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[Andrew Y. Joe](https://orcid.org/0000-0003-4376-7386), Andrés M. Mier Valdivia, [Luis A. Jauregui](https://orcid.org/0000-0002-7813-8005), [Kateryna Pistunova](https://orcid.org/0000-0002-3170-1657), Dapeng Ding, [You Zhou](https://orcid.org/0000-0002-9854-545X), [Giovanni Scuri](https://orcid.org/0000-0003-1050-3114), Kristiaan De Greve, Andrey Sushko, [Bumho Kim](https://orcid.org/0000-0002-5671-5641), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [James C. Hone](https://orcid.org/0000-0002-8084-3301), [Mikhail D. Lukin](https://orcid.org/0000-0002-8658-1007), [Hongkun Park](https://orcid.org/0000-0001-9576-8829), [Philip Kim](https://orcid.org/0000-0002-8255-0086)

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[Controlled interlayer exciton ionization in an electrostatic trap in atomically thin heterostructures](https://mdr.nims.go.jp/datasets/cc60e097-3736-412f-a969-3e154d6e5d92)

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Controlled interlayer exciton ionization in an electrostatic trap in atomically thin heterostructuresArticle https://doi.org/10.1038/s41467-024-51128-9Controlled interlayer exciton ionization in anelectrostatic trap in atomically thinheterostructuresAndrew Y. Joe 1,10,11, Andrés M. Mier Valdivia2,11, Luis A. Jauregui 3,Kateryna Pistunova 1, Dapeng Ding1,4, You Zhou 1,4,5, Giovanni Scuri 1,6,Kristiaan De Greve1,4, Andrey Sushko1, Bumho Kim 7, Takashi Taniguchi 8,Kenji Watanabe 9, James C. Hone 7, Mikhail D. Lukin 1, Hongkun Park 1,4 &Philip Kim 1,2Atomically thin semiconductor heterostructures provide a two-dimensional(2D) device platform for creating high densities of cold, controllable excitons.Interlayer excitons (IEs), bound electrons and holes localized to separate 2Dquantum well layers, have permanent out-of-plane dipole moments and longlifetimes, allowing their spatial distribution to be tuned on demand. Here, weemploy electrostatic gates to trap IEs and control their density. By electricallymodulating the IE Stark shift, electron-hole pair concentrations above2 × 1012 cm−2 can be achieved. At this high IE density, we observe an exponen-tially increasing linewidth broadening indicative of an IE ionization transition,independent of the trap depth. This runaway threshold remains constant atlow temperatures, but increases above 20K, consistent with the quantumdissociation of a degenerate IE gas. Our demonstration of the IE ionization in atunable electrostatic trap represents an important step towards the realizationof dipolar exciton condensates in solid-state optoelectronic devices.Semiconductor van der Waals (vdW) heterostructures offer a uniqueplatform where strong light-matter interactions enable novel devicecapabilities that expand our ability to study fundamental mesoscopicphenomena. As their building blocks, monolayer transition metaldichalcogenides (TMDs) provide a synergy of electronic and photonicdegrees of freedom that manifest as excitons, optically generatedbound electron-hole pairs, with large binding energies1 and spin-valleylocking properties2,3. In type-II TMD heterostructures, such as MoSe2 /WSe2, electrons and holes are localized on separate 2D quantum welllayers. This band alignment leads to the formation of IEs withpermanent out-of-plane dipole moments4–7, extended lifetimes4,8,9,and long interaction-driven diffusion lengths4,7,10, while maintainingstrong binding energies11–13. These properties also make IEs ideal forthe design of excitonic devices with engineered spatial emission pro-files and controllable IE density with electrostatic gates.The generation and control of large IE concentrations is desirableto explore the rich physics predicted by the excitonic phase diagram.In GaAs double quantum wells, indirect excitons have been shown tocondense into a degenerate state14–16 that is expected to be a super-fluid, providing a route to dissipationless optoelectronic devices.Received: 22 May 2024Accepted: 30 July 2024Check for updates1Department of Physics, Harvard University, Cambridge, MA, USA. 2John A. Paulson School of Engineering and Applied Sciences, Harvard University,Cambridge, MA, USA. 3Department of Physics, University of California, Irvine, CA, USA. 4Department of Chemistry and Chemical Biology, Harvard University,Cambridge, MA, USA. 5Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA. 6E. L. Ginzton Laboratory, StanfordUniversity, Stanford, CA, USA. 7Department of Mechanical Engineering, Columbia University, New York, NY, USA. 8International Center for MaterialsNanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan. 9Research Center for Electronic and Optical Materials, NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba, Japan. 10Present address: Department of Physics and Astronomy, University of California, Riverside, CA,USA. 11These authors contributed equally: Andrew Y. Joe, Andrés M. Mier Valdivia. e-mail: pkim@physics.harvard.eduNature Communications |         (2024) 15:6743 11234567890():,;1234567890():,;http://orcid.org/0000-0003-4376-7386http://orcid.org/0000-0003-4376-7386http://orcid.org/0000-0003-4376-7386http://orcid.org/0000-0003-4376-7386http://orcid.org/0000-0003-4376-7386http://orcid.org/0000-0002-7813-8005http://orcid.org/0000-0002-7813-8005http://orcid.org/0000-0002-7813-8005http://orcid.org/0000-0002-7813-8005http://orcid.org/0000-0002-7813-8005http://orcid.org/0000-0002-3170-1657http://orcid.org/0000-0002-3170-1657http://orcid.org/0000-0002-3170-1657http://orcid.org/0000-0002-3170-1657http://orcid.org/0000-0002-3170-1657http://orcid.org/0000-0002-9854-545Xhttp://orcid.org/0000-0002-9854-545Xhttp://orcid.org/0000-0002-9854-545Xhttp://orcid.org/0000-0002-9854-545Xhttp://orcid.org/0000-0002-9854-545Xhttp://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0003-1050-3114http://orcid.org/0000-0002-5671-5641http://orcid.org/0000-0002-5671-5641http://orcid.org/0000-0002-5671-5641http://orcid.org/0000-0002-5671-5641http://orcid.org/0000-0002-5671-5641http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8084-3301http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0002-8658-1007http://orcid.org/0000-0001-9576-8829http://orcid.org/0000-0001-9576-8829http://orcid.org/0000-0001-9576-8829http://orcid.org/0000-0001-9576-8829http://orcid.org/0000-0001-9576-8829http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://orcid.org/0000-0002-8255-0086http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51128-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51128-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51128-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-51128-9&domain=pdfmailto:pkim@physics.harvard.eduWhile increasing exciton density is generally favorable for condensa-tion, increasing wavefunction overlap eventually leads to completescreening of the IE binding energy at the Mott density17–19. Even belowthis critical condition, a fraction of the IEs can be thermally ionized at afinite temperature, enhancing the screening effect. Previous theore-tical studies showed that this density dependent screening leads to arunway IE dissociation process near the ionization threshold20–25. InTMD heterostructures, the orders of magnitude larger binding ener-gies allow the system to sustain larger IE populations before ionizationeffects become relevant9. This property opens the door to the reali-zation of electrically tunable high-temperature condensates13,26,27.Electrostatics traps are a useful tool for exploring the IE phasediagram. They allow us to deterministically localize IEs and increasetheir density, bypassing the need for high laser powers that lead toheating or nonlinear Auger recombination28,29, and potentially evendamage to the sample. Furthermore, the control over their diffusiondynamics opens the avenue for reliably designing excitonic devices, asother trapping approaches like moiré localization depend sensitivelyon sample homogeneity30–33. Separate control of the IE density andtemperature paves the way towards constructing tunable coherentoptoelectronic devices and studying correlated phenomena emergingfrom them.ResultsElectrostatic tunability of interlayer exciton emissionIn this article, we design a multi-gated structure to create electrostatictraps that allow us to generate high densities of IEs, control theirspatial distribution, and determine their critical dissociation density asa function of temperature. All the data shown is from device D1 unlessotherwise stated. Figure 1a shows a schematic of the device design. Ahigh quality, h-BN encapsulated MoSe2/WSe2 heterostructure is fabri-cated with matching top and bottom metal gates (Methods). Amatching set of grounded ~250 nm-wide stripe gates maintains aconstant IE energy in the trap region. On either side of the stripe aretwo sets of top and bottom gates separated by ~500nm that controlthe IE energy in the outside region. Applying voltages to the outergates creates a neighboring electric field, Eog =εh�BNεTMDVtg�Vbgttotal, whereεh-BN = 3.9, εTMD = 7.2 are the h-BN and TMD dielectric constants, Vtgand Vbg are the top and bottom gate voltages, and ttotal is the totalh-BN thickness. Applying positive Eog raises the IE energy in the outerregion due to the linear Stark effect4. We note that the intralayerexciton energies are not affected in this gating configuration sincetheir dipole moments are in the TMD plane4. The electric field for thecenter stripe gates is approximately zero since these are grounded.The relative field difference between the stripe gate region and theouter area creates a confinement potential along the former so that ahigh IE density can accumulate in the trap without diffusing away (redcurve in Fig. 1b). Figure 1c shows an optical image of the devicedetailing the spatial region for the experiment.Wedemonstrate our gatemodulated trapbyperforming scanningphotoluminescence (PL) spectroscopy at various Eog across the stripegates (Methods). All PLmeasurements are performed at T = 4K, unlessotherwise stated, with an excitation wavelength of 660nm (1.87 eV),and a diffraction limited spot. In Fig. 1d, wemeasure the PL spectra as aFig. 1 | Modulating the interlayer exciton energy with electric fields. a Deviceschematic showing the stripe gate and large outer gates on either side. Vtg and Vbgare applied to create electric fields in the outer gate (Eog) regions while the stripegates are grounded.b IE energy schematic as a function of x-position perpendicularto the stripe gate. The red (black dashed) curves represent the electric field profilefelt by the IEs with (without) Eog in a trapping configuration. The blue curverepresents the anti-trap regime. c Optical image of the device. Red and greendashed lines outline the WSe2 and MoSe2 regions, respectively. Blue line outlinesthe heterostructure region. Gold arrows identify the relevant top gate and bottomgate structures. The black dashed square indicates the approximate region for thePL diffusion measurements. d IE spectra as a function of Eog. The linearly shiftingpeak at higher energy is from the outer gate region while the lower energy peak isfrom within the stripe gate region. e–g Scanning PL spectroscopy, where the laserexcites at x =0 μm and the spectra is collected across the stripe gate at Eog = 0 and±0.114 V/nm, showing spatially modulated IE energy.Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 2function of Eog at a power (P) of 50μW at the edge of the stripe gates.As Eog increases, a second peak splits off, with only the higher energypeak shifting linearly with the external field. We extract a dipoleseparation of d ≈ 0.6 nm from the slope of the energy shift ΔE = �edEog (e is the elementary charge), corresponding to the expectedinterlayer separation between the electron and hole wavefunctionslocalized on the TMD layers. In Fig. 1e–g, we excite the heterostructurewith P = 500μW at the center of the stripe gate and measure the PLspectra at a transverse distance x away from the center of the stripegate for three representative fields, Eog = 0V/nm and ±0.114 V/nm.When Eog = 0V/nm, the PL energy is constant at ∼1.38 eV across thespatial linecut, consistentwith the expected electrostatic profile.WhenEog =0.114 V/nm, the PL energy in the outer gate region rises to∼1.44 eV, consistent with the gate dependent spectra, while the stripegate region emits lower energy. Thus, we conclude that the higherenergy peak originates from IEs outside the trap, and we identify thelower energy peak as the trapped IEs. Regardless of the trappingpotential, we observe that the higher-energy free IE emission extendsnearly 3μm away from the center of the stripes. The observed longdiffusion lengths of IEs in TMDs is caused by dipolar repulsion4.However, we note that the high energy emission is darker when theconfinement potential is active, hindering IE diffusionperpendicular tothe stripe, while favoring localization in the trap. We also demonstratean anti-trap potential when Eog = −0.114 V/nm (Fig. 1g), where theoverall emission is darker because the electrostatic profile helps IEsdiffuse away from the excitation spot (see also Supplementary Fig. S1).Spatial control over interlayer exciton dynamicsTo understand the diffusive behavior under confinement, we takespectrally filtered PL intensitymaps at the IE energy. Figure 2a–c showsthe spatially dependent IE PL emission for anti-trap, flat, and trappotentials when the excitation spot is fixed near the edge of the stripegate for P = 550μW (red circle in Fig. 2a). For Eog = −0.023 and 0V/nm,we observe emission around the laser spot and at uncontrolleddisorder-related bright spots. In the absence of the externally appliedtrapping potential, IEs diffuse and localize in these naturally occurringtraps (Supplementary Fig. S2b, c). However, when Eog = 0.114 V/nm, weobserve uniform and elongated emission along the stripe, implyingthat the IE diffusion is constrained along it. In Fig. 2d, we average theemission along the stripe (y-direction) and plot the normalized inten-sity as a function of x perpendicular to the stripe for various Eog. Weobserve a narrowing of the spatial IE cloud width when the trap isactive and a broadening when an anti-trap is created. In Fig. 2e, weshow three characteristic spatial PL profiles obtained along the line-cuts shown in Fig. 2d, at constant Eog corresponding to anti-trap (yel-low), no-trap (black), and trap (red) configurations. These profilesexhibit a spatially narrowed (broadened) distribution for Eog =0.114 V/nm (−0.023 V/nm) compared to 0 V/nm. We perform a similar analysisalong the stripe gate and find that the emission is uniform aboveEog ≈0.09V/nm (Supplementary Fig. S3), corresponding to a trapdepth of ∼55meV. This estimated natural trap energy scale is con-sistent with reports of defect or strain-trapped IEs in theseheterostructures34,35.The emissionprofile across the stripe gate canbedescribedby thebalance between the diffusion of laser-generated IEs near the edge ofthe stripe, and the electrostatic trap (anti-trap) that hinders (favors)exciton transport. We obtain the spatial full-width half-maximum(FWHM) centered at the trap using a Gaussian fit. Figure 2f shows theFWHM as a function of Eog. We observe that the trap diffusion widthsaturates near 0.95μmat Eog ≈0.04 V/nm.The FWHM iswider than the1 �m(b) (c)xEog = 0.114 V/nmPL int. (kcts/s)2.50Eog = 0 V/nm(a)VogVog VsgNorm PL (arb. units)01Eog = -0.023 V/nmNorm PL (arb. units)0 1E og(V/nm)0.000.050.10(e)(f)(d)0 1 2-2 -1xavg (�m)-0.023 V/nmEog = 0.000 V/nm0.114 V/nmDiffusion width (�m)Relative Peak PL (arb. units)1.61.41.21.01.01.21.41.60.8Eog (V/nm)0.00 0.05 0.100.150.15Fig. 2 | Controlling the diffusion behavior. a–c Spatial mapping of the diffused IEPL emission at Eog = −0.023, 0, and 0.114 V/nm. The outer gate and the stripe gateareas are labeled Vog and Vsg, respectively. White dashed arrow indicates positive xdirection. Red circle is the excitation position. Bright spots that naturally occur onthe sample are reduced with the trapping potential. d Normalized PL along the xdirection, averaged over the uniform y-cut trap region, as a function of Eog. Thedotted lines correspond to the Eog line cuts in (e). The white dashed lines indicatethe expected trap width of ∼ 500nm. e Line cuts (scatter) and Gaussian fittings(lines) at Eog = −0.023, 0, and 0.114 V/nm showing narrowing (broadening) of thediffusion width when forming a trap (anti-trap). f Extracted diffusion width andrelative peak intensity (PLpeak(Eog)/PLpeak(Eog = 0)) as a function of Eog. We observethe trap saturates near Eog≈0.04V/nm. Error bars come from the fitting of thespatial PL distribution. Note that “a.u.” is the abbreviation for “arbitrary units”.Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 3expected trapwidth (~500 nm),which could be explainedby imperfectalignment of the top and bottom gates or by convolution with thepoint spread function of the system (Supplementary Information S4).We note that the FWHM increases slightly for Eog >0.12 V/nm, prob-ably due to a shorter IE lifetime and greater emission outside the trapfor larger electric fields4. The relative peak PL (normalized to theemission at Eog =0V/nm) also increases rapidly until Eog reaches~0.04V/nm, before increasing at a slower rate. We observe the longestIE lifetime at the center stripe region when a trapping potential isapplied, which increases by up to 20% at the largest Eog (Supplemen-tary Fig. S5). These signatures indicate stronger confinement at higherIE densities.Generation of a high-density trapped electron-hole ensembleThe PL peak energy shifts as a function of electron-hole pair densitydue to interactions. In the excitonic limit, strong dipolar repulsionleads to a blueshift for increasing IE density4,5,9,18,19,36–38. Similarly, anincreasing density of unbound electrons and holes on opposite layersgenerates an electric field leading to a blueshift18,39,40. Figure 3a showsthe PL spectra as a function of the excitation power P at the center ofthe trap (see Fig. 2). Even without trap activation (i.e., Eog = 0), the PLpeak exhibits a strong blueshift as P increases (Fig. 3a). This increase ofthe IE emission energy ΔE can be described by a balance between thediffusion, generation, and emission of IEs4. With increasing P in theexcitonic regime, the electron-hole pair density neh under the stripegates increases as excitons diffuse from the excitation site, leading toan increase in ΔE. The pair density can be further increased by dee-pening the confinement potential: a larger Eog hinders diffusion out ofthe trap as in Fig. 2f, leading to a larger blueshift (Fig. 3b) for the samepower range compared to the flat potential case.For a more quantitative estimate of neh, we employ a formulaobtained by considering dipolar excitonic interactions using a mean-field approach39: ΔE =neh�n0ð Þe2dεTMDε0, where n0 is the initial density fromwhich we reference ΔE, and ε0 is the vacuum permittivity. Althoughthis linear relationship tends to underestimate the pair density40, wetreat ΔE as an indication of increasing electron-hole concentration inthe trap. In Fig. 3c, we plot the measured ΔE (left axis) and the esti-mated neh (right axis) at the center of the stripe gate region as afunction of P with (orange symbols) and without (black symbols) thetrap potential activated. We estimate a small initial density n0 for thelowest measured excitation power (P = 1μW) (Supplementary Infor-mation S6). Since n0 and the blueshift at low powers are small, thisestimation contributes only a small error at higher densities. At lowpowers (P < 10−4W), wefind thatneh behaves similarlywith andwithouta trap potential, increasing slowly with increasing P. This behaviorsuggests that IEdiffusion is confined to the trap region, independent ofthe trap depth, and therefore neh is limited by the IE generation andrecombination rates. However, at high powers (P > 10−4 W), the max-imum neh with the trap on is nearly twice as large as with the trappotential off, indicating that the electrostatic profile confines electron-hole pairs that would otherwise diffuse away at the same generationrate. Without a trap, we obtain a maximum neh = 1.38 × 1012 cm−2, inagreement with previous measurements4. With the trapping potential,we reach almost twice this density: neh = 2.40 × 1012 cm−2. We note thatthe enhanced blueshift occurs only for trapped IEs and not for IEsoutside of the trap even at Eog = 0.114 V/nm (Supplementary Fig. S6).This confirms that the blueshift enhancement is a consequence ofincreasing interactions from higher local electron-hole densities.In addition to the blueshifts, we observe a broadening of thelinewidth, shown by the contour lines of half maximum normalizedintensity (Fig. 3a, b). Figure 3d shows the fitted linewidth as a functionof power for Eog = 0 and 0.114 V/nm. At lower excitation powers, wehave a linewidth of∼10meV in both cases. At higher Eog, weobserve anincrease in the linewidth with lower power, similar to the deviationsobserved in neh as discussed above. We rule out heating as the mainmechanism causing this trend, since a temperature increase due tolaser heating would lead to linewidth broadening and peak redshiftingregardless of the trap potential set by Eog (see S.11).Interlayer exciton ionization phase diagramThe rapid increase of the spectral linewidth at high power invites amore detailed investigation. Figure 4a shows the density dependentPower (W)10-5 10-4 10-3Power (W)10-5 10-4 10-3neh  (×1012 cm-2)(a) (b)0.50.502Power (W)10-5 10-4 10-3(c)Ehs = 0.114 V/nmEhs = 0 V/nm0 1Norm. PL (arb. units)Ehs = 0.114 V/nmEhs = 0 V/nm1.351.40Energy (eV)1.45110Linewidth (meV)(d)10-63050Ehs = 0.114 V/nmEhs = 0 V/nm�E (meV)02040Power (W)10-5 10-4 10-310-61.351.40Energy (eV)1.45Fig. 3 | Tuning the interlayer exciton density. aNormalized power dependent PLemission from the stripe gate region at Eog = 0 V/nm, when the excitation laser isslightly outside the region. The dotted white line shows a contour of 0.5 for theintensity of the trapped IEs. b Same as (a) for Eog = 0.114 V/nm. c The blueshiftenergy, ΔE, for Eog = 0 and 0.114 V/nm as a function of power. Right axis (blue)shows the corresponding calculated electron-hole pair density, neh. d Fitted trap-ped PL linewidth for Eog = 0 and0.114 V/nmas a functionof power. The error bars in(c) and (d) are from the fitting of the spectral peaks.Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 4linewidth w(neh) at different Eog and P. As discussed in Fig. 3, neh canvary over a wide range (109 to 2 × 1012 cm−2). Interestingly, we find thatw(neh) follows a universal curve determined solely by neh, indepen-dent of Eog and P: We find that the linewidth increases exponentiallywith neh (inset of Fig. 4a), suggesting that we can fit the behavior withthe functional form w neh� �=w0 expnehn*eh� �, where w0 is an intrinsiclinewidth at low pair density and n*eh is a characteristic density for theexponential upturn. We consider a rapid increase in the spectrallinewidth for neh>n*eh as a signature of the ionization threshold ofIEs, equivalent to the Mott transition9,17,20–24,37,41. At base temperature,we estimate n*ehð4KÞ = 1.30 ( ± 0.09) ×1012 cm−2 (Fig. 4a). We observedsimilar behavior exponential behavior in two additional devices,D2 and D3, with different stacking orientations and interlayer h-BNspacing (see Fig. S11 and Supplementary Section S10 forfurther discussion). Interestingly, all heterostructures exhibit ann*eh ∼ 1� 2:5 × 1012 cm�2. For D1, we repeated similar measurementsat different temperatures T ranging from 4K to 70K, where n*ehðTÞcan be similarly obtained from the exponentially increasing linewidth(see Fig. 4b, c for representative data at higher temperatures andmore data is available in Supplementary Fig. S8). Figure 4d shows thenormalized linewidth as a function of neh and T. In this plot we alsoshow n*ehðTÞ obtained from the exponential fit. For T ≤ 20K, we findthat n*ehðTÞ is constant within our fitting uncertainty, while above20K, n*ehðTÞ increases with increasing temperature.The broadening of the spectral linewidth as a function of neh hasbeen previously observed for indirect excitons in GaAs double quan-tumwells17,18,38,41 and for IEs in MoSe2 /WSe2 heterostructures9,37, and isattributed to the dissociation of the IEs. Similarly, we attribute n*eh tothe density driven ionization threshold for IEs. As neh increases, Cou-lomb screening becomes more pronounced, reducing the bindingenergy and gradually increasing the fraction of ionized carriers21. Atn*eh, the mixed IE-plasma system reaches a threshold and ionizationbecomes a runaway process20–25, which can explain the rapid increaseof the PL linewidth, although a complete theoretical model of theexponential dependence is beyond the scope of our work. Followingthis scenario, the temperature dependent behavior of n*eh Tð Þ shown inFig. 4d is understood by considering the competing effects ofscreening and bosonic degeneracy. Here, the three different lengthscales that characterize this competition are the excitonic Bohr radiusaB, the mean interpair distanceD =n�1=2eh , and the excitonic thermal de+-+-+-(a)1010 1011 1012402060Linewidth (meV)Ehs (V/nm)0 0.068T = 4 K0402060Linewidth (meV)(b)T (K)0T = 30 K0neh (×1012 cm-2)neh (cm-2)1 2+-+-+-Classicalexciton gasDegenerateexciton gas109020406080100(d)Normalized linewidth (arb. units)1 2 3 4 50.137Linewidth (meV)101100neh (×1012 cm-2)1 20Linewidth (meV)101100neh (×1012 cm-2)1 20TDneh*Exciton + electron-holeplasma mixtureT = 50 K402060Linewidth (meV)0Linewidth (meV)101100neh (×1012 cm-2)1 20(c)+-+-+-+-+-+-+-+-Fig. 4 | Interlayer exciton phase diagram. a Scatter plot of linewidth vs. electron-hole density for various trap depths at T = 4 K. The error bars indicate the uncer-tainty of the fittings. The black dashed line shows the exponential fit giving auniversal critical density n*eh(4K) = 1.30( ± 0.09)×1012cm−2. Inset: Same data butwhere linewidth is on a log scale and density on linear scaling, showing the expo-nential fit is shown as a linear curve. b, c Same as (a) but at 30K withn*eh(30K) = 1.37( ± 0.06)×1012cm−2 and 50K with n*eh(50 K) = 1.77( ± 0.32)× 1012cm−2,respectively. d Plot of the fitted normalized linewidth over the collected data rangeas a function of pair density and measured temperature. The blue data shows theextracted n*eh(T) at different temperatures with the error bars showing the uncer-tainty of the fits. The red dashed line is the degeneracy temperature, TD as afunction of exciton density per flavor.Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 5Broglie wavelength λT =2π_2mIEkBT� ��12, where mIE is the total IE mass. Inthe low temperature and high density regime where D<λT , the quan-tum statistical nature of the bosonic IE becomes appreciable. Thecondition λT =D defines the degeneracy temperature per flavorTD =2π_2kBmIE neh(red dashed line in Fig. 4d), which marks the crossoverbetween the classical (non-degenerate) and quantum (degenerate) IEs.Experimentally, we find that the temperature-dependent ionizationthreshold n*ehðTÞ occurs well below this line for all measured tem-peratures in our experiment, indicating that the transition we observeis related to the quantum dissociation of the IEs. Below 20K, we findthat n*eh(T) remains at a nearly constant value of ~1.3 × 1012 cm−2. Thisn*eh behavior can be understood in terms of the charge-neutral natureof IEs leading to a self-stabilization effect20,21 and is consistent withclaims of a temperature-independent Mott transition at the lowesttemperatures13. It is worth noting that theMott density nM atwhich thebinding energy vanishes is larger than n*IE , but of the same order21.Theoretically, the excitonic Mott density is expected to be given bynMa2B ∼0:1 in our experiment13,42,43 (see Supplementary Informa-tion S9). Using aB≈1:9 nm11, we estimate nM ~ 2.8 × 1012 cm−2, providinga consistent upper bound for our measured n*eh below 20K. At highertemperatures, we find that n*ehðT Þ increases with increasing T with asimilar slope to the degeneracy limit defined by λT =D. Here, as Tincreases, λT becomes smaller and a higher IE density is required for IEwavefunction overlap to become significant enough to reach theionization threshold20–22,24.DiscussionWe note that in similar systems with an h-BN spacer layer, an oppositetrend for the IE phase diagramhas been observed44–47. However, due tothe increased electron-hole separation, the IEs in those systems have abinding energy that is an order ofmagnitude smaller than in our study.For weakly bound IEs, temperature might be relevant in promoting IEdissociation, resulting in a reduction of the Mott density. In a stronglybound IE system, as studied here, the temperature is always below 10%of the binding energy and ionization physics is dominated by thequantum ionization process described above. Our arguments aresupported by a recent exciton drag experiment, which observed asimilar n*ehðTÞ trend as in our work at the lowest temperatures, beforetransitioning to a thermal ionization dominated regime45.Using a gate-tunable trap architecture, we have demonstrated anovel feature of critical IE dissociation dynamics: an exponential line-width broadening. This reveals a crucial piece of the IE phase diagram,and we hope future theoretical studies will help address its micro-scopic origins. Combining these strong many-body effects with highlygate tunable devices paves the way for novel optoelectronic devicessuch as exciton transistors10,48,49 or high population density invertedcavity-less lasers50. Furthermore, depth-tunable traps are an importantstep towards funneling a controlled density of cold dipolar excitonsaway from the excitation spot, thereby eliminating any laser-inducedheating or coherence effects that could prevent unambiguous identi-fication of a condensate.MethodsDevice fabricationFigure 1c shows our h-BN encapsulated MoSe2/WSe2 heterostructuredevice D1 with electrical contacts to each layer. The MoSe2, WSe2, andh-BN layers are prepared via mechanical exfoliation on 285 nm SiO2substrates. The MoSe2 and WSe2 bulk crystals are grown by the fluxmethod. The h-BN thicknesses are 36 nm and 59nm for the top andbottom h-BN, respectively. The stack is assembled by picking up eachlayer starting with the top h-BN using a standard dry transfer method.The final stack is placed on ultra-flatCr/PdAu alloy (1 nm/9nm) bottomgates written on a 285 nm SiO2 substrate. The stripe gate width(∼250nm) and outer gate separations (∼500nm) are measured viascanning electron microscopy images (Supplementary Fig. S13). Thesame gates are evaporated on top of the completed heterostructure.Edge contacts were fabricated by reactive ion etching parts of themonolayer region with O2/CHF3/Ar gas mixture and then evaporatingCr / Au leads (5 nm/120nm). It should be noted these contacts are notsufficient for electronic transport but can be used for electrostaticdoping measurements.Measurement detailsOptical measurements were performed using a 4f confocal microscopesystemwith a 0.75 NA 100x objective in aMontana Instruments, closed-loop optical 4K cryostat. Measurements were performed at T=4K,except for temperature dependent measurements. PL measurementswere performed with a Thorlabs continuous wave diode laser withexcitationwavelength of 660nmand collected into a spectrometerwitha PIXIS:256BR or BLAZE:400HR camera (both Princeton Instruments)unless otherwise noted. Scanning images were taken by fiber couplinginto an avalanche photodiode (Excelitas SPCM-900-14-FC). Timeresolved PL measurements are performed with a supercontinuum laserfrom NKT with an 80MHz repetition rate and through a tunable band-pass filter (SuperK VARIA). The laser is synchronized to a single photoncountingmodule (Excelitas Technologies) and a picosecond event timer(Picoharp 300, PicoQuant). Scanning confocal photoluminescencespectra are taken by using two separate optical paths to excite andcollect from separate positions. The optical path is split using a 50:50pellicle beamsplitter, each with a set of controllable two-axis galvan-ometer mirrors. The excitation channel has a co-aligned collection linethat can be used to choose the excitation position based on PL map.With the excitation fixed, the collection channel is scanned to measurePL emission counts or spectra from the various parts of the sample. AllPL measurements presented in the manuscript are measured this wayunless stated otherwise. The PL map in Fig. S2b is taken where theexcitation and collection are co-aligned. All electrostatic gates are con-trolled via Keithley 2400 sourcemeters.Data availabilityAll data needed to evaluate the conclusions in the paper are present inthe paper and/or the Supplementary Information. All raw data gener-ated during the current study are available from the correspondingauthor upon request.References1. Chernikov, A. et al. Exciton binding energy and nonhydrogenicRydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802(2014).2. Mak,K. F.,He,K., Shan, J. &Heinz, T. 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V., Hanson, M. & Gossard, A.C. Control of exciton fluxes in an excitonic integrated circuit. Sci-ence 321, 229–231 (2008).49. Liu, Y. et al. Electrically controllable router of interlayer excitons.Sci. Adv. 6, eaba1830 (2020).50. Paik, E. Y. et al. Interlayer exciton laser of extended spatial coher-ence in atomically thin heterostructures. Nature 576, 80–84 (2019).AcknowledgementsWe thank Ilya Esterlis and Eugene Demler for helpful discussions. P.K.acknowledges the support from the ONR MURI program (N00014-21-1-2377). A.Y.J. is supported by Samsung Electronics. A.M.M.V. is supportedby AFOSR (FA2386-21-1-4086). K.W. and T.T. acknowledge support fromthe JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and WorldPremier International Research Center Initiative (WPI), MEXT, Japan.Author contributionsA.Y.J., L.A.J., and P.K. conceived the study. A.Y.J., A.M.M.V., L.A.J., K.P.,D.D., Y.Z., G.S., K.D.G. and A.S. performed the experiments. A.Y.J.,L.A.J., and K.P. fabricated the device. B.K. and J.H. performed the TMDcrystal growth. T.T. and K.W. performed the h-BN crystal growth. M.D.L.,H.P., and P.K. supervised the experiments. A.Y.J., A.M.M.V., and P.K.analyzed the data and wrote the manuscript with extensive input fromall authors.Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 7https://doi.org/10.48550/arXiv.2309.14940https://doi.org/10.48550/arXiv.2309.14940https://doi.org/10.48550/arXiv.2309.15357https://doi.org/10.48550/arXiv.2309.15357Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-51128-9.Correspondence and requests for materials should be addressed toPhilip Kim.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-51128-9Nature Communications |         (2024) 15:6743 8https://doi.org/10.1038/s41467-024-51128-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/ Controlled interlayer exciton ionization in an electrostatic trap in atomically thin heterostructures Results Electrostatic tunability of interlayer exciton emission Spatial control over interlayer exciton dynamics Generation of a high-density trapped electron-hole ensemble Interlayer exciton ionization phase diagram Discussion Methods Device fabrication Measurement details Data availability References Acknowledgements Author contributions Competing interests Additional information