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Hassan Lamsaadi, Dorian Beret, Ioannis Paradisanos, Pierre Renucci, Delphine Lagarde, Xavier Marie, Bernhard Urbaszek, Ziyang Gan, Antony George, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Andrey Turchanin, Laurent Lombez, Nicolas Combe, Vincent Paillard, Jean-Marie Poumirol

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[Kapitza-resistance-like exciton dynamics in atomically flat MoSe2-WSe2 lateral heterojunction](https://mdr.nims.go.jp/datasets/16c19fa5-f117-4bb1-aea7-c65a9dd7cba2)

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Kapitza-resistance-like exciton dynamics in atomically flat MoSe2-WSe2 lateral heterojunctionArticle https://doi.org/10.1038/s41467-023-41538-6Kapitza-resistance-like exciton dynamics inatomically flat MoSe2-WSe2 lateralheterojunctionHassan Lamsaadi 1, Dorian Beret2, Ioannis Paradisanos 2,3, Pierre Renucci2,Delphine Lagarde2, Xavier Marie 2, Bernhard Urbaszek2,4, Ziyang Gan5,Antony George 5,6, Kenji Watanabe 7, Takashi Taniguchi 8,Andrey Turchanin 5,6, Laurent Lombez 2 , Nicolas Combe 1,Vincent Paillard1 & Jean-Marie Poumirol 1Being able to control the neutral excitonic flux is a mandatory step for thedevelopment of future room-temperature two-dimensional excitonic devices.Semiconducting Monolayer Transition Metal Dichalcogenides (TMD-ML) withextremely robust and mobile excitons are highly attractive in this regard.However, generating an efficient and controlled exciton transport over longdistances is a very challenging task. Here we demonstrate that an atomicallysharp TMD-ML lateral heterostructure (MoSe2-WSe2) transforms the isotropicexciton diffusion into a unidirectional excitonic flow through the junction.Using tip-enhanced photoluminescence spectroscopy (TEPL) and a modifiedexciton transfer model, we show a discontinuity of the exciton density dis-tribution on each side of the interface. We introduce the concept of excitonKapitza resistance, by analogy with the interfacial thermal resistance referredto as Kapitza resistance. By comparing different heterostructures with orwithout top hexagonal boron nitride (hBN) layer, we deduce that the transportproperties can be controlled, over distances far greater than the junctionwidth, by the exciton density through near-field engineering and/or laserpower density. This work provides a new approach for controlling the neutralexciton flow, which is key toward the conception of excitonic devices.Electronics relies on the control of the motion of charge carriers toprocess information. The losses causedby the chargedparticle currentand the resulting need to improve thepower efficiency have fueled lotsof interest in recent years1,2. As it is based on the control of electricallyneutral quasi-particles (excitons), insensitive to long-range Coulombscattering mechanisms, excitronics is by nature much more powerefficient as it presents only negligible ohmic losses3,4. Nevertheless,developing excitronic devices is challenging, as it requires the ability tocontrol the neutral exciton properties, such as the recombinationrates, diffusion length (LD) and propagation direction, in an opticallyactive medium at room temperature, without the help of externalelectric or magnetic fields3,5.Received: 9 June 2023Accepted: 8 September 2023Check for updates1CEMES-CNRS, Université de Toulouse, Toulouse, France. 2Université de Toulouse, INSA-CNRS-UPS, LPCNO, 135 Avenue Rangueil, 31077 Toulouse, France.3Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion 70013, Greece. 4Institute of Condensed MatterPhysics, Technische Universität Darmstadt, Darmstadt, Germany. 5Friedrich Schiller University Jena, Institute of Physical Chemistry, 07743 Jena, Germany.6AbbeCentre of Photonics, 07745 Jena,Germany. 7ResearchCenter for FunctionalMaterials, National Institute forMaterials Science, 1-1Namiki, Tsukuba 305-0044, Japan. 8International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.e-mail: laurent.lombez@insa-toulouse.fr; jean-marie.poumirol@cemes.frNature Communications |         (2023) 14:5881 11234567890():,;1234567890():,;http://orcid.org/0000-0003-2265-7276http://orcid.org/0000-0003-2265-7276http://orcid.org/0000-0003-2265-7276http://orcid.org/0000-0003-2265-7276http://orcid.org/0000-0003-2265-7276http://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/0000-0002-7772-2517http://orcid.org/0000-0002-7772-2517http://orcid.org/0000-0002-7772-2517http://orcid.org/0000-0002-7772-2517http://orcid.org/0000-0002-7772-2517http://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://orcid.org/0000-0001-7895-913Xhttp://orcid.org/0000-0001-7895-913Xhttp://orcid.org/0000-0001-7895-913Xhttp://orcid.org/0000-0001-7895-913Xhttp://orcid.org/0000-0001-7895-913Xhttp://orcid.org/0000-0003-0582-2970http://orcid.org/0000-0003-0582-2970http://orcid.org/0000-0003-0582-2970http://orcid.org/0000-0003-0582-2970http://orcid.org/0000-0003-0582-2970http://orcid.org/0000-0003-4211-4033http://orcid.org/0000-0003-4211-4033http://orcid.org/0000-0003-4211-4033http://orcid.org/0000-0003-4211-4033http://orcid.org/0000-0003-4211-4033http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41538-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41538-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41538-6&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-41538-6&domain=pdfmailto:laurent.lombez@insa-toulouse.frmailto:jean-marie.poumirol@cemes.frOwing to their promising optical properties, Transition MetalDichalcognenide monolayers emerged as a highly versatile platformfor excitonics system at the nanoscale6–11. In particular, their largeexciton binding energy allows operating at room temperature. Due totheir unique band properties, excitonic transport in TMD-MLs has ledto the discovery of new fundamental phenomena such as a valley halleffect12–14, or theobservation of nonlinear behavior such as a halo in thespatial profile15 or negative effective diffusion16. With the increasingmaturity of the field, several basic components necessary to controlexciton information have been developed, like room temperatureexcitonic transistor in a Van der Waals vertical heterostructure17, or anexcitonic diode able to filter excitons in lateral heterostructures18–20.The physical mechanisms involved in the exciton transfer processesthrough lateral heterojunctions, as well as their influence on the exci-ton distribution, dynamics and the resulting photoluminescenceobserved in previous work18 are still unclear. This is mainly due to:(i) the extreme sharpness of lateral heterojunctions making complexits optical characterization, (ii) the strong influence of external para-meters like defects, strain and dielectric environment on excitontransport, making the fabrication of high-quality samples with con-trolled dielectric environment crucial to extract the intrinsic junctionproperties, (iii) the lack of a complete theoretical description ableto describe the asymmetric exciton transfer through the junction.Exciton diffusion at sharp interfaces have been previously studied inother materials like organic semiconductors in so-called bulk-heterojunction21,22. In the context of solar cells, efficient fast excitondiffusion and harvesting have stimulated strong theoretical andexperimental efforts. Nevertheless, in such system the interface isdesigned to dissociate the exciton into free charges and not to transferthe entire quasi-particle through the junction21,22. Up to now, inTMD-ML the exciton diffusion is mainly driven either by strain23,24or dielectric gradient engineering in TMD based verticalheterostructure19. Both approaches require complex architectures,with nanometric precision of the strain or the electrostatic potentialover large distances (micrometers). The fabrication of those excitonicguides as well as their coupling with other circuit elements is thus verychallenging.In this paper, we investigate experimentally and theoretically theeffect of an atomically sharp MoSe2-WSe2 lateral heterostructure (LH)on exciton diffusion and distribution. We performed tip-enhancedphotoluminescence (TEPL) spectroscopy experiments, allowing sub-wavelength spatial resolution down to 30 nm, and developed anexciton transfer model. We show that the difference in the energy gapat the LH generates a discontinuity in the exciton density distributionanalog to the temperaturediscontinuity found at interfaces presentingthermal resistance (Kapitza resistance). In steady state conditions, thepresence of this discontinuity results in unique non-reciprocal excitontransport properties, taking place over distances far greater (twoorders of magnitude) than the junction width and experimentallyevidencedby: a highly asymmetric photoluminescence (PL) profile, thequenching of the WSe2-related PL and an enhancement of the MoSe2-related PL. Furthermore, by comparing the diffusion properties of fullyhBN-encapsulated LH and hBN supported LH (without top hBN layer),we demonstrate that the diffusion properties of the LH can be tuned,by the generated exciton population either by increasing the laserpower density or by modifying the optical near-field configuration (atconstant laser power).Experimental resultsSample preparation and characterizationThe high quality monolayer MoSe2-WSe2 LH is grown using amodifiedCVD method described in Ref. 25. We then use water-assisted deter-ministic transfer to pick up the LH from the as-grown substrate andtransfer it on a supporting flake of exfoliated hBN on SiO2/Si substrate.Finally, a second exfoliated hBN flake is transferred to cover thestructure partially26. As a result, we obtain two distinct areas, as shownin Fig. 1a, a fully encapsulated area hBN/WSe2-MoSe2/hBN/SiO2/Si(e-LH), and an uncapped area WSe2-MoSe2/hBN/SiO2/Si (un-LH). Thedashed white and yellow line in Fig. 1a highlight the boundaries of thebottom and top hBN flakes, respectively.Figure 1c, f displays the room temperature μ-PL spectrameasured on WSe2 and MoSe2, far from the junction on theencapsulated (e-LH) and uncapped (un-LH) regions, respectively.For the e-LH zone, the PL spectrum measured on MoSe2 MLexhibits a pronounced peak centered around 1.575 eV with a fullwidth at half maximum (FWHM) of 50 meV that, in agreementwith previous room temperature measurements27, can beassigned to the neutral exciton (AMoSe21s ). In the case of WSe2, thePL spectrum is asymmetric, due to an intense peak linked to theAWSe21s transition located around 1.65 eV (FWHM ~ 30 meV) and asecond weaker peak ~ 40 meV below A1s, attributed to the spin-forbidden dark exciton (XD)27. For the un-LH region, all previouslydescribed PL features appear. Furthermore, we observe a slightincrease of the broadening of all transitions, of the order of 5%.One can also notice that all PL spectra are more asymmetric. Thiscould be attributed to an increased contribution of the chargedexcitons (trions), as the unprotected sample can get chemicallycharged when exposed to ambient air. In any case, one can noticethat the integrated PL intensity I1PL(AWSe21s ) measured far from theinterface is ≈3 times stronger than I1PL(AMoSe21s ). Figure 1d, g isspectrally integrated μ-PL intensity color maps. The red (respec-tively blue) color intensity is the value of integrated PL (shadedareas in c and f) from 1.620 eV to 1.650 eV (respectively from1.550 eV to 1.580 eV). Figure 1d (g) corresponds to the mapping ofthe encapsulated (uncapped) region. One can clearly see that theMoSe2 layer is organized in 6 folded stars surrounded by WSe2.The white regions, signature of low emission regions, have dif-ferent origin. They correspond to bilayer inclusions when locatedat the center of MoSe2 stars, but also reveal cracks or/andinclusions that are related to the transfer process. We used thefar-field PL color maps in combination with Raman mappings toselect interfaces away from any visible defects.Near-field studies of the lateral heterojunctionIn this type of LH, the junction between the two materials WSe2 andMoSe2 is extremely sharp, down to ~3 nm as measured by electronmicroscopy18. Therefore, in order to gain insight into the transportproperties around the junction, we use a sub-wavelength resolutiontool, TEPL imaging and spectroscopy. Figure 2a displays a schematic ofthe experimental set-up, showing the linearlypolarized laser excitationof 633 nm wavelength (≈1.96eV) focused onto the apex of an atomicforce microscope (AFM) silver-coated tip. The exciton generationprofile is then linked to the electric field exaltation under the tip, aGaussian profile with a full width at half maximum of ~30 nm, and a tipposition (xtip) controlled with AFM resolution. As illustrated in theFig. 2a excitons diffuse away from the excitation spot over long dis-tances before recombining. The collection of emitted photons isensured by a long working distance high numerical aperture (0.7 NA)microscope objective, with a fully open collection aperture. Theposition of the junction is determined very precisely (~30 nm) usingtip-enhanced Raman spectroscopy (TERS), as described in ref. 18 andsupplementary information (Fig. 6).TEPL line scans with 30 nm step size are obtained by scanning thetip along a lineperpendicularly to the LH junction. Figure 2b, d displaystypical TEPL spectra measured for three tip positions (xtip) along themeasured line for both encapsulated and uncapped samples.The spectra (1) and (3) recorded far from the interface (500 nm insidetheMoSe2 region and 1.25 μminside theWSe2 region) are similar to theones described in Fig. 1. The spectra of WSe2 in locations (2)are recorded at 100 nm (respectively 300 nm) from the interface forArticle https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 2the e-LH (resp. un-LH) sample. They showcontributions of bothMoSe2and WSe2.All TEPL spectra can be fitted using three Lorentzian peaks toaccount for the previously described relative contributions of AWSe21s(dashed red line), XDWSe2(dashed green line) and AMoSe21s (dashed blueline) as illustrated by the diagram in Fig. 2a. Figure 2c, e displays theresult of this fitting procedure. The peak positions and FWHMs(shaded area) of the bright excitons AMoSe21s and AWSe21s are shown as afunction of the tip position xtip in the upper panels, while theintegrated PL intensity (IPL) appears in the lower panels. For clarity,the contribution of XDWSe2is not displayed (see supplementaryinformation). First, we point out that the AMoSe21s signature (blue star)is clearly observed while the excitation is taking place inside WSe2,(xtip > 0, right side of the solid gray line in Fig. 2c, e). A contrario, nosignature of AWSe21s is observed when the excitation takes place inMoSe2 (xtip < 0, left side of the solid gray line). This reveals thatnonreciprocal filtering is taking place at the interface, allowing theexcitons to cross the junction from WSe2 to MoSe2. The otherFig. 1 | Lateral heterostructure farfield optical characterization. aOptical imageof the sample, thewhite (yellow) dashed contour shows the bottom (top) hBN flakeboundaries. The continuous (respectively dashed) black square contour highlightsthe MoSe2-WSe2 LH, encapsulated in hBN (e-LH) region (respectively the hBNsupported LH (un-LH) region). b (e) Schematic representation of the e-LH (un-LH).c (f) typical μ-PL spectrameasured in theWSe2 andMoSe2 regions of e-LH (un-LH).d (g) Spectrally integrated PL intensity maps of e-LH (un-LH). The PL intensity isobtained by integrating MoSe2 (WSe2) PL spectra over the spectra range repre-sented by the blue (red) shaded area. PL spectra are recorded every 500 nm (stepsize), using a 633 nm ( ≈ 1.96eV) excitation laser, 400 μW laser power. The dottedblue lines in (d) and (g) highlight the boundaries between the two materials.Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 3transport direction being forbidden by the junction, in agreementwith18,28. The difference in the local dielectric environment betweene-LH and un-LH has no impact on the diode-like effect. There is novisible influence on both the energy and FWHM of the PL spectraafter crossing or being blocked at the junction. This suggests thatthere is no alteration of the nature of the excitons in each TMD-MLnear the vicinity of the junction.It is very interesting to notice that, in both e-LH and un-LH, theTEPL intensity originating fromWSe2 (red stars) strongly decreases asthe excitation takes place closer to the interface (xtip→0). As aFig. 2 | Tip-enhanced spectroscopy of the MoSe2-WSe2 interface. a Left panel:Schematic of the lateral heterojonction, TEPL measurement and the resultingexcitonic diffusion properties. Right panel: Diagram of the different excitonicprocesses observed in our system. b (d) Typical TEPL spectra taken across theinterface in e-LH (respectively un-LH) (1) 500 nm to the left of the interface, (2) 100nm (300 nm) and (3) 1,25 μm to the right of the interface. The excitoniccontributions are fitted using individual Lorentzian function, neutral WSe2 excitonin red (AWSe21s ), neutral MoSe2 exciton in blue (AMoSe21s ) and the dark exciton (out-of-plan) in green (XWSe2D ). c (e) Top: Energy and FWHM of each Lorentzian peakobtained from the fitting procedure as shown in (b). d. Bottom: Amplitude of eachLorentzian peak obtained from the fitting procedure as shown in (b).d The red andblue stars indicate AWSe21s and AMoSe21s , respectively.Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 4consequence, the resulting signal measured near the LH interface isstrongly dominated by AMoSe21s (see Fig. 2c, e bottom panels). In otherwords, even if the tip is located inside WSe2, most of the generatedexcitons migrate through the LH junction into MoSe2 before recom-bining. This behavior can only be explained by a strongly anisotropictransport, with the diffusion toward the junction becoming moreefficient than the other directions. The second effect resulting fromsuch an efficient exciton transfer AWSe21s →AMoSe21s is that as the tipapproaches the interface from the WSe2 side the MoSe2 PL intensityIPL(AMoSe21s ) increases and nearly reaches the values of the integrated PLintensity of WSe2 far from the interface (I1PL(AWSe21s )). Far from thejunction, MoSe2 is three times less bright thanWSe2, meaning that thejunction is enhancing the MoSe2 flake brightness at its vicinity.Finally, a pronounced difference can be seen between the twosystems, with A1sMoSe2signature extending ~1.2 μm away from theinterface in un-LH versus ~400 nm for e-LH. Both distances beingconsiderably larger than the physical junction width (≈3 nm18)Modified exciton transfer modelIn order to get a better understanding of the underlying physicalphenomena taking place close to the interface, we developed anexciton transfer model, which is detailed in supplementary informa-tion. We theoretically investigate, in the low exciton density regime(typically 1011 cm−2), the variation of neutral exciton density versus tipposition, to be compared to the TEPL results. To do so, we analyticallysolved the linear 1D steady-state diffusion equation in each material i(1 = WSe2, 2 = MoSe2), given by :Did2nðx, xtipÞdx2� nðx, xtipÞτi+ Γiðx, xtipÞ=0 ð1Þn(x, xtip) is the exciton density at x position with the excitation takingplace at xtip, the x-axis origin being placed at the LH interface, Di theeffective diffusion coefficient and τi the effective lifetime, radiative (τri )and non-radiative (τnri ) (1/τi = 1/τri + 1/τnri ). Li =ffiffiffiffiffiffiffiffiffiDiτiprepresents theeffective diffusion length in the material i. We useΓiðx, xtipÞ= Γ0iðP,αi, νÞe�ðx�xtip Þ2w2 to simulate the exciton generationunder the tip, centered at xtip. The width w corresponds to the tipdiameter (~30 nm), P is the enhanced laser power under the tip and αithe absorption coefficient of the material i at the laser energy hν. Weset boundary conditions to be n(x→ ±∞, xtip) = 0. In agreement withexperimental results, we impose the continuity of the integrated PLintensity for all values of xtip. Finally, we considered that brightexcitons are not interacting with other types of excitons (darkexcitons, B-excitons, momentum-forbidden excitons).As illustrated in Fig. 3a, we model the junction as an ideally thininterface of fixed width (ϵ) much smaller than the excitonic diffusionlength inside the barrier (≪LD), where no electron-hole pair recombi-nation can occur. To model the asymmetric local effective drift ofneutral exciton through the junction, we introduce a local uniformforce field:F!= � ∇!EA1s’ � E AWSe21s� �� E AMoSe21s� �� �=ϵ bx ð2ÞAs a result, the junction imposes the continuity of the excitonicflux density on both sides of the interface by a local constant fluxdensity j!n =μb F!n� Db ∇!n, where μb andDb are the excitonmobilityand diffusion coefficient inside the interface.Figure 3b displays the calculated n(x, xtip) for two different tippositions.We emphasize first on the lateral heterostructure specificity:the exciton density is discontinuous at the interface (see continuouslines). As a reference, the continuous exciton density calculated forclassical diffusion (F =0) is display in dashed lines. When the tipexcitation takes place inside MoSe2, the excitons are blocked by thejunction, and the excitondensity on the other side of the junction staysclose to zero (see continuous green line). Excitons interacting with thejunction loose a velocity v* = μbF blocking the diffusion process. Thisblocking phenomenon causes a redistribution of the exciton thatFig. 3 | Exciton distribution and near field optical spectrocopy of the junction.a Illustration of the exciton drift inside the interface, the shaded area correspondsto the partition zone between the two materials. b Exciton density n(x, xtip) calcu-lated with the near-field model for two tip positions xtip = LD (black line) andxtip = − LD (green line) with: Γ01= 3Γ02= Γ0, τ1 = τ2 = τ, L1 = L2 = LD =0.1 μm. Thedashed lines indicate the exciton density with no junction influence (F =0).cNormalized PL intensity of AMoSe21s (blue) andAWSe21s (red) in e-LHarea.d Sameas (c)in the un-LH area. The solid black line represents the PL intensities calculated usingEqs. (5) and (6).Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 5strongly accumulate at the interface. On the other hand, when theexcitation takes place insideWSe2, the excitons cross the junction, andare accelerated, hence acquiring an extra velocity v*. One can clearlysee that this drives those excitons further inside theMoSe2 layer, whilebringing the excitonic density down to zero near the interface on theWSe2 side (see continuous black line).To facilitate further developments, and better characterize theexciton discontinuity at junction we define a partition coefficientlinking the exciton densities n(x =0+) and n(x =0−) on both sides of theinterface. Because of the asymmetrical behavior of the junction, thispartition coefficient κ = n(x =0+)/n(x =0−) can be written, dependingon the direction of excitonic flux, as follows:κ ’κ + = 1� L2μbFτ2� �e�μbFϵDb + L2μbFτ2xtip > 0κ� = 1 + L1μbFτ1� �eμbFϵDb � L1μbFτ1� ��1xtip < 08>><>>:ð3Þwith L1, L2 the diffusion lengths of both materials. κ quantifies thediscontinuity of the exciton density at the junction, with κ+ = κ(xtip > 0)describing the exciton diffusion from WSe2 to MoSe2 andκ− = κ(xtip < 0) the diffusion from MoSe2 to WSe2. In our case, as thelocal equilibrium is established in the steady state, κ+ ~ κ− (see Table 1),to simplify the discussion we will therefore refer simply to κ inde-pendently of the direction of excitonic flux. When κ = 1, the excitondistribution, displayed as a dashed line in Fig. 3b, is continuous asobserved in classical diffusion. When κ≪ 1, corresponding to the pre-sent case, the exciton distribution is strongly asymmetric (see con-tinuous line in Fig. 3b). Our finding can be interpreted as anextrapolation of the interfacial thermal resistance so-called Kapitzaresistance, which describes the temperature discontinuity at atom-ically flat interface between twomaterials29,30. For high-quality LHs, theabsolute value of the exciton Kapitza resistance can be defined as afunction of the partition coefficient as follows: (See more detailsin supplementary information).Rn =nðx =0�Þ � nðx =0+ Þjn’ κ � 1v*1� ev*ϵ=Db1� κev*ϵ=Dbð4ÞTo compare directly the prediction of our near-field model withthe experimental results, we calculate IPL(AMoSe21s ) and IPL(AWSe21s ), theintegrated PL intensities of each material as a function of the tipposition. In the linear regime, thenormalizedPL intensity ofMoSe2 andWSe2 can be written as (see supplementary information for details):INormPL AMoSe21s� �ðxtipÞ=AκffiffiffiffiπpwZ 10dxe�x=L1 e�ðx�xtip Þ2w2+1ffiffiffiffiπpβwZ 0�1dx 1 + ðβAκ � 1Þex=L2� �e�ðx�xtip Þ2w2ð5ÞINormPL AWSe21s� �ðxtipÞ=1ffiffiffiffiπpwZ 10dx 1� ð1� BκÞe�x=L1� �e�ðx�xtip Þ2w2+BκffiffiffiffiπpwZ 0�1dxex=L2 e�ðx�xtip Þ2w2ð6Þwith I1PLðAWSe21s Þ used for normalization. The experimental PL is fittedusing four fitting parameters: Aκ and Bκ, amplitude parameters, givingus access to κ, the partition coefficient and L1, L2. Figure 3c, d shows theexperimental normalized PL intensities of MoSe2 (blue dots) andWSe2(red dots) for both e-LH and un-LH configurations, respectively. Theblack solid lines represent the fits using Eqs. (5) and (6). The resultingfitting parameters are displayed in Table 1. In both systems, the κ≪ 1values for e-LH and un-LH confirm the strong asymmetry of thejunction and the resulting strong Kapitza exciton resistance.DISCUSSIONOne can see that the model describes extremely well the strongquenching of the WSe2-related PL and the appearance of MoSe2-rela-ted PL when approaching the junction from the right (xtip > 0), shed-ding light on the experimental results on unidirectional excitonictransport across the junction. It is also able to quantitatively describethe enhancement of IPL(AMoSe21s ) at the junction and its progressivedecrease to the typically lower value I1PL(AMoSe21s ) ofmonolayerMoSe2 asthe tip is moved away from the junction (xtip < 0). We would like topoint out that this observation is far from trivial, it indicates that toconserve the experimentally observed continuity of the PL intensity,the exciton density at the interface (n(x = 0±)) is enhanced. We believethat this could be linked to the drastic change in the exciton velocity atthe interface. Indeed, when the tip is inside MoSe2, excitons diffusingtoward WSe2 are abruptly stopped at the junction, their averagevelocity going to zero. The non-radiative lifetime (τnr2 ), being in partlinked to the probability for the exciton to encounter non-radiativetraps during its lifetime, is by consequence increased31, resulting in anincreased population at the interface. This would explain why the sizeof PL enhancement area (where IPL(AMoSe21s ) ≥ I1PL(AMoSe21s )) is a functionof the diffusion length (see Fig. 3), as it only occurs when excitons startaccumulating at the junction. Other phenomenon may contribute tothis variation as a modification of the non-radiative Auger recombi-nation due to the local enhancement of the exciton density.Finally, the model reveals that the important difference observedin the PL profile between e-LH and un-LH is linked to drastically dif-ferent values of the diffusion length, much shorter in e-LH than in un-LH (see experimental results in Fig. 2 and theoretical results in Table 1).To understand why Le�LHD < Lun�LHD we need to consider that even if theTEPL experiments on e-LH and un-LH were performed using the samelaser power (400μW), the presence or absence of the top hBN layer,strongly impacts the near-field configuration under the tip. In firstapproximation, and considering a spherical tip of 30nm diameter, wecan estimate the near-field intensity ratio on the TMD layer as:E!��� ���2un�LHE!��� ���2e�LH’ Ze�LHZun�LH�  6 nBNnair�  4ð7ÞZe−LH and Zun−LH are the distances from the tip center to the TMD-ML ine-LH and un-LH areas, respectively. nBN and nair are hBN and airrefractive index, respectively. Considering a 3 nm-thick hBN top layer(measured by AFM), we can estimate the enhancement ratio to be ~23.We can then expect the exciton density generated under the tip in un-LH to be more than one order of magnitude larger than in e-LH. Tocharacterize the exciton transport properties of the WSe2 layer versusexciton density we use spatio-temporal PL signal in a confocalmicroscope. A local pulsed laser excitation (λ= 692 nm, pulse duration1.5 ps), generates excitons, and we record the time evolution of the PLprofile. We then extract the time evolution of the squared widthw2(t) =w2(0) +Δw2(t) which is used to determine an effective diffusioncoefficient in the 80 first picosecond where 90% of the PL signaloriginates : Δw2(t) = 4Defft. An important point is to be able todecorrelate the effective lifetime τeff (linked to the PL decay) and theTable 1 | Results of the PL fits using the near-field model forboth e-LH and un-LH systemsArea L1(nm) L2(nm) κ Rn(sm−1)e-LH 120 ± 6 110 ± 5.5 ~1 × 10−3 ~1 × 10−5un-LH 550 ± 55 450± 45 ~1 × 10−3 ~1 × 10−5Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 6diffusion coefficients, from which we deduce the effective diffusionlength Leff =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDeffτeffp. Experimental conditions and detailed resultsare given in the supplementary information (Figs. 2–4). The excitationpower density was varied over several order of magnitude and theresults comparedbetween the e-LHandun-LH samples. Figure 4 showsthat, for both samples, Leff increases with the excitation power density(i.e. the excitonic density) which is mainly due to the increase of theeffective diffusion coefficient (See supplementary information). Thistrend, attributed to a weak Auger contribution has been previouslyobserved in WS231,32 and explain the large difference observed in thediffusion lengths we observed in e-LH and un-LH. The experimentalresults have beenmodeled by using a Auger coefficient of 0.210−6cm2/s(See supplementary information). This value is two orders ofmagnitude lower than the one estimated on non encapsulated WS2(without top and bottom hBN) where a large difference of thetransport properties values with a fully encapsulated layer wasobserved31. In summary, we show that both samples exhibit similarexciton transport properties, indicating the importance of the hBNbottom layer that prevents strong Auger scattering effect.One can notice here that, according to Eq. (7), the enhancementratio is dominated by the tip-TMD layer distance. This offers a uniqueopportunity, as using plasmonic tips or nanoantennas in combinationwith hBN encapsulation allows to control the diffusion length in thistype of structures. As a matter of fact, controlling the thickness of thetop hBN layer from a single layer to 20 layers, for example, wouldchange the enhancement factor by a factor 10,modifying the diffusionlength by the same amount, all the while avoiding the flaws, loweroptical quality and exposition to environment, that are observed in theuncapped LH.In summary, we have performed a detailed tip-enhanced spec-troscopy study of a MoSe2-WSe2 lateral heterostructure, and havedeveloped a model to render the observation of the unilateral trans-port across the junction observed in near-field PL experiment. Itaccounts for a discontinuity of the exciton density at the interface. Wehave thus shown that the exciton diffusion properties follow a semi-classical process, due to the difference in the energy gap between thetwo materials: the usual isotropic in-plane diffusion of the excitons isfrustrated by the junction, leading to anasymmetric diffusion, inwhichall generated excitonsmove away fromthe highbandgapWSe2 layer torecombine in the low bandgap MoSe2 layer. This transfer causes nearthe interface the quenching of WSe2-related PL and the enhancementof the MoSe2-related PL, well above the one observed in “bulk”MoSe2far from the junction. Interestingly, we observe similar asymmetricdiffusion property for samples with or without top hBN. Both samplespresent similar intrinsic transport properties, probably linked to anefficient screening of the dielectric disorder by the bottom encapsu-lation by hBN layer. Finally, we have shown that the diffusion length inWSe2 is strongly dependent on the exciton density. This offers a newdegree of freedom, as changing the laser power density or the near-field enhancement (for instance using optically resonant nanoanten-nas instead of the plasmonic tip) would allow tuning the diffusionlength to any wanted value from tens of nanometer up to few micro-meters. TMD-based lateral heterostructure is a rapidly evolvingresearch field that could offer to combine TMDs with very differentbandgaps, thus allowing partition zone engineering, or creating morecomplex designs using three ormore TMDs (lateral excitonic quantumwells). This work offers both the theoretical and experimental tools topredict and control the new diffusion properties that will be at theorigin of new excitronic devices.MethodsWe use water-assisted deterministic transfer to pick up the chemicalvapor deposition LH from the as-grown substrate using poly-dimethylsiloxane (PDMS) and transfer it on a supporting flake ofexfoliated hBN on SiO2/Si substrate26. TERS and TEPL are carried outwith state-of-the-art commercial system (Trios OmegaScope-R cou-pled with LabRAM spectrometer, Horiba Scientific). Silver-coated tipswith an apex radius of 15nm were used for tip-enhanced measure-ments. The Time evolution of the PL profile experiment is based on adiffraction-limited laser excitation that induces lateral diffusion of thephotogenerated excitonic species. We used a Streak camera system torecord the time evolution of the PL spatial profile IPL = I(x, t) with a timeresolution of 5.5 ps. TheTi:Sa laser excitation is set to Eex = 1.79 eV,witha 80 MHz repetition frequency, 1.5 ps pulse width and we vary theexcitation power from 10 μW to 1 mW.Data availabilityThe data for all figures in themain text are available in the Source Datafile. The data presented in Supplementary information are availableupon request due to their large file size. Source data are provided withthis paper.References1. Butov, L. Excitonic devices. Superlattices Microstruct. 108, 2 (2017).2. Miller, D. Rationale and challenges for optical interconnects toelectronic chips. Proc. IEEE 88, 728 (2000).3. High, A. A., Novitskaya, E. E., Butov, L. V., Hanson, M. & Gossard, A.C. Control of exciton fluxes in an excitonic integrated circuit. Sci-ence 321, 229 (2008).4. Peng, R. et al. Long-range transport of 2D excitons with acousticwaves. Nat. Commun. 13, 1334 (2022).5. High, A.A., Hammack,A. T., Butov, L. V., Hanson,M.&Gossard,A.C.Exciton optoelectronic transistor. Opt. Lett. 32, 2466 (2007).6. Wang, G. et al. Colloquium : Excitons in atomically thin transitionmetal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).7. Wang, J., Verzhbitskiy, I. & Eda, G. Electroluminescent devicesbased on 2D semiconducting transition metal dichalcogenides.Adv. Mater. 30, 1802687 (2018).8. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H.2D materials and van der Waals heterostructures. Science 353,aac9439 (2016).9. Cheiwchanchamnangij, T. & Lambrecht,W. R. L.Quasiparticle bandstructure calculation of monolayer, bilayer, and bulk MoS 2. Phys.Rev. B 85, 205302 (2012).0 1x109 2x109 3x109 4x1090306090120150180210L eff (nm)Laser density (W.m-2)e-LHun-LH3x1071103x108 3x109un-LHe-LH Deff(cm2 /s)Laser density (W.m-2)Fig. 4 | Power dependence of exciton transport properties. Evolution of theeffective diffusion length (Leff) with the excitationpower densitymeasured inWSe2.Results obtained from time revolved PL profiles (see supplementary information).Error bars are mainly due to the fitting errors (linear fitting of the squared width,and bi-exponential fitting for τ (see supplementary information)). The inset showsthe power dependence of the effective diffusion coefficient (Deff).Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 710. Yuan, L., Wang, T., Zhu, T., Zhou, M. & Huang, L. 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Pollack, G. L. Kapitza resistance. Rev. Mod. Phys. 41, 48 (1969).31. Zipfel, J. et al. Exciton diffusion in monolayer semiconductors withsuppressed disorder. Phys. Rev. B 101, 115430 (2020).32. Uddin, S. Z. et al. Enhanced neutral exciton diffusion in monolayerWS2 by exciton-exciton annihilation. ACS Nano 16, 8005 (2022).AcknowledgementsToulouse acknowledges partial funding from ANR IXTASE (ANR-20-CE30-0032), ANR HiLight (ANR-19-CE24-0020-01), ANR Ti-P (ANR-21-CE30-0042), NanoX project 2DLight (ANR-17-EURE-0009), the InstitutUniversitaire de France, and the EUR grant ATRAP-2D NanoX ANR-17-EURE-0009 in the framework of the “Programme des Investissementsd’Avenir”, the Institute of quantum technology in Occitanie IQO and aUPS excellence PhD grant. Growth of hexagonal boron nitride crystalswas supported by JSPS KAKENHI (Grants No. 19H05790, No. 20H00354and No. 21H05233). The Jena group received financial support of theDeutsche Forschungsgemeinschaft (DFG) through a research infra-structure grant INST 275/257-1 FUGG, CRC 1375 NOA (Project B2),SPP2244 (Project TU149/13-1) as well as DFG grant TU149/16-1. Thisproject has also received funding from the joint European Union’s Hor-izon 2020 and DFG research and innovation program FLAG-ERA undergrant TU149/9-1.Author contributionsZ.G., A.G., and A.T. developed the growth method and fabricated thelateral heterostructures. T.T. and K.W. grew the hBN crystals. I.P. carriedout hBN encapsulation. D.B., L.L., P.R, D.L, and X.M. developed, per-formed and analyzed effective diffusion coefficient and exciton lifetimeexperiments. H.L. and J.-M.P. performed TEPL and TERS. V.P. and J.-M.P.optimized the TEPL and TERS set-up. H.L., J.-M.P., N.C, and V.P devel-oped the analytical modeling. J-M.P., V.P., L.L., B.U. wrote the manu-script with inputs from all the authors and supervised the project.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-41538-6.Correspondence and requests for materials should be addressed toLaurent Lombez or Jean-Marie Poumirol.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work.A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in 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 any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-41538-6Nature Communications |         (2023) 14:5881 8https://doi.org/10.1038/s41467-023-41538-6http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Kapitza-resistance-like exciton dynamics in atomically flat MoSe2-WSe2 lateral heterojunction Experimental results Sample preparation and characterization Near-field studies of the lateral heterojunction Modified exciton transfer model DISCUSSION Methods Data availability References Acknowledgements Author contributions Competing interests Additional information