween CT and intralayer MoSe2 excitons increases significantly inhBN-encapsulated heterostructures (ε ≈ 4.5), but this comes at theprice of a smaller binding energy of XbCT ≈ 20meV.In a nutshell, high-dielectric substrates lead to bound CT excitonsthat are located much below the intralayer exciton and thus carry alarge occupation, however, they are weakly bound and hence ther-mally unstable. The optimal case is reached for ε ≈ 2−5 where we findCT excitons with a considerably large binding energy and still a suffi-cient occupation.Optical spectraNow, we investigate whether bound CT excitons can be observed inphotoluminescence spectra. First, we calculate a PL spectrum of anhBN-encapsulated MoSe2–WSe2 lateral heterostructures (with theband offsetΔEv = 0.215 eV and the interfacewidthw = 2.4 nm) and thenwe perform cryogenic PL measurements. The starting point of ourcalculation is a focused laser excitation spot with an FWHM of 700nmas in a typical experiment36. In a homogeneously excited system, the PLcan be expressed by the Elliott formula describing the emission ofbright exciton states37. In our case, this Elliott formula has to beextended to take into account the spatially confined laser excitationand excitonic states. To this purpose, we assume a Gaussian excitonicdistribution N(x0,Rx) localized around x0 � R0x with a spatial width Δxin agreement to the FWHM of the laser pulse. Here, Rx is the excitoncenter-of-mass position. In the case without a junction, the spectraldistribution is governed by the Boltzmann distribution. In the pre-sence of a junction, however, thewavefunction of each state ∣ψn�playsan important role and determines the relative occupation of the statevia a weight coefficient cn(Rx), i.e. Nn(Rx) =N(x0, Rx)cn(Rx) (cf. “Meth-ods” section for more details). This makes sure that we have a localthermal distribution. We generalize the Elliott formula for the PLintensity In(E) of the state ∣ψn�taking into account that the laser pulseexcites a spatially inhomogeneous exciton distribution. Thus, thespatially dependent PL reads after an optical excitation centered at x0Iðx0, EÞ=XnInðEÞZdRxcnðRxÞNðx0,RxÞ, ð3Þi.e. we sumover all emitting states ∣ψn�andweight the emission by thecoefficient cn(Rx). Note that we limit our study to momentum-directradiative recombination since phonon sidebands are expected only inthe WSe2 but not in the MoSe2 monolayer (as here momentum-darkexcitons are not the energetically lowest states, cf. the Supplementarymaterial)38–40. As a result, we also do not expect efficient indirectrecombination of CT excitons as here the electron is located in theMoSe2 layer (Fig. 1b). Furthermore, funneling effects41 and excitonFig. 3 | Dielectric engineering. a Bound and unbound CT exciton energies XCT andE0CT (relative to the intralayer MoSe2 exciton XMo), b CT binding energy XbCT, andc the corresponding CT exciton dipole de−h as a function of the dielectric constantof the substrate (for the band offset ΔEv = 0.215 eV and the interfacewidth w = 2.4 nm).Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 5thermalization/charge transfer effects42,43 are beyond the scope ofthis work.Now, we evaluate Eq. (3) and calculate spatially and spectrallydependent PL spectra at different temperatures for the hBN-encapsulated MoSe2–WSe2 lateral heterostructures. We tune thelaser pulse position x0 and fix the junction characteristics to values ofΔEv = 0.215 eV and w = 2.4 nm in accordance with predicted and mea-sured values14,18. Atmoderate and high temperatures far away from thejunction, we reproduce the regular monolayer PL spectrum and findthe XMo and XW excitons on the right-hand and the left-hand side,respectively (cf. Fig. 4a, b). When exciting at the interface, both fea-tures are still visible reflecting the large spatial width of the laser pulse(FWHM of 700nm) that excites both sides of the heterojunction.Interestingly, when decreasing the temperature, a low-energy reso-nance appears approximately 90meV below XMo (cf. Fig. 4c, d). Thiscan be clearly ascribed to the position of the CT exciton XCT (Fig. 2d).At low temperatures, CT excitons can result in a strong PL despite theirlow oscillator strength due to their large occupation as energeticallylowest states. The PL emitted from CT excitons is particularly strongcompared to XW, as the bright exciton XW in theWSe2 layer is higher inenergy than XMo, and is thus only weakly populated. For the samereason, we find that XMo is more intense than XW at low temperatures(Fig. 4c). Importantly, the new low-energy peakXCT is visible only in thepresence of a narrow junction, (i.e.w = 2.4 nm), while it disappears forlarger junction widths, as shown by the dashed orange line in Fig. 4d.This can be explained by the smaller spectral separation of CT excitonsfrom themonolayer resonance at broader junctions (Fig. 2d), resultingin a smaller occupation of the CT state. In addition, the CT excitonbinding energy also considerably drops, and the electron–holeseparation drastically increases (Fig. 2e). As a direct consequence, theradiative decay rate γ0, which is given by the wavefunction overlap ofelectrons and holes (cf. “Methods” section), decreases by 4 orders ofmagnitude when moving from w = 2.4 nm to w = 12 nm.To test the theoretical prediction we perform spatially dependentcryogenic PLmeasurements on the very same sample system, i.e. hBN-encapsulated MoSe2-WSe2. This sample set has shown high structuralquality at the junction in electron microscopy and clear excitontransport from WSe2 to MoSe2 through the junction14. This allows usto show a direct comparison between theory and experiment(cf. Fig. 4d–f). In Fig. 4e, f we present the spectra from two differentjunctions. We find in the experiment a clear PL emission of about80–100meV below the XMo resonance at several junctions. The emis-sion in the CT-exciton energy range is absent far away from the junc-tion (cf. thin bright blue line in Fig. 4e, f). This is in excellent agreementwith the theoretical prediction (Fig. 4d) and is a strong indication ofthe direct emission from CT excitons. To further support this assign-ment, we have performed power-dependent studies, cf. the Supple-mentary material. The integrated intensity of the low-energy peakincreases linearly with the excitation power, contrary to the saturatingbehaviour expected from defects44,45. In addition, we also observe ablue-shift of the peak with increasing excitation powers, similar to thebehaviour of interlayer excitons, which blueshift due to dipole–dipolerepulsion46. The observed shift could thus further confirm the dipolarorigin of the low-energy peak.By investigating samples in PL at cryogenic temperatures, thechances for the observation of the CT exciton are optimized also bythe hBN encapsulation which, besides reducing the disorder (resultingin linewidth of less than 10 meV for XMo), leads to large energyseparations between XCT and XMo excitons, as explained in thedielectric engineering part of the manuscript (Fig. 3). We emphasizethat both the narrow linewidth and the large-energy separationbetween XCT and XMo are needed to observe CT excitons. The broadernature of the CT exciton in the experiment is likely to be related tosample imperfections or strain. A moderate red-shift of 20–30meV ofXW close to the junction14 suggests the presence of strain that couldresult in an inhomogeneous broadening of XCT, together with dielec-tric disorder and impurities. Furthermore, we observe trionic featuresresulting in multiple peaks around the energy of the MoSe2 excitonthat have not been taken into account in the theory. Note that PLemission at the calculated CT exciton energy has been observed inseveral junctions (cf. Fig. 4e, f). From amaterial perspective, it is likelythat the junction width wmight vary for junctions grown on the samesubstrate. As a result, CT exciton formation does not necessarily occurat all junctions, due to the strong dependence on w as shown in ourcalculations (Fig. 2f).DiscussionWe have presented a joint theory–experiment study investigating thebound charge-transfer excitons at the interface of lateral two-dimensional heterostructures. We find in theory and experiment firstsignatures for the appearance of bound charge transfer excitons incryogenic photoluminesce spectra of hBN-encapsulated lateralMoSe2–WSe2 heterostructures. We perform interface and dielectricengineering in our calculations and reveal critical conditions for theobservation of charge transfer excitons including narrow junctionwidths (in the range of a few nm), relatively large band offsets (above100meV), and an intermediate dielectric screening (ε ≈ 2−5).Our studyprovides novel insights into the characteristics of bound chargetransfer excitons and will trigger future experimental and theoreticalstudies in the growing research field of lateral heterostructures. Thelatter also has a large technological potential as ultrathin junctionspresent quasi-one-dimensional channels with a strongly suppressedscattering with phonons and thus significantly enhanced excitonFig. 4 | Optical signatures. Photoluminescence (PL) spectra of hBN-encapsulatedMoSe2–WSe2 lateral heterostructures with the band offset ΔEv = 0.215 eV and theinterface width w = 2.4 nm studied at a 300K, b 150K, and c 30K. We excite thematerial with a laser excitation spot with an FWHM of 700nm. d Cuts of the PLspectrum at the interface at 30K. We also show the comparison to the largerinterface width of 12 nm (dashed orange line). e, f Experimental PL spectrum at thejunction and at MoSe2 monolayer region, with two different interfaces considered.We find both in experiment and theory a low-energy resonance that we assign to abound CT exciton.Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 6mobility47. Additionally, the large intrinsic dipole of CT excitons isexpected to lead to an efficient dipole–dipole repulsion that togetherwith the 1D confinement could lead to excitonic highways as recentlyproposed13. A further key for technological application is exciton dis-sociation, i.e. the conversion of light absorption into electrical cur-rents. Due to the huge excitonic binding energies of hundreds of meV,the charge separation is largely ineffective in TMD monolayers. Incontrast, weakly bound CT excitons in lateral heterostructures willefficiently dissociate and thus facilitate charge separation. In our work,we showhowtoengineer lateral TMDheterostructures toobtain stableand highly dipolar CT excitons that have a high potential to boostexciton transport and exciton dissociation—both highly relevant foroptoelectronic applications.MethodsMicroscopic modelingTo microscopically model charge transfer excitons in lateral TMDheterostructures, we solve the Schrödinger equation includingthe strong Coulomb interaction in TMD monolayers and the space-dependent dispersion relations induced by the junction (Fig. 1b).The Coulomb interaction VC(r) is described introducing a generalizedKeldysh potential30,31,48 for charges in a thin-film surrounded by adielectric environment that is spatially homogeneous along the planein termsof thickness anddielectric constant30,31,48. The in-plane variationof energy is described via spatially dependent single-particle energiesE0c=vðrÞ of electrons and holes, respectively. In particular, we takeE0c=vðrÞ=ΔEc=v=2ð1� tanhð4x=wÞÞ+ E0Moð1 ± 1Þ=2, which recovers thesituation in Fig. 1b15. The Schrödinger equation can be separated intoequations for the relative and the center-of-mass motion (Eqs. (1) and(2)). We focus on electrons and holes located at the K valley in MoSe2and WSe2, respectively, as all other CT electron–hole pairs are energe-tically higher, cf. the Supplementary material. While lateral hetero-structures involving TMDswith different chalcogen atomshave a latticemismatch, in MoSe2–WSe2 we can assume a strain-free interface11,19.Finally, we solve the coupled Eqs. (1) and (2) with space-independentWSe2 electronmasses49 to obtain the eigenenergies and eigenfunctions,which in turn allow to determine the radiative recombination rateand the dipole de�h � ∣de�h∣= ∣RdRxdrr∣ΨðRx ,rÞ∣2∣. Note that finitedipoles are present only for CT states and only across the interface, i.e.de−h =dxe�h and dye�h = 0, where dx=ye�h describes the component acrossand along the interface of de−h, respectively.To model the spatially dependent PL, we must take into accountthe junction in lateral heterostructures yielding thePL formula in Eq. (3).The appearing coefficients cn(Rx) canbeobtained starting from the totalcenter-of-mass excitonic distribution NðRÞ / Pnn0 hX̂yn0 X̂niψ*n0 ðRÞψnðRÞ,where X̂yn, X̂n are the creation/annihilationoperators of anexciton in thestate n and where hX̂yn0 X̂ni is the single-exciton density matrix. In theequilibriumofhomogeneous low-density excitations,wefind hX̂yn0 X̂ni �ce�En=kBTδnn0 with c being the normalization constant reflecting thelocal density.Applying such equilibrium condition to the general definition ofN(R) yieldsNðRÞ � cXne�EnkBT ∣ψnðRÞ∣2 =NðRÞXncnðRÞ ð4Þwith cnðRÞ= e�EnkBT ∣ψnðRÞ∣2�Pn0e� En0kBT ∣ψn0 ðRÞ∣2��1providing the localoccupation of state ∣ni. In the monolayer limit one has ∣ψn(R)∣2 = 1/Awith A being the area of the sample. Hence, the coefficients cn(R)become the normalized spatially independent Boltzmann distribution.A highly non-trivial dynamics is expected at the interface, where thecharge transfer42,43 into bound CT states is likely to lead to localfeatures similar to those of phonon-induced carrier-capture50,51. In thiswork, we focus on stationary PL after exciton thermalization hasoccurred.The space-independent PL of InðEÞ= ~γn~γn + ΓnðE�EnÞ2 + ð~γn + ΓnÞ2enteringEq. (3) describes the emission spectrum after radiative recombinationof the state ∣ni according to the excitonic Elliott formula37,38. Phonon-assisted mechanisms are not included as they are expected to bestrong only on the WSe2 side of the junction but negligible for bothMoSe2 and CT excitons in the junction. The oscillator strength~γn = γn ∣ψQx =0∣2 is given by the product of the radiative rate γn and theQx =0 component of the squared wavefunction in center-of-massmomentum spaceψQxin view of the conservation of momentum afterrecombination into photons52. The radiative rate γn can be extractedfrom the monolayer case48 as γn = ~M∣ϕðr=0Þ∣2=En with ~M dependingon the material and the substrate (via optical dipole moment orrefractive index), while En and ∣ϕðr=0Þ∣2 = RdRx ∣ψðRxÞ∣2∣ϕRx ðr =0Þ∣2are obtained from the solution of Eqs. (1) and (2), i.e. in particularincluding effects from the junction. While ~γn determines the oscillatorstrength, i.e. the height of the resonances, Γn describes the impact ofexciton–phonon scattering on the shape of the resonances. As a fullmicroscopic calculation of the latter including the junction is beyondthe scope of this work, we estimate Γn with the values obtained in thelow-density limit for MoSe2 and WS2 monolayers53.Sample fabrication and photoluminescence measurementsOur MoSe2–WSe2 lateral monolayer heterojunction is grown by che-mical vapor deposition (CVD) synthesis thatwe reported recently20. Forthe hBN encapsulation we follow the water-assisted transfermethod topick up as-grown, chemical vapor deposition (CVD) lateral hetero-structures using polydimethylsiloxane (PDMS) and deterministicallytransfer and encapsulate them in hBN54,55. Photoluminescence spectraare collected at T = 4K in a closed-loop liquid helium (LHe) system.A 633 nm HeNe laser is used as an excitation source with a spot sizediameter of ≈ 1μm and 6μW power, while in the Supplementarymaterial wepresent results gradually increasing thepower up to 25μW.Data availabilityThe datasets generated during and/or analysed during the currentstudy are available from the corresponding authors on reasonablerequest.Code availabilityThe codes used to generate the data are available from the corre-sponding authors on reasonable request.References1. Wang, G. et al. Colloquium: excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).2. Mueller, T. &Malic, E. Excitonphysics anddevice applicationof two-dimensional transition metal dichalcogenide semiconductors. npj2D Mater. Appl. 2, 29 (2018).3. Rivera, P. et al. Observation of long-lived interlayer excitons inmonolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6,6242 (2015).4. 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Controlling interlayer excitons in MoS2layers grown by chemical vapor deposition. Nat. Commun. 11,1–7 (2020).Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 8AcknowledgementsWeacknowledge funding from theDeutscheForschungsgemeinschaft(DFG) via SFB 1083 and project 512604469 as well as from the Eur-opean Union’s Horizon 2020 research and innovation program undergrant agreement no. 881603 (Graphene Flagship). Toulouseacknowledges partial funding from ANR IXTASE, Growth of hexagonalboron nitride crystals was supported by JSPS KAKENHI (Grants Nos.19H05790, 20H00354, and 21H05233). Jena group financial supportof the Deutsche Forschungsgemeinschaft (DFG) through CRC 1375NOA (Project B2), SPP2244 (Project TU149/13-1), DFG grant TU149/16-1.Author contributionsR.R. and E.M. developed the theoretical model for CT-exciton engi-neering and optics. I.P., L.L., P.R., and B.U. devised and performed the PLmeasurements. Z.G., A.G., and A.T. grew theCVD samples. T.T. and K.W.grew the hBN bulk. All authors contributed to the writing of themanuscript.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/s41467-023-37889-9.Correspondence and requests for materials should be addressed toRoberto Rosati.Peer review information Nature Communications thanks Carino Fer-rante, Junyi Liu and Alessandro Surrente for their contribution to thepeer review of this work. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-37889-9Nature Communications |         (2023) 14:2438 9https://doi.org/10.1038/s41467-023-37889-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Interface engineering of charge-transfer excitons in 2D lateral heterostructures Results Methodology and key quantities Charge-transfer excitons Interface engineering Dielectric engineering Optical spectra Discussion Methods Microscopic modeling Sample fabrication and photoluminescence measurements Data availability Code availability References Acknowledgements Author contributions Funding Competing interests Additional information