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Dorian Beret, Ioannis Paradisanos, Hassan Lamsaadi, Ziyang Gan, Emad Najafidehaghani, Antony George, Tibor Lehnert, Johannes Biskupek, Ute Kaiser, Shivangi Shree, Ana Estrada-Real, Delphine Lagarde, Xavier Marie, Pierre Renucci, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Sébastien Weber, Vincent Paillard, Laurent Lombez, Jean-Marie Poumirol, Andrey Turchanin, Bernhard Urbaszek

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[Exciton spectroscopy and unidirectional transport in MoSe2-WSe2 lateral heterostructures encapsulated in hexagonal boron nitride](https://mdr.nims.go.jp/datasets/98b3d28c-6fcf-43e1-a3bc-eb1171f6cf68)

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Exciton spectroscopy and unidirectional transport in MoSe2-WSe2 lateral heterostructures encapsulated in hexagonal boron nitrideARTICLE OPENExciton spectroscopy and unidirectional transportin MoSe2-WSe2 lateral heterostructures encapsulated inhexagonal boron nitrideDorian Beret 1,11, Ioannis Paradisanos1,11, Hassan Lamsaadi2,11, Ziyang Gan 3,11, Emad Najafidehaghani3, Antony George 3,4,Tibor Lehnert 5,10, Johannes Biskupek5, Ute Kaiser 5, Shivangi Shree6, Ana Estrada-Real1,7, Delphine Lagarde1, Xavier Marie1,Pierre Renucci1, Kenji Watanabe 8, Takashi Taniguchi 9, Sébastien Weber2, Vincent Paillard2, Laurent Lombez1✉,Jean-Marie Poumirol2✉, Andrey Turchanin 3,4✉ and Bernhard Urbaszek 1,7✉Chemical vapor deposition (CVD) allows lateral edge epitaxy of transition metal dichalcogenide heterostructures. Critical for carrierand exciton transport is the material quality and the nature of the lateral heterojunction. Important details of the optical propertieswere inaccessible in as-grown heterostructure samples due to large inhomogeneous broadening of the optical transitions. Here weperform optical spectroscopy of CVD grown MoSe2-WSe2 lateral heterostructures, encapsulated in hBN. Photoluminescence (PL),reflectance contrast and Raman spectroscopy reveal optical transition linewidths similar to high quality exfoliated monolayers,while PL imaging experiments uncover the effective excitonic diffusion length of both materials. The typical extent of the covalentlybonded MoSe2-WSe2 heterojunctions is 3 nm measured by scanning transmission electron microscopy (STEM). Tip-enhanced, sub-wavelength optical spectroscopy mapping shows the high quality of the heterojunction which acts as an excitonic diode resultingin unidirectional exciton transfer from WSe2 to MoSe2.npj 2D Materials and Applications            (2022) 6:84 ; https://doi.org/10.1038/s41699-022-00354-0INTRODUCTIONResearch on semiconducting transition metal dichalcogenide(TMDs) monolayers1–3 and their heterostructures is motivatedby collective effects of the electronic system4–6 and thepotential for emerging optoelectronic and quantum technologydevices7–17. The optical and electronic properties of thesematerials can be tuned by combining different monolayers viavan der Waals stacking to create vertical heterostructures18–20.But interestingly, tuning of optical properties of TMDs can alsobe achieved while staying in the ultimate monolayer limit.Recent progress is based on innovative growth techniques suchas for Janus monolayers with different top and bottomchalcogen21–24, as well as in lateral heterostructures (LHs)25,26within the monolayer plane with an atomically-sharp 1Dinterface which exhibits p-n junction characteristics27,28. Exam-ples of potential applications for LHs are photodetectors29, p-njunction diodes25,30,31, photovoltaic30, electroluminescent30and quantum devices32.LHs can be fabricated following one-step25,26,28,31 or multiple-step33,34 growth processes either by physical vapor deposition(PVD) or by chemical vapor deposition (CVD). Electron beamlithography has also been used for the fabrication of LHs35. One-step CVD approaches with suitable growth conditions are simplerand have the advantage to grow large area TMD LHs at lowertemperatures25. Accessing the quality of the monolayer hetero-junction is so far mainly based on electron microscopy techniques.A depletion width on the order of few nanometers is reportedusing scanning tunneling microscopy and spectroscopy techni-ques36. The electronic structures and band alignments of TMD LHshave been calculated using density functional theory37 and theformation of interface excitons is predicted by tight-bindingmodels, as well as effective mass models38.To further access carrier dynamics and excitonic properties atthe interface optical spectroscopy is needed as a powerful andnon-invasive tool. But in as-grown CVD samples details aremasked due to the large inhomogeneous broadening reportedfor the optical transitions, mainly investigated at roomtemperature26,28,30,31.Here we perform optical spectroscopy and microscopy experi-ments in high quality CVD-grown MoSe2-WSe2 monolayer LHs25.We first lift the LHs from the growth substrate. This procedureshows that transfer of the LH to other substrates is possible fordevice processing. Second, we encapsulate the LHs in high qualityexfoliated hBN flakes39 (Fig. 1a). Encapsulation of the TMDmonolayer in high quality hexagonal boron nitride (hBN)39 iscrucial to access the intrinsic optical properties of exfoliated andCVD grown flakes40–48. We report optical transition linewidth ofthe LH monolayer (≈5meV at T= 4 K) comparable to high qualityexfoliated layers. Our step-by-step scans across the heterojunc-tions in optical spectroscopy experiments show an abrupt changefrom WSe2 to MoSe2. In atomic-resolution transmission electronmicroscopy on our samples we find a transition with a nm-sharp1Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Avenue Rangueil, 31077 Toulouse, France. 2CEMES-CNRS, Université de Toulouse, Toulouse, France. 3Friedrich SchillerUniversity Jena, Institute of Physical Chemistry, 07743 Jena, Germany. 4Abbe Centre of Photonics, 07745 Jena, Germany. 5Ulm University, Central Facility of Electron Microscopy,Group of Material Science Electron Microscopy, D-89081 Ulm, Germany. 6Department of Physics, University of Washington, Seattle, WA, USA. 7Institute of Condensed MatterPhysics, Technische Universität Darmstadt, Darmstadt, Germany. 8Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044,Japan. 9International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 10Present address: Karlsruhe Instituteof Technology, Laboratory for Electron Microscopy, 76131 Karlsruhe, Germany. 11These authors contributed equally: Dorian Beret, Ioannis Paradisanos, Hassan Lamsaadi,Ziyang Gan. ✉email: laurent.lombez@cnrs.fr; jean-marie.poumirol@cemes.fr; andrey.turchanin@uni-jena.de; bernhard.urbaszek@pkm.tu-darmstadt.dewww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00354-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00354-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00354-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-022-00354-0&domain=pdfhttp://orcid.org/0000-0002-7434-1882http://orcid.org/0000-0002-7434-1882http://orcid.org/0000-0002-7434-1882http://orcid.org/0000-0002-7434-1882http://orcid.org/0000-0002-7434-1882http://orcid.org/0000-0001-5707-5765http://orcid.org/0000-0001-5707-5765http://orcid.org/0000-0001-5707-5765http://orcid.org/0000-0001-5707-5765http://orcid.org/0000-0001-5707-5765http://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/0000-0002-4904-9580http://orcid.org/0000-0002-4904-9580http://orcid.org/0000-0002-4904-9580http://orcid.org/0000-0002-4904-9580http://orcid.org/0000-0002-4904-9580http://orcid.org/0000-0003-0582-4044http://orcid.org/0000-0003-0582-4044http://orcid.org/0000-0003-0582-4044http://orcid.org/0000-0003-0582-4044http://orcid.org/0000-0003-0582-4044http://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://orcid.org/0000-0003-0226-7983http://orcid.org/0000-0003-0226-7983http://orcid.org/0000-0003-0226-7983http://orcid.org/0000-0003-0226-7983http://orcid.org/0000-0003-0226-7983https://doi.org/10.1038/s41699-022-00354-0mailto:laurent.lombez@cnrs.frmailto:jean-marie.poumirol@cemes.frmailto:andrey.turchanin@uni-jena.demailto:bernhard.urbaszek@pkm.tu-darmstadt.dewww.nature.com/npj2dmaterialsjunction from MoSe2 to WSe2. The structural quality is alsodemonstrated in Raman spectroscopy. Photoluminescence (PL)imaging experiments allow us to investigate excitonic transportgoverned by the different effective lifetime of the exciton speciesfor MoSe2 and WSe2 at T= 4 K and 300 K. We study excitontransport in sub-wavelength, tip-enhanced PL (TEPL) and Ramanscattering (TERS) experiments at T= 300 K. Owing to our spatialresolution of 40 nm we uncover unidirectional exciton transportacross the lateral heterojunction from WSe2 to MoSe2, that wemodel numerically.RESULTS AND DISCUSSIONSample preparation, electron microscopy and optical qualityOur MoSe2-WSe2 lateral monolayer heterojunction is grown byCVD synthesis that we reported recently25. A schematicrepresentation of the encapsulated MoSe2-WSe2 structure isshown in Fig. 1a. Figure 1b shows high-angle annular dark fieldscanning transmission electron microscopy (HAADF-STEM)image recorded at the boundary region of the MoSe2-WSe2structures. The image was recorded at an operating voltage of200 kV, see supplement. The atomically resolved HAADF imageallows the detection of the roughness of the interface at sub-nm resolution due to exploiting of the Z-contrast, where lighterMo atoms show darker contrast than heavier W atoms49. Thus,MoSe2 appears darker and WSe2 appears brighter. From thesemeasurements we estimate the transition width of theboundary region between MoSe2 and WSe2 to be as narrowas ≈3 nm. This sharp, high quality junction enables us to gaininsights into exciton transport experiments across the hetero-juntion with sub-wavelength resolution, see discussion below.We use water-assisted deterministic transfer to pick up as-grown, CVD LHs using polydimethylsiloxane (PDMS) anddeterministically transfer and encapsulate them in hBN47,50.We use these encapsulated samples for all optical spectroscopymeasurements.We first analyze the PL and differential white light reflectivityspectra of the individual monolayer areas (away from theheterojunction), collected at T= 4 K. Figure 1c shows super-imposed PL (black) and reflectivity (red) spectra of MoSe2 (top)and WSe2 (bottom) monolayers after transfer and encapsulation inhBN. We measure in PL a neutral exciton (A1s) linewidth of 7 meVin MoSe2 and 5.5 meV in WSe2 (Fig. 1c). These FWHM values arecomparable to high-quality exfoliated MoSe2 and WSe2 mono-layers15,43–45. MoSe2 monolayers exhibit two pronounced PLemission peaks at 1.665 eV and 1.635 eV, assigned to neutral(A1s) and charged (T) excitons, respectively51. In the case of WSe2,the A1s transition is located at 1.734 eV with the singlet trions (T)and dark excitons (XD) lying 35meV and 40meV below A1s,consistent with previous reports52. Additional peaks appear atlower energies, attributed to contributions from neutral, chargedbiexcitons and localized emission from defects53,54. At theheterojunction, additional low energy emission could be expectedunder certain conditions from the formation of interlayerexcitons38.In Fig. 1c strong excitonic resonances appear in differentialreflectivity for both materials with negligible Stokes shift in energycompared to the PL emission, which is a sign of negligible excitonlocalization effects for these spectra. Clear signatures of B1sexciton states are also observed in both materials. For WSe2 theappearance of the A2s excited exciton state, which has a largerBohr radius, shows the good quality of the CVD-grown monolayersof the LHs55.We collect the Raman, PL and reflectivity spectra within ourdetection spot while moving the sample over a ≈10 μmdistance with a step size of ≈150 nm using attocube nanoposi-tioners. Typical Raman PL and reflectivity scans across aheterojunction are shown in the contour plots of Fig. 2a–c. Ablack dashed line indicates the position of the heterojunction ineach contour plot. As a common feature for all three contourplots, we observe abrupt changes in the optical spectra as wescan across the lateral heterojunction, as a result of distinctlydifferent phonon energies and exciton transition energies inthe two materials.Now we discuss Raman spectroscopy results in Fig. 2a formonolayer MoSe2 and WSe2, collected at T= 4 K using anexcitation laser wavelength of λ= 633 nm. The main Raman peaksof MoSe2 and WSe2 can be identified in the contour plot (detailedRaman spectra can be found in the Supplementary Material,section B). For monolayer MoSe2 we observe the A01(Γ) phonon at241 cm−1 and the E0(Γ) at 291 cm−156, while a strong peak at458 cm−1 has been associated to other peaks to form triplets57.Fig. 1 Lateral heterostructure spectroscopy and microscopy. a Schematic representation of the MoSe2-WSe2 LH, encapsulated in hBN. Grey,orange and red spheres represent Mo, W and Se atoms, respectively. b HAADF-STEM image showing a MoSe2-WSe2 boundary (between thered lines). The MoSe2 and WSe2 areas are located between the yellow and the cyan lines, respectively. c Corresponding PL (black) andreflectance contrast (red) spectra of MoSe2 (top) and WSe2 (bottom). The PL linewidth of neutral excitons (A1s) is 7 meV in MoSe2 and 5.5 meVin WSe2.D. Beret et al.2npj 2D Materials and Applications (2022)    84 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;Interestingly, we also observe a strong peak at 531 cm−1, recentlyassigned to multi-phonon processes associated with either both Kand M point phonons or a combination of Γ point phonons57. Theobservation of this Raman peak is a signature of resonantexcitation with an excited exciton state in MoSe2. WSe2 phononsare spectrally different compared to MoSe2. The degenerate A01(Γ)/E0(Γ) phonons are located at 250 cm−1 and, similar to MoSe2, astrong and recently discovered peak at 495 cm−1 is also observedhere and attributed to multi-phonon processes at K and M pointsor combination of Γ point phonons57.The PL linescan in Fig. 2b shows emission from the main excitontransitions in WSe2 and MoSe2 (indicated by arrows) and a clearchange in transition energy is discernible as we go across thelateral junction, with similar energies as for the individual spectrashown in Fig. 1c. Due to the extreme sensitivity of the PL emissionenergy spectrum on the defect concentration and dielectricenvironment19, we see spectral shifts between spectra taken atdifferent positions. This makes the PL contour plot appear lesssmooth than the Raman and reflectivity linescans.The reflectivity linescan shown in Fig. 2c shows a clear changein the main exciton energies as we scan from one material to theother. The main neutral exciton A1s feature in MoSe2 in reflectivityis at an energy of 1.665 eV, whereas for WSe2 this transition energyis clearly shifted to 1.734 eV. Reflectivity is less sensitive to thelocal defect and dielectric environment and therefore themeasured transition energies remain comparatively constant fromone spectrum to the other19.A PL imaging experiment is used to probe the effectivediffusion length in the two TMD materials that are connected atthe junction. First, we concentrate on results away from the lateraljunction i.e. neither the excitation nor the PL emission profile haveany spatial overlap with the lateral junction. The experimentconsists in a local photogeneration of excitons with a He:Ne laserfocused on a spot size of about 0.7 μm (see black curve in Fig. 2)and an excitation power of 5 μW. The generated spatial gradientof the exciton concentration (i.e. chemical potential gradient)induces lateral diffusion of excitons which is probed by recordingthe spatial PL profile with a CMOS camera, see supplement, wherewe integrate over the full spectral range of the monolayeremission. Figure 2d shows the PL profiles obtained at T= 4 K onWSe2 (red line) and MoSe2 (blue line). We clearly observe that PLemission occurs over a larger spot diameter than the laserexcitation58–60. At this temperature WSe2 shows a longer effectivediffusion length than MoSe2. This difference is also visible in theinset by directly comparing the images of the PL profile from thetwo materials.Interestingly, this behavior is reversed at T= 300 K whereMoSe2 shows a longer effective diffusion length than WSe2(Fig. 3b). This is possibly linked to dark excitonic states which havelonger lifetimes (PL emission times)61,62. Indeed, the lowest energystate of the conduction band is a dark state in WSe2 while it is abright state in MoSe2. The PL intensity evolution with thetemperature shows opposite trends: WSe2 is darker at lowtemperature and brighter at room temperature as compared toMoSe263. The contribution of dark exciton states with longerlifetime would increase the effective diffusion length as comparedto MoSe2, as dark exciton emission is negligible for MoSe264,65.Therefore, when we compare the two materials WSe2 has a longerdiffusion length at 4 K and a shorter one at T= 300 K.Near-field studies of the lateral heterojunctionDue to the extremely sharp nature of the junction (2–3 nm, seeFig. 1b) between the two materials, tip-enhanced Raman and PLspectroscopy are necessary to characterize the junction with sub-wavelength resolution. TEPL and TERS were carried out at roomFig. 2 Far field optical study. Contour plot of (a) Raman (λL= 633nm), (b) PL (λL= 633nm) and (c) white light reflectivity spectra scans across aWSe2-MoSe2 heterojunction at T= 5 K. The black horizontal dashed line indicates the position of the heterojunction. Color bars for panels (a),(b) and (c) are normalized from 0 to 1. d Exciton diffusion measurements at a temperature of T= 4 K for the MoSe2 monolayer region (blue)and WSe2(red). In the inset we show the MoSe2 diffusion PL profile compared to the WSe2 one. The laser intensity profile (black) is shown toindicate over which area excitons are initially generated, with small intensity oscillations due to Airy discs visible in logarithmic scale. e Sameas d but at T= 300 K.D. Beret et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    84 Fig. 3 Tip-enhanced spectroscopy of the MoSe2-WSe2 interface. a Schematic of the TEPL, TERS experimental set-up. b Spectrally integratedTEPL intensity colormap of the interface area. The red (respectively blue) color intensity is the value of integrated PL from 1.620 eV to 1.650 eV(respectively from 1.550 eV to 1.580 eV). c Typical TEPL spectra taken along the dashed line in b. Zone (1) on the left: 500 nm from the interfaceinside the MoSe2 area (x=−0.5 μm). Zone (2) at the center: 100 nm from the interface inside the WSe2 area (x= 0.1 μm). Zone (3) on the right:500 nm from the interface inside the WSe2 area (x= 0.5 μm). Three different excitonic components are observed in these curves: the WSe2neutral exciton(AWSe21s ), the dark (out-of-plane) exciton (XDWSe2 ), and the MoSe2 neutral exciton (AMoSe21s ) and their respective contributions areused to fit the experimental data using individual Lorentzian function: red, black and light blue dashed lines respectively. d A01(Γ) phononwavenumber measured by TERS along the dashed line in b as a function of the tip position. e Energy of the individual Lorentzian peaksobtained from the fitting procedure displayed in c. f Amplitude of the individual Lorentzian peaks obtained from the fitting proceduredisplayed in c. In figure d, e, f the position of the interface appears as a vertical black dashed line. The positions where the PL spectra of c weretaken appear as light vertical grey dashed lines.D. Beret et al.4npj 2D Materials and Applications (2022)    84 Published in partnership with FCT NOVA with the support of E-MRStemperature and the spatial resolution, determined by the tipdiameter, is estimated to be ≈ 40 nm, far below the measuredexcitonic diffusion lengths we observed in the individualmaterials66–68. For TEPL (TERS) a 633 nm (532 nm) linearlypolarized laser was focused onto the silver tip apex using a longworking distance x100 objective (0.7 NA). The collection apertureis kept open to ensure that photons emitted a few micrometersaway from the tip can be collected. The sample is scanned whilerecording PL spectra both with the tip in contact mode and 30 nmaway from the surface. The near field contribution is thenobtained by taking the difference between both recorded signals.Figure 3 shows a color map of the near field PL integratedintensity, excitation power was fixed to 0.4 mW and the samplescanning step size to 60 nm. The transition between WSe2 andMoSe2 can be clearly identified, and those images were used toselect an interface region which gives uniform PL.We then record PL spectra every 30 nm following the dashedline on the color map. Figure 3c displays three typical spectrameasured at (1) 500 nm from the interface inside the MoSe2 area,(2) at 100 nm from the interface inside the WSe2 area and (3) at500 nm from the interface inside the WSe2 area. All measured PLspectra are fitted using a combination of the different excitoniccontributions from MoSe2 and WSe2: the WSe2 neutral exciton (AWSe21s ) at about 1.66 eV (see dashed red line), the dark (out-of-plane)exciton (XDWSe2 ) near 1.61 eV (see dashed black line), and the MoSe2neutral exciton (AMoSe21s ) at about 1.57 eV (see dashed blue line), inagreement with the different transitions identified in the literatureat room temperature69. Figure 3d–f show the results of the globalfitting procedure of the PL spectra as a function of tip position.The position of the interface (see vertical dashed line) can beidentified precisely thanks to the TERS spectra that show a sharpvariation of the A01(Γ) phonon energy at the interface. Figure 3e, fdisplay the energy and amplitude of each component of the PLspectra as a function of the tip position. We find the same phononwavenumbers and exciton transition energies in our near-field andfar-field measurements.We note that the energy of both bright and dark WSe2 excitonare constant away from the interface but show a slight decreasewhen approaching the interface (≈200 nm), this could be anindication that tensile strain is present in the WSe2 layer toaccount for the lattice mismatch at the junction with MoSe270,71.Scanning across the junction, the amplitude of both WSe2 brightand dark exciton emission increases, going from zero at theinterface to a plateau hundreds of nm away from the interface(see red and black stars in Fig. 3f). Importantly a clear contributionof the MoSe2 bright exciton can be seen when tip-enhancedexcitation happens deep inside the WSe2 area (see light bluestars). The amplitude of this AMoSe21s contribution is decreasing asthe excitation (tip) moves away from the interface, reaching zeroat 400 nm away from the interface in WSe2.This behavior indicates that excitons excited under the tipinside the WSe2 area are diffusing through the interface andrecombine inside the MoSe2 area. Excitons are by consequenceable to travel through 400 nm (roughly ten times our spatialresolution) of WSe2 before reaching the interface. Interestingly thisis not a symmetric phenomenon: we do not detect any WSe2related PL emission when the tip (and hence the opticalexcitation) is positioned inside the MoSe2 area. This behaviorshows that the junction acts as an exciton diode, allowing excitonsto cross from WSe2 to MoSe2 but not the other way around. Thisnon reciprocal behavior is in agreement with the excitonic energylandscape at the interface and previously observed behavior in farfield measurement72. Indeed as illustrated in Fig. 4 a AWSe21sis ≈90meV above AMoSe21s presenting a potential barrier that excitoncannot cross even at room temperature.To get more quantitative understanding of measured excitontransport we perform numerical modeling of the experiment bysolving a one-dimensional steady-state diffusion equation in thetwo materials and through the interface:GðxÞ þ Dd2nðxÞdx2� nðxÞτðxÞ � μFðxÞ dnðxÞdx¼ 0 (1)Where n(x) is the local excitons density, D the diffusion coefficientset to 1 cm2/s and τ is the exciton lifetimes that we set to 200 psand 150 ps for MoSe2 and WSe2 respectively. We consider aGaussian generation profile under the tip given byGðxÞ ¼ G0 expð� x2w2Þ, where G0 is the amplitude and w is thewidth of the Gaussian distribution (set to 40 nm, our effective tipdiameter in the experiment).A change in the exciton energy (i.e. chemical potential variation ofthe exciton) can act as an effective drift contribution that we simplymodel by adding an effective field μF in the equation (see Fig. 4a).The mobility is set to μ= 500 cm2/V/s58 and the F is set to 1 mV/nm.The latter value is taken sufficiently high to let the current flow onlyin one direction. Also the effective field is applied to a small region of20 nm at the interface. Figure 4b displays the experimental spatiallyintegrated PL value as a function the tip position. To ease thenumerical modeling, the contributions of the bright and darkexcitons in WSe2 have been added and the PL intensity of eachmaterial has been normalized away from the junction. Figure 4cdisplays the results of the modeling when we spatially integrate thePL profiles. The inset shows the same modeling without consideringthe effective field F= 0 where a more symmetrical behavior is seenat the interface. The model reproduces the main experimental result:PL signal from MoSe2 is seen when exciting WSe2 up to 400 nm fromthe junction, whereas exciton transport in the other direction is notpossible. This underlines that the junction acts as an excitonic diode(i.e. an excitonic current can only flow from WSe2 to MoSe2). Figure4d presents the calculated PL intensity taken at the maximum of thePL profile. The main tendency is conserved but we see an increase ofthe PL intensity of MoSe2 at the interface, indicating an accumulationof excitons as they cannot cross the junction. This PL intensityincrease is also seen experimentally. The light density of states linkedto the plasmonic resonance at the silver tip can possibly modify theexciton emission rate locally73.In conclusion, we have performed detailed spectroscopicstudies on CVD grown lateral MoSe2-WSe2 heterostructures. Asan important step towards device processing and for accessingthe intrinsic optical quality of the junction, we have firsttransferred the sample from its original growth substrate andthen encapsulated the lateral heterostructures in top and bottomflakes of high quality hBN. Our experiments give access to theexcitonic structures at cryogenic temperatures, with neutralexciton transition linewidth of the order of 5 meV. In excitondiffusion experiments we show that the MoSe2 and WeSe2 excitontransport show opposite trends in temperature dependentexperiments, as dark excitons contribute to the PL signal inWSe2 and not in MoSe2. Our near field optical study using tip-enhanced experiments shows the important role of the hetero-junction, as we measure that an excitonic current can only flowfrom WSe2 to MoSe2 and not the other way. This behavior isreproduced by a simple diffusion model where the exciton energydifference between the two materials acts as a barrier over adistance of a few nm. Our findings highlight the high structuralquality of the heterojunction at the interface that can be regardedas an efficient excitonic diode, in the context of the broaderresearch field of excitonic devices11,74–76.METHODSWe use water-assisted deterministic transfer to pick up as-grown,chemical vapor deposition (CVD) LHs using polydimethylsiloxane(PDMS) and deterministically transfer and encapsulate them inhBN47,50. Raman, PL and differential white light reflectivity spectra arecollected at T= 5 K in a closed-loop liquid helium (LHe) system. ForD. Beret et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    84 the Raman and PL experiments we use a 633 nm HeNe laser as anexcitation source with a spot size diameter of ≈1μm and 6 μW power.In reflectivity we use a tungsten-halogen white light source with apower of a few nW to collect the intensity reflection coefficient of thesample with the monolayer (RML) and the reflection coefficient of thesubstrate (RS) so that ΔR= (RML− RS)/RS. The PL images are recordedby a Hamamatsu Fusion-BT CMOS camera. For STEM investigation,the samples were transferred to Quantifoiltm grids using PMMAassisted transfer protocol. The high-angle annular dark-field scanningtransmission electron microscopy (HAADF-STEM) image was acquiredwith a Thermofisher Talos 200X microscope operated at 200 kV. TERSand TEPL are carried out with state-of-the-art commercial system(Trios OmegaScope-R coupled with LabRAM spectrometer, HoribaScientific). Silver coated tips with an apex radius of 20 nm were usefor tip enhanced measurements. More details on experimental set-ups and procedures are given in the supplement.DATA AVAILABILITYThe data that support the findings of this study are available from the correspondingauthors upon request.Received: 13 April 2022; Accepted: 14 October 2022;REFERENCES1. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett.10, 1271 (2010).2. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a newdirect-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).3. Tonndorf, P. et al. Photoluminescence emission and raman response of mono-layer MoS2, MoSe2, and WSe2. Opt. Express 21, 4908–4916 (2013).4. Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantumsimulator. Nat. Phys. 17, 155–163 (2021).5. Gu, J. et al. Dipolar excitonic insulator in a moire lattice. Nat. Phys. 18, 395–400(2022).6. Li, H. et al. 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Superlattices Microstruct. 108, 2–26 (2017).ACKNOWLEDGEMENTSToulouse acknowledges partial funding from ANR IXTASE, ANR HiLight, ANR Ti-P,NanoX project 2DLight, the Institut Universitaire de France, and the EUR grant ATRAP-2D NanoX ANR-17-EURE-0009 in the framework of the “Programme des Investisse-ments d’Avenir”, the Institute of quantum technology in Occitanie IQO and a UPSexcellence PhD grant. Growth of hexagonal boron nitride crystals was supported byJSPS KAKENHI (Grants No. 19H05790, No. 20H00354 and No. 21H05233). The Jenagroup received financial support of the Deutsche Forschungsgemeinschaft (DFG)through a research infrastructure grant INST 275/257-1 FUGG, CRC 1375 NOA (ProjectB2), SPP2244 (Project TU149/13-1) as well as DFG grant TU149/16-1. This project hasalso received funding from the joint European Union’s Horizon 2020 and DFGresearch and innovation programme FLAG-ERA under grant TU149/9-1.AUTHOR CONTRIBUTIONSZ.G., E.N., A.G. and A.T. developed the growth method and fabricated the lateralheterostructures. T.T. and K.W. grew the hBN crystals. D.B., L.L., and P.R. performedand analyzed exciton transport experiments. U.K., T.L., J.B. performed and analyzedtransmission electron microscopy. I.P. and S.S. carried out hBN encapsulation. I.P., S.S.,A.E.-R., D.L., X.M., B.U. performed and interpreted PL, Raman and reflectivityexperiments. H.L. and J.-M.P. performed TEPL and TERS. S.W., V.P. and J.-M.P.optimized the TEPL and TERS set-up. D.B., H.L., J.-M.P. and L.L. performed thenumerical modeling. L.L., J-M.P., A.T., and B.U. wrote the manuscript with inputs fromall the authors and supervised the project.D. Beret et al.7Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2022)    84 FUNDINGOpen Access funding enabled and organized by Projekt DEAL.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-022-00354-0.Correspondence and requests for materials should be addressed to Laurent Lombez,Jean-Marie Poumirol, Andrey Turchanin or Bernhard Urbaszek.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022D. Beret et al.8npj 2D Materials and Applications (2022)    84 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-022-00354-0http://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Exciton spectroscopy and unidirectional transport in�MoSe2-�WSe2 lateral heterostructures encapsulated in hexagonal boron nitride Introduction Results and Discussion Sample preparation, electron microscopy and optical quality Near-field studies of the lateral heterojunction Methods DATA AVAILABILITY References Acknowledgements Author contributions Funding Competing interests ADDITIONAL INFORMATION