# Fileset

[boosting-the-emission-of-momentum-indirect-interlayer-excitons-by-an-optical-near-field-in-misaligned-2d.pdf](https://mdr.nims.go.jp/filesets/af825a0c-c299-4e69-82b1-d4476567633b/download)

## Creator

Qixing Wang, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Jurgen H. Smet

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Boosting the Emission of Momentum Indirect Interlayer Excitons by an Optical Near Field in Misaligned 2D Heterostructures](https://mdr.nims.go.jp/datasets/fe7c5a17-0f5f-4f9a-8a68-647483036bd1)

## Fulltext

Boosting the Emission of Momentum Indirect Interlayer Excitons by an Optical Near Field in Misaligned 2D HeterostructuresBoosting the Emission of Momentum Indirect Interlayer Excitons byan Optical Near Field in Misaligned 2D HeterostructuresQixing Wang, Takashi Taniguchi, Kenji Watanabe, and Jurgen H. Smet*Cite This: Nano Lett. 2025, 25, 14800−14807 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: The moire ́ superlattice potential in van der Waalsheterostructures localizes the interlayer excitons and modifies the bandstructure so that their emission wavelength can be adjustedsubstantially. However, twisted structures suffer from poor emissionquantum yield and long radiative lifetimes due to the angle-inducedmomentum mismatch. Moreover, the vertical orientation of theinterlayer exciton hampers the collection efficiency. Here, wedemonstrate that these unfavorable conditions can be fully overcomeby embedding the heterostructure in a plasmonic circular nanocavity.By adjusting the cavity radius, the emission enhancement factor for theinterlayer excitons can exceed 4 orders of magnitude due to thesynergistic effect of photon momentum enlargement and promotion of the excitation rate, quantum yield, and collection efficiencyby the optical near field. This strategy for engineering light−matter interactions can make these atomically thin heterostructures asalluring as their direct-band-gap opponents in the field of optoelectronics.KEYWORDS: van der Waals heterostructures, momentum mismatch, interlayer excitons, emission enhancement, optical near fieldOptical absorption and emission in semiconductors needto satisfy the requirements of both energy andmomentum conservation.1 In direct-band-gap semiconductors,absorption and emission can occur efficiently by directinterband transitions because the conduction band minimum(CBM) and the valence band maximum (VBM) are located atthe same momentum in the Brillouin zone. In indirect-band-gap semiconductors, however, the momenta of the CBM andthe VBM are distinct and the momenta of photons are typically2−3 orders of magnitude smaller than the momentummismatch.1−3 To compensate for the band momentummismatch, phonons must get involved in the interbandtransition process (Figure 1a).4 Because optical absorptionand emission now demand a three-particle interaction betweenphotons, electrons, and phonons, their efficiency dropssignificantly.4,5 Hence, indirect-band-gap semiconductors,such as for example silicon, are not ideal for light-emittingdevice applications5 without additional measures, and aconsiderable effort has been devoted in the community toimprove their optical absorption and emission efficiency.6 Forexample, by utilization of the Purcell effect of a compactplasmonic nanocavity, the PL intensity of momentum indirectinterlayer excitons of a 30°-twisted MoS2/WS2 heterobilayerwas enhanced over 2 orders of magnitude due to the Purcelleffect.7 Here, we demonstrate that for van der Waalsheterostructures with smaller twist angles a boost of 4 ordersof magnitude is possible by exploiting the momentum offeredby the optical near field (ONF) in the cavity.Indeed, a viable strategy to promote the optical absorptionand emission in indirect-band-gap semiconductors is toaggrandize the photon momentum, so that there is no longera need for phonon participation. This can be accomplished byexploiting the consequences of the Heisenberg uncertaintyprinciple for the position (x) and momentum (p) variables8,9of the photon. When the photon is confined to a small volume,its position uncertainty Δx is reduced and the momentumuncertainty Δp gets enhanced accordingly: ΔxΔp ≥ ℏ/2. Thebroadening of the momentum distribution of the photonoutwits the momentum conservation rule and enablesinterband transitions in indirect-band-gap semiconductorswithout the assistance of phonons (Figure 1b).2−5,10 Thetwo-particle interaction between the light in the ONF and theelectron then guarantees a reasonable efficiency for opticalabsorption and emission also in indirect-band-gap semi-conductors.3−5,10−12Monolayer transition-metal dichalcogenides (TMDCs) are aburgeoning class of materials with strong light−matterinteraction. This makes them appealing candidates for theapplication in optoelectronic and light-emitting devices.13−18Received: May 20, 2025Revised: September 23, 2025Accepted: October 2, 2025Published: October 7, 2025Letterpubs.acs.org/NanoLett© 2025 The Authors. Published byAmerican Chemical Society14800https://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−14807This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on October 22, 2025 at 11:13:57 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Qixing+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jurgen+H.+Smet"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.5c02703&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/25/41?ref=pdfhttps://pubs.acs.org/toc/nalefd/25/41?ref=pdfhttps://pubs.acs.org/toc/nalefd/25/41?ref=pdfhttps://pubs.acs.org/toc/nalefd/25/41?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/With the help of van der Waals stacking techniques, it ispossible to generate vertical homo- or heterostructures withenticing optical properties19−28 that strongly depend on thetwist angle between the layers. The twist angle can beestimated from polarization-dependent second-harmonic-gen-eration measurements, as shown in Section S2.29,30 For aligned(0°) and antialigned (60°) van der Waals structures, stronginterlayer coupling causes a hybridization of the electronicbands, and they behave as direct-band-gap semiconductorswith large optical oscillator strength31−36 and in-planeinterlayer exciton transition dipoles.37 In contrast, misalignedstructures with twist angles away from 0° and 60° behavewithout any additional measures as indirect-band-gap semi-conductors that exhibit low optical oscillator strength31−33,38and show an interlayer exciton emission pattern thatcorresponds to an out-of-plane transition dipole.39 A specificexample is shown in Figure 1d,e. They illustrate themomentum mismatch between the CBM of MoSe2 and theVBM of WSe2. Because the dipole formed by interlayerexcitons is oriented perpendicular to the plane, its opticalradiation propagates in the plane and is difficult to collect inreflected light microscopy. Despite these unfavorable con-ditions, it would be rewarding to overcome both the lack ofoscillator strength and collection efficiency in these twistedstructures. In this study, we demonstrate that indeed in suchintentionally engineered indirect-band-gap systems intenseoptical emission can still be achieved from these interlayerexcitons in a plasmonic nanocavity through photon confine-ment that is accompanied by an increase in the uncertainty ofthe photon momentum. A giant emission enhancement as largeas 4 orders of magnitude can be achieved.These studies were performed on a twisted WSe2/MoSe2heterostructure sandwiched between a gold film and ahexagonal boron nitride (hBN) multilayer on one side andan hBN multilayer and gold nanopillar on the other side. Across-sectional schematic of the device is depicted in Figure 2a.The hBN layers act as spacers between the gold film and thegold nanopillar to diminish the optical losses of the metallicplasmonic nanocavity that is formed (Figure 1f).40−42 Thescanning electron microscopy (SEM) images of a periodicarray of pillars are shown in Figure S2 (see also Section S3 andS4). For small twist angles θ, the momentum mismatchbetween electrons near the KM point of MoSe2 and holes nearthe KW point of WSe2 is abouta3602 , where a is the latticeconstant of the hexagonal real space lattice of MoSe2 and WSe2and the angle θ is in degrees.19,38,43 The lattice constants ofMoSe2 and WSe2 are 3.326 and 3.325 Å, respectively.44 For atwist angle of 4°, this yields an in-plane momentum mismatchof approximately 0.21 nm−1. The momentum of light for awavelength λ0 of, for example, 730 nm in free space is k0 = 2π/λ0 = 0.86 × 10−2 nm−1, which is more than 1 order ofmagnitude smaller than the momentum mismatch. However,Figure 1. Momentum indirect interlayer excitons in a twisted WSe2/MoSe2 heterostructure. (a) Schematic illustration of the optical excitationprocess in an indirect-band-gap semiconductor. Such an excitation requires the interaction of photons, electrons, and phonons. (b) Illustration ofdirect excitation of an electron in an indirect-band-gap semiconductor without the assistance of phonons but with the help of photons with largermomenta from the ONF in a confined volume. (c) Schematic illustration of the dipole orientation of interlayer excitons in a WSe2/MoSe2heterostructure and intralayer excitons in a MoSe2 monolayer. (d) Illustration of the direct nature of intralayer excitons in both real and reciprocalspace as well as the indirect nature of interlayer excitons in both real space and reciprocal space for a twisted WSe2/MoSe2 heterostructure. Theinterlayer exciton is composed of a hole located near the KW symmetry point in k space of WSe2 and an electron at the KM point of MoSe2. (e)Band structure of a twisted WSe2/MoSe2 heterostructure. Only the conduction band edges of the MoSe2 monolayer and the valence band edges ofthe WSe2 monolayer are shown. As a result of the real space twist θ, also the Brillouin zone with the KW and KW′ symmetry points of the WSe2monolayer is rotated away by the same angle θ from the Brillouin zone of the MoSe2 monolayer. (f) Schematic of a plasmonic nanocavity consistingof a gold nanopillar placed on top of a gold film on the substrate and separated from this gold film by the van der Waals heterostructure composedof a multilayer of hBN, a WSe2 monolayer, a MoSe2 monolayer, and a multilayer of hBN. For the samples fabricated here, the heterostructure has atotal thickness of about 7.5 nm.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714801https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig1&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asdue to the spatial confinement of the near-field light in thenanocavity, an electric field composed of an angular spectrumof plane waves and evanescent waves exists in the cavity. Theevanescent waves possess an imaginary component of the wavevector in the z direction (kz) with a maximum magnitude setby the vertical distance separating the gold film and the goldpillar d. For d = 7.5 nm in the device studied here, thismagnitude amounts to 0.84 nm−1. This effectively alsobroadens the in-plane photon wave vector (kin) andmomentum because the magnitude of the overall wave vectorstill equals the far-field value and the large negativecontribution from the evanescent part should be compensatedfor (k k k nz c2in2= + = ).45The calculated extinction cross section at d = 7.5 nm withvarying cavity radius (R) is plotted in Figure 2b. Here, we showthe spatial distribution of the electric field intensity |E|2 as wellas the three different electric field components in the selecteddevice geometry. The calculations are performed for a cavityradius R of 35 nm. Figure 2c displays a color rendition of theoverall electric field intensity in the x−z plane for y = 0 (seethe coordinate system in Figure S3) and 730 nm excitationlight. The “hot spot” of the field intensity is in the hBN/WSe2/MoSe2/hBN spacer region. The x−y cross section of the fieldintensity at the interface between MoSe2 and the top hBN isshown in Figure 2d. This field intensity in the spacer regionstems from a magnetic dipole mode and is primarily located atthe boundary of the area covered by the gold nanopillar. Panelse−g are color renditions of the amplitude of the x, y, and zcomponents of the electric field across the (x, z) plane at y = 0.Only the amplitude of Ez is very significant in the spacer region(Figure 2e−g). Because the dipole moment of the interlayerexcitons is parallel to the z axis (Figure 1c), this fieldcomponent can couple effectively to the interlayer excitons,and we anticipate a strong local density of optical states(LDOS) in the spacer region.42,46 The magnitude of the fastFourier transform of the complex Ez is included in Section S7and reveals that this field component indeed has intensity atsufficiently large momenta to overcome the twist angle inducedmomentum mismatch and assist with indirect electronictransitions between MoSe2 and WSe2 without phononparticipation due to the momentum “broadening” by spatialconfinement imposed by the nanocavity.Not only the momentum content of the ONF but also thestrong LDOS enhances the interlayer exciton emission throughseveral additional contributions. The above electric fieldsimulations can be used to calculate the enhancement factorfor optical excitation γexc/γexc0 = |E|2/|E0|2, where γexc and |E|2 arethe excitation rate and field intensity, if the sample isembedded in the cavity.40,42 The corresponding quantities inthe region without the top nanopillar carry a super- orsubscript 0. The calculation results for different R can be foundin Figure S7a.Also the spontaneous emission rate γsp gets boosted.According to Fermi’s golden rule, γsp of a dipole is givenby42,47,48p rr( )3( , )sp02= | |(1)where ω is the emission frequency, ϵ0 is the permittivity of freespace, p is the transition dipole moment of the emitter, andρ(r,ω) is the LDOS at frequency ω and emitter position r. Byplacement of the WSe2/MoSe2 heterostructure in a cavity, thespontaneous emission rate benefits from the enlarged LDOSthrough the Purcell effect.42,47,48 This effect has been exploitedFigure 2. Electric field distribution for a WSe2/MoSe2 heterostructure embedded in a plasmonic nanocavity. (a) Cross section of a WSe2/MoSe2based van der Waals heterostructure incorporated into a plasmonic nanocavity. The radius of the nanopillar on top of the heterostructure is R,whereas d is the distance between the gold film deposited on the substrate and nanopillar. (b) Simulation results of the extinction cross section ofthe cavity as a function of the wavelength λ for R varying from 30 to 50 nm. (c) Calculated spatial distribution of the electric field intensity |E|2 inthe x−z plane in the vicinity of the cavity for y = 0. For a definition of the coordinate system, see Section S4 and Figure S3. (d) Spatial distributionof |E|2 in the x−y plane near the cavity for z = −3 nm (black dotted line in panel c). Same as panel c but for the magnitude of each electric fieldcomponent: |Ex| (e), |Ey| (f), and |Ez| (g). The distribution of these field components in the x−y plane is shown in Section S6.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714802https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aspreviously for improving the radiation efficiency of ex-citons.18,22−25 The Purcell factor (FP) can be written as46,48FnQV34Psp023mode= = ikjjj y{zzz(2)Here, γ0 is the spontaneous emission rate of the emitter in freespace, Q is the quality factor of the cavity, Vmode is the cavitymode volume, n is the refractive index of the spacer medium,and λ is the resonant wavelength. Q varies from 11.8 to 14.6and Vmode varies from 440 to 2020 nm3 with a change of Rfrom 35 to 50 nm, as can be seen in Figure S8.The calculated Purcell factor depends on the position of theemitter underneath the pillar, as shown in Figure 3a. Fordipoles oriented along the z direction, the Purcell factor isabout 9000 near the boundary of the pillar with R = 35 nm(Figure 3b). In view of the indirect nature of the interlayerexcitons in reciprocal space, we adopt the case of low quantumyield (QY) for which the nonradiative decay γnr ≫ FPγsp. Theenhancement of the emission quantum yield is then equal toQY/QY0 ≈ FP/FP0, where FP and FP0 are the Purcell factors withand without the gold nanopillar above the top hBN.40,49 Thedependence of the quantum yield enhancement on R isillustrated in Figure S7b.Finally, also the collection efficiency for the emittedradiation from interlayer excitons is improved in the selectedgeometry. The simulated distribution of the power of the far-field radiation from an hBN-encapsulated WSe2/MoSe2heterostructure placed on a gold film or between a gold filmand a gold pillar for an objective with a numerical aperture of0.81 is plotted in Figure 3c,e. In the absence of the pillar, theemission pattern has the shape of a butterfly (Figure 3d) andthe collection efficiency (η) from the emission from z-orienteddipoles is estimated to be only 38%. For a nanopillar with R =35 nm on top of the van der Waals heterostructure, the spatialdistribution of the far-field radiation power is modified into asingle upward lobe, as seen in Figure 3f,42 and the collectionefficiency for this case is calculated to be 73% instead (Figure3e,f). Hence, the enhancement factor η/η0, with η and η0 thecollection efficiency with and without plasmonic cavity,40,42 isas large as 1.92. The expected variation of this enhancement asa function of R is shown in Figure S7c.The emission enhancement for the cavity geometry isconfirmed by the experimental data. Figure 4a illustrates thephotoluminescence (PL) spectrum obtained in reflectionmicroscopy on a misaligned WSe2/MoSe2 heterostructurewhen the heterostructure is not embedded in a cavity. Theemission signal is very weak and exhibits a maximum near 870nm. To confirm that this emission stems from interlayerexcitons, photoluminescence excitation (PLE) measurementsare performed. As the excitation wavelength is tuned, theemission at 870 nm intensifies at two resonant wavelengths, asseen in Figure 4b. These are identified more precisely by takingthe integral of the emission intensity across the full spectralrange and plotting the result as a function of the excitationwavelength (Figure 4c). Peaks appear at 729 nm as well as 764nm, the wavelengths where light is absorbed in WSe2 andMoSe2 monolayers due to A excitons or trions (see the PL inSection S10). We conclude that the emission at 870 nminvolves both WSe2 and MoSe2 and originates from interlayerexcitons that form at their heterointerface.25We now turn our attention to the impact of embedding thetwisted heterostructure into a plasmonic nanocavity to boostthe emission from the momentum indirect interlayer excitons.The evolution of the experimental PL spectrum recorded onthe WSe2/MoSe2 heterostructure covered with gold pillars fordifferent radii (35, 40, 45, and 50 nm) is shown in Figure 4d.Even for the smallest radii, the enhancement is significantcompared to the case where no cavity is formed, but itFigure 3. Emission efficiency enhancement and radiation pattern. (a) Calculated spatial distribution of the Purcell factor in the x−y plane at theposition of the WSe2/MoSe2 heterostructure inside the nanocavity formed by the gold substrate film and gold pillar. (b) Purcell factor along theblack dashed line in panel a. (c) Spatial distribution of the normalized far-field radiation power of hBN/WSe2/MoSe2/hBN heterostructure placedon top of a gold film. (d) Polar diagram for the far-field radiation shown in panel c. The gray shaded area corresponds to the region from which nosignal can be collected with the chosen objective lens with a numerical aperture of 0.81. (e) Same as panel c but for the case where theheterostructure is embedded in a gold cavity. The out-of-plane dipole is put at the boundary of the gold nanopillar. (f) Polar diagram for the far-field radiation shown in panel e. The emission wavelength of the dipole is set at 880 nm.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714803https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asbecomes truly gigantic for larger radii. Besides, the moire ́potential may compress the exciton wave function and increasethe electron−hole overlap integral, resulting in a higher LDOSand oscillator strength for localized excitons. Figure 4d showsthat the broad emission spectrum of the interlayer excitonsfeatures some maxima. These can be attributed to the presenceof interlayer excitons trapped in the moire ́ potential.25 Thesefeatures too get enhanced when the van der Waalsheterostructure is embedded in a cavity. To quantify theboost in the PL intensity, we introduce the PL enhancementfactor (EFPL) defined as40,42IAIAEFPLcavitycavityW/Olaser1=ikjjjjjy{zzzzz (3)Here, Icavity and IW/O are the PL intensity integrated over therecorded spectral range when the heterostructure is embeddedinside a cavity (Icavity) or just placed on top of the gold film(IW/O). Both intensities are weighted by the area the emissionstems from. When the hBN-encapsulated heterostructure isjust placed on the gold film this area is equal to the laser spotsize, Alaser. For the heterostructure with photon confinement, itis the cavity area (Acavity = nπR2) under the laser spot. For R =50 nm, EFPL is as large as 2 × 104. Because most of theemission originates from the boundary of the gold pillar, theactual area from which PL is gathered is smaller and, hence, thecalculated EFPL is an underestimate. The experimental EFPLdrops a lot for heterostructures with larger twist angles becauseof insufficient near-field momentum (Section S11).We also consider the calculated total enhancement factor,EFtotal. It combines the excitation enhancement (γexc/γexc0 ), thequantum yield enhancement (QY/QY0), as well as thecollection efficiency enhancement (η/η0) and is just equal tothe product of these three:40,42,48EFQYQYtotalexcexc0 0 0=(4)Its calculated value as a function of R is included in Figure4e (right vertical axis). The simulated EFtotal is much largerthan the experimental EFPL because in the calculation thehighest γexc/γexc0 , QY/QY0, and η/η0 are utilized.Figure 4. Experimental evidence for enhanced emission from momentum indirect excitons in a twisted WSe2/MoSe2 heterostructure. (a) PLspectrum recorded for an excitation wavelength of 730 nm laser when the hBN-encapsulated heterostructure is just placed on the gold substratefilm. (b) False color image of the intensity of the interlayer exciton emission as a function of the excitation and emission wavelengths for the samplein panel a. (c) Integrated intensity of the interlayer exciton emission as a function of the excitation wavelength in panel b. (d) Comparison of thePL spectrum recorded on a twisted WSe2/MoSe2 heterostructure when the heterostructure is just placed on top of a gold film (without cavity, w/ocavity) or embedded in a cavity with different radii. The incident laser power is 1 μW and has a wavelength of 730 nm. (e) PL enhancement factorEFPL as extracted from the experiment (blue squares) and the calculated total enhancement factor EFtotal (red circles) as a function of the radius Rof the gold pillar. (f) Circular polarization-resolved PL spectra recorded on an antialigned (60° twist angle) WSe2/MoSe2 heterostructure withoutcavity. (g and h) Circular polarization-resolved PL spectra recorded on a twisted WSe2/MoSe2 heterostructure placed on top of the gold substratefilm (g) and located within a cavity (h). The data were recorded for R = 35 nm. The 730 nm laser light with a power of 1 μW incident on thesample was circularly polarized (σ+ polarization). All measurements were recorded at 2 K.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714804https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asThe resonant wavelength of the plasmonic cavity exhibits ared shift by more than 300 nm when its radius R is tuned from30 to 50 nm, as shown in Figure 2b. In the experiment, we canaddress cavities starting from 35 nm due to processinglimitations, but we find that this smallest cavity is not optimal,neither in experiment nor in calculations. Due to the interplayof the various contributions to the enhancement factor, R = 50nm yields the highest enhancement. For instance, the Purcellfactor exhibits an additional maximum at the emissionwavelength for R = 50 nm. Further details on the origin ofthis peak can be found in Section S12.The drastic enhancement of the interlayer exciton emissionin the chosen sample configuration is attributed to two factors:the momentum content in the ONF, which assists indirectelectronic transitions, in conjunction with the influence ofplasmons. The importance of the former can be experimentallyconfirmed by studying the circular polarization dependence ofthe PL. For aligned or antialigned heterostructures where thereis no mismatch in momentum, phonon scattering is notrequired to establish interlayer excitons and valley polarizationcan build up upon excitation with circularly polarized light. Asa result, the emission exhibits a strong polarization depend-ence, as illustrated in Figure 4f. Because the device is excitedwith σ+ polarization, σ+ emission dominates. In contrast, for atwisted heterostructure not embedded in a cavity the emissionstrength is essentially identical for both circular polarizationdirections (Figure 4g). The momentum mismatch calls forphonon assisted scattering and valley polarization is lost. If theheterostructure is embedded in a cavity, the polarizationdependence is partially recovered (Figure 4h), because phononscattering is no longer required during interlayer excitonformation and recombination. For heterostructures with alarger twist angle, the larger momentum mismatch becomesharder to compensate for with the momentum content of theONF, and the enhancement factor is expected to dropsubstantially. This is corroborated by an experiment on asample with a 14° twist shown in Section S11. For the sake ofcompleteness, we note that the enhancement of the radiativerecombination by the Purcell effect may also play a role in theincrease of circular polarization because of the reducedinteraction time for depolarization processes.The twist angle has long been identified as a powerful knobto tune the optical properties of van der Waals heterostructuresbased on TMDCs. A drawback has, however, been the lowintensity of the optical emission due to the twist-angle-inducedmomentum mismatch that converts these systems intoindirect-gap materials. Here we have demonstrated that it ispossible to overcome this weak light−matter interaction andfully benefit from the properties of the twist-angle-engineeredinterlayer excitons by placing the heterostructure inside aplasmonic nanocavity. Both the radius and thickness of thecavity are key design parameters to adjust the Purcell effect andadapt the momentum of the near-field light to the electronicmomentum mismatch in order to outwit the indirect nature ofthe electronic gap. A boost in the optical emission ofmomentum indirect interlayer excitons of up to 4 orders ofmagnitude was achieved in this way.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703.Details of the experimental methods, determination ofthe twist angle, SEM images of the fabricated nano-cavities, sample configurations and definition of thecoordinate system, estimate of the in-plane momentaavailable in the ONF, absorption and scattering crosssection, in-plane dependence of the electric fieldcomponents, radius-dependent enhancement of theexcitation, quantum yield, and collection efficiency, Qand Vmode of the plasmonic nanocavity, PL spectrumrecorded on a WSe2 and MoSe2 monolayer, PL and EFPLfor a WSe2/MoSe2 heterostructure with a 14° twistangle, and discussion of the dependence of EFPL on thecavity size (PDF)■ AUTHOR INFORMATIONCorresponding AuthorJurgen H. Smet − Max Planck Institute for Solid StateResearch, Stuttgart D-70569, Germany; orcid.org/0000-0002-4719-8873; Phone: +49 711 689-5244;Email: j.smet@fkf.mpg.deAuthorsQixing Wang − Department of Physics, College of PhysicalScience and Technology, Xiamen University, Xiamen 361005,China; Jiujiang Research Institute, Xiamen University,Jiujiang 332000, China; Max Planck Institute for Solid StateResearch, Stuttgart D-70569, Germany; orcid.org/0000-0003-0623-1910Takashi Taniguchi − Research Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0047, Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Electronic and OpticalMaterials, National Institute for Materials Science, Tsukuba305-0047, Japan; orcid.org/0000-0003-3701-8119Complete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.5c02703FundingOpen access funded by Max Planck Society.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSQ.W. acknowledges financial support from the NationalNatural Science Foundation of China (grant 62304186),Jiangxi Provincial Natural Science Foundation (grant20252BAC200013), and Natural Science Foundation ofJiujiang (grant S2024KXJJ0001). J.H.S. acknowledges financialsupport from the Priority Program SPP2244 of the DFG. K.W.and T.T. acknowledge support from the JSPS KAKENHI(grant nos. 21H05233 and 23H02052) , the CREST(JPMJCR24A5), JST and World Premier InternationalResearch Center Initiative (WPI), MEXT, Japan.■ REFERENCES(1) Kharintsev, S. S.; Noskov, A. I.; Battalova, E. I.; Katrivas, L.;Kotlyar, A. B.; Merham, J. G.; Potma, E. O.; Apkarian, V. A.; Fishman,D. A. Photon Momentum Enabled Light Absorption in Silicon. ACSNano 2024, 18, 26532−26540.(2) Kirkengen, M.; Bergli, J.; Galperin, Y. M. Direct Generation ofCharge Carriers in C-Si Solar Cells Due to Embedded Nanoparticles.J. Appl. Phys. 2007, 102, No. 093713.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714805https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.5c02703/suppl_file/nl5c02703_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jurgen+H.+Smet"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-4719-8873https://orcid.org/0000-0002-4719-8873mailto:j.smet@fkf.mpg.dehttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Qixing+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-0623-1910https://orcid.org/0000-0003-0623-1910https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3701-8119https://pubs.acs.org/doi/10.1021/acs.nanolett.5c02703?ref=pdfhttps://doi.org/10.1021/acsnano.4c02656?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1063/1.2809368https://doi.org/10.1063/1.2809368pubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(3) Bharadwaj, P.; Deutsch, B.; Novotny, L. Optical Antennas. Adv.Opt. Photonics 2009, 1, 438−483.(4) Yamaguchi, M.; Nobusada, K. Indirect Interband TransitionInduced by Optical near Fields with Large Wave Numbers. Phys. Rev.B 2016, 93, 195111.(5) Noda, M.; Iida, K.; Yamaguchi, M.; Yatsui, T.; Nobusada, K.Direct Wave-Vector Excitation in an Indirect-Band-Gap Semi-conductor of Silicon with an Optical near-Field. Phys. Rev. Appl.2019, 11, No. 044053.(6) Priolo, F.; Gregorkiewicz, T.; Galli, M.; Krauss, T. F. SiliconNanostructures for Photonics and Photovoltaics. Nat. Nanotechnol.2014, 9, 19−32.(7) Feng, B.; Zhao, S.; Razdolski, I.; Liu, F.; Peng, Z.; Wang, Y.;Zhang, Z.; Ni, Z.; Xu, J.; Lei, D. Room-Temperature, Strong Emissionof Momentum-Forbidden Interlayer Excitons in Nanocavity-CoupledTwisted Van Der Waals Heterostructures. Nano Lett. 2025, 25, 1609−1616.(8) Heisenberg, W. ber Den Anschaulichen Inhalt Der Quanten-theoretischen Kinematik Und Mechanik. Zeitschrift für Physik 1927,43, 172−198.(9) Sen, D. The Uncertainty Relations in Quantum Mechanics. Curr.Sci. 2014, 107, 203−218.(10) Kurman, Y.; Rivera, N.; Christensen, T.; Tsesses, S.; Orenstein,M.; Soljacǐc,́ M.; Joannopoulos, J. D.; Kaminer, I. Control ofSemiconductor Emitter Frequency by Increasing Polariton Momenta.Nat. Photonics 2018, 12, 423−429.(11) Shalaev, V. M.; Douketis, C.; Haslett, T.; Stuckless, T.;Moskovits, M. Two-Photon Electron Emission from Smooth andRough Metal Films in the Threshold Region. Phys. Rev. B 1996, 53,11193−11206.(12) Trolle, M. L.; Pedersen, T. G. Indirect Optical Absorption inSilicon Via Thin-Film Surface Plasmon. J. Appl. Phys. 2012, 112,No. 043103.(13) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.;Strano, M. S. Electronics and Optoelectronics of Two-DimensionalTransition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699−712.(14) Chen, P.; Atallah, T. L.; Lin, Z.; Wang, P.; Lee, S.-J.; Xu, J.;Huang, Z.; Duan, X.; Ping, Y.; Huang, Y.; Caram, J. R.; Duan, X.Approaching the Intrinsic Exciton Physics Limit in Two-DimensionalSemiconductor Diodes. Nature 2021, 599, 404−410.(15) Ross, J. S.; Klement, P.; Jones, A. M.; Ghimire, N. J.; Yan, J.;Mandrus, D. G.; Taniguchi, T.; Watanabe, K.; Kitamura, K.; Yao, W.;Cobden, D. H.; Xu, X. Electrically Tunable Excitonic Light-EmittingDiodes Based on Monolayer WSe2 P-N Junctions. Nat. Nanotechnol.2014, 9, 268−72.(16) Withers, F.; Del Pozo-Zamudio, O.; Mishchenko, A.; Rooney,A. P.; Gholinia, A.; Watanabe, K.; Taniguchi, T.; Haigh, S. J.; Geim, A.K.; Tartakovskii, A. I.; Novoselov, K. S. Light-Emitting Diodes byBand-Structure Engineering in Van Der Waals Heterostructures. Nat.Mater. 2015, 14, 301−306.(17) Wu, S.; Buckley, S.; Schaibley, J. R.; Feng, L.; Yan, J.; Mandrus,D. G.; Hatami, F.; Yao, W.; Vuckovic, J.; Majumdar, A.; Xu, X.Monolayer Semiconductor Nanocavity Lasers with Ultralow Thresh-olds. Nature 2015, 520, 69−72.(18) Ye, Y.; Wong, Z. J.; Lu, X.; Ni, X.; Zhu, H.; Chen, X.; Wang, Y.;Zhang, X. Monolayer Excitonic Laser. Nat. Photonics 2015, 9, 733−737.(19) Ciarrocchi, A.; Tagarelli, F.; Avsar, A.; Kis, A. Excitonic Deviceswith Van Der Waals Heterostructures: Valleytronics Meets Twist-ronics. Nat. Rev. Mater. 2022, 7, 449−464.(20) Yu, H.; Liu, G.-B.; Tang, J.; Xu, X.; Yao, W. Moire ́ Excitons:From Programmable Quantum Emitter Arrays to Spin-Orbit−Coupled Artificial Lattices. Sci. Adv. 2017, 3, No. e1701696.(21) Ciorciaro, L.; Smolenśki, T.; Morera, I.; Kiper, N.; Hiestand, S.;Kroner, M.; Zhang, Y.; Watanabe, K.; Taniguchi, T.; Demler, E.;Iṁamoğlu, A. Kinetic Magnetism in Triangular Moire ́ Materials.Nature 2023, 623, 509−513.(22) Jin, C.; Regan, E. C.; Yan, A.; Iqbal Bakti Utama, M.; Wang, D.;Zhao, S.; Qin, Y.; Yang, S.; Zheng, Z.; Shi, S.; Watanabe, K.;Taniguchi, T.; Tongay, S.; Zettl, A.; Wang, F. Observation of Moire ́Excitons in WSe2/WS2 Heterostructure Superlattices. Nature 2019,567, 76−80.(23) Liu, E.; Barré, E.; van Baren, J.; Wilson, M.; Taniguchi, T.;Watanabe, K.; Cui, Y.-T.; Gabor, N. M.; Heinz, T. F.; Chang, Y.-C.;Lui, C. H. Signatures of Moire ́ Trions in WSe2/MoSe2 Heterobilayers.Nature 2021, 594, 46−50.(24) Ma, L.; Nguyen, P. X.; Wang, Z.; Zeng, Y.; Watanabe, K.;Taniguchi, T.; MacDonald, A. H.; Mak, K. F.; Shan, J. StronglyCorrelated Excitonic Insulator in Atomic Double Layers. Nature2021, 598, 585−589.(25) Seyler, K. L.; Rivera, P.; Yu, H.; Wilson, N. P.; Ray, E. L.;Mandrus, D. G.; Yan, J.; Yao, W.; Xu, X. Signatures of Moire-́TrappedValley Excitons in MoSe2/WSe2 Heterobilayers. Nature 2019, 567,66−70.(26) Regan, E. C.; Wang, D.; Jin, C.; Bakti Utama, M. I.; Gao, B.;Wei, X.; Zhao, S.; Zhao, W.; Zhang, Z.; Yumigeta, K.; Blei, M.;Carlström, J. D.; Watanabe, K.; Taniguchi, T.; Tongay, S.; Crommie,M.; Zettl, A.; Wang, F. Mott and Generalized Wigner Crystal States inWSe2/WS2 Moire ́ Superlattices. Nature 2020, 579, 359−363.(27) Zhang, Y.; Xiao, C.; Ovchinnikov, D.; Zhu, J.; Wang, X.;Taniguchi, T.; Watanabe, K.; Yan, J.; Yao, W.; Xu, X. Every-Other-Layer Dipolar Excitons in a Spin-Valley Locked Superlattice. Nat.Nanotechnol. 2023, 18, 501−506.(28) Li, Y.-M.; Li, J.; Shi, L.-K.; Zhang, D.; Yang, W.; Chang, K.Light-Induced Exciton Spin Hall Effect in Van Der WaalsHeterostructures. Phys. Rev. Lett. 2015, 115, 166804.(29) Hsu, W.-T.; Zhao, Z.-A.; Li, L.-J.; Chen, C.-H.; Chiu, M.-H.;Chang, P.-S.; Chou, Y.-C.; Chang, W.-H. Second HarmonicGeneration from Artificially Stacked Transition Metal DichalcogenideTwisted Bilayers. ACS Nano 2014, 8, 2951−2958.(30) Mennel, L.; Paur, M.; Mueller, T. Second HarmonicGeneration in Strained Transition Metal Dichalcogenide Monolayers:MoS2, MoSe2, WS2, and WSe2. APL Photonics 2019, 4, No. 034404.(31) Alexeev, E. M.; Ruiz-Tijerina, D. A.; Danovich, M.; Hamer, M.J.; Terry, D. J.; Nayak, P. K.; Ahn, S.; Pak, S.; Lee, J.; Sohn, J. I.;Molas, M. R.; Koperski, M.; Watanabe, K.; Taniguchi, T.; Novoselov,K. S.; Gorbachev, R. V.; Shin, H. S.; Fal’ko, V. I.; Tartakovskii, A. I.Resonantly Hybridized Excitons in Moire ́ Superlattices in Van DerWaals Heterostructures. Nature 2019, 567, 81−86.(32) Zhang, L.; Zhang, Z.; Wu, F.; Wang, D.; Gogna, R.; Hou, S.;Watanabe, K.; Taniguchi, T.; Kulkarni, K.; Kuo, T.; Forrest, S. R.;Deng, H. Twist-Angle Dependence of Moire ́ Excitons in WS2/MoSe2Heterobilayers. Nat. Commun. 2020, 11, 1−8.(33) Barre, E.; Karni, O.; Liu, E.; O’Beirne, A. L.; Chen, X.; Ribeiro,H. B.; Yu, L.; Kim, B.; Watanabe, K.; Taniguchi, T.; Barmak, K.; Lui,C. H.; Refaely-Abramson, S.; da Jornada, F. H.; Heinz, T. F. OpticalAbsorption of Interlayer Excitons in Transition-Metal DichalcogenideHeterostructures. Science 2022, 376, 406−410.(34) Hsu, W.-T.; Lin, B.-H.; Lu, L.-S.; Lee, M.-H.; Chu, M.-W.; Li,L.-J.; Yao, W.; Chang, W.-H.; Shih, C.-K. Tailoring Excitonic States ofVan Der Waals Bilayers through Stacking Configuration, BandAlignment, and Valley Spin. Sci. Adv. 2019, 5, eaax7407.(35) Zhao, S.; Huang, X.; Gillen, R.; Li, Z.; Liu, S.; Watanabe, K.;Taniguchi, T.; Maultzsch, J.; Hone, J.; Högele, A.; Baimuratov, A. S.Hybrid Moire ́ Excitons and Trions in Twisted MoTe2−MoSe2Heterobilayers. Nano Lett. 2024, 24, 4917−4923.(36) Gogoi, P. K.; Lin, Y.-C.; Senga, R.; Komsa, H.-P.; Wong, S. L.;Chi, D.; Krasheninnikov, A. V.; Li, L.-J.; Breese, M. B. H.; Pennycook,S. J.; Wee, A. T. S.; Suenaga, K. Layer Rotation-Angle-DependentExcitonic Absorption in Van Der Waals Heterostructures Revealed byElectron Energy Loss Spectroscopy. ACS Nano 2019, 13, 9541−9550.(37) Sigl, L.; Troue, M.; Katzer, M.; Selig, M.; Sigger, F.; Kiemle, J.;Brotons-Gisbert, M.; Watanabe, K.; Taniguchi, T.; Gerardot, B. D.;Knorr, A.; Wurstbauer, U.; Holleitner, A. W. Optical DipoleOrientation of Interlayer Excitons in MoSe2-WSe2 Heterostacks.Phys. Rev. B 2022, 105, No. 035417.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714806https://doi.org/10.1364/AOP.1.000438https://doi.org/10.1103/PhysRevB.93.195111https://doi.org/10.1103/PhysRevB.93.195111https://doi.org/10.1103/PhysRevApplied.11.044053https://doi.org/10.1103/PhysRevApplied.11.044053https://doi.org/10.1038/nnano.2013.271https://doi.org/10.1038/nnano.2013.271https://doi.org/10.1021/acs.nanolett.4c05647?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.4c05647?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.4c05647?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1007/BF01397280https://doi.org/10.1007/BF01397280https://doi.org/10.1038/s41566-018-0176-6https://doi.org/10.1038/s41566-018-0176-6https://doi.org/10.1103/PhysRevB.53.11193https://doi.org/10.1103/PhysRevB.53.11193https://doi.org/10.1063/1.4746699https://doi.org/10.1063/1.4746699https://doi.org/10.1038/nnano.2012.193https://doi.org/10.1038/nnano.2012.193https://doi.org/10.1038/s41586-021-03949-7https://doi.org/10.1038/s41586-021-03949-7https://doi.org/10.1038/nnano.2014.26https://doi.org/10.1038/nnano.2014.26https://doi.org/10.1038/nmat4205https://doi.org/10.1038/nmat4205https://doi.org/10.1038/nature14290https://doi.org/10.1038/nature14290https://doi.org/10.1038/nphoton.2015.197https://doi.org/10.1038/s41578-021-00408-7https://doi.org/10.1038/s41578-021-00408-7https://doi.org/10.1038/s41578-021-00408-7https://doi.org/10.1126/sciadv.1701696https://doi.org/10.1126/sciadv.1701696https://doi.org/10.1126/sciadv.1701696https://doi.org/10.1038/s41586-023-06633-0https://doi.org/10.1038/s41586-019-0976-yhttps://doi.org/10.1038/s41586-019-0976-yhttps://doi.org/10.1038/s41586-021-03541-zhttps://doi.org/10.1038/s41586-021-03947-9https://doi.org/10.1038/s41586-021-03947-9https://doi.org/10.1038/s41586-019-0957-1https://doi.org/10.1038/s41586-019-0957-1https://doi.org/10.1038/s41586-020-2092-4https://doi.org/10.1038/s41586-020-2092-4https://doi.org/10.1038/s41565-023-01350-1https://doi.org/10.1038/s41565-023-01350-1https://doi.org/10.1103/PhysRevLett.115.166804https://doi.org/10.1103/PhysRevLett.115.166804https://doi.org/10.1021/nn500228r?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn500228r?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nn500228r?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1063/1.5051965https://doi.org/10.1063/1.5051965https://doi.org/10.1063/1.5051965https://doi.org/10.1038/s41586-019-0986-9https://doi.org/10.1038/s41586-019-0986-9https://doi.org/10.1038/s41467-020-19466-6https://doi.org/10.1038/s41467-020-19466-6https://doi.org/10.1126/science.abm8511https://doi.org/10.1126/science.abm8511https://doi.org/10.1126/science.abm8511https://doi.org/10.1126/sciadv.aax7407https://doi.org/10.1126/sciadv.aax7407https://doi.org/10.1126/sciadv.aax7407https://doi.org/10.1021/acs.nanolett.4c00541?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.4c00541?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.9b04530?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.9b04530?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsnano.9b04530?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1103/PhysRevB.105.035417https://doi.org/10.1103/PhysRevB.105.035417pubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(38) Kunstmann, J.; Mooshammer, F.; Nagler, P.; Chaves, A.; Stein,F.; Paradiso, N.; Plechinger, G.; Strunk, C.; Schüller, C.; Seifert, G.;Reichman, D. R.; Korn, T. Momentum-Space Indirect InterlayerExcitons in Transition-Metal Dichalcogenide Van Der WaalsHeterostructures. Nat. Phys. 2018, 14, 801−805.(39) Aly, M. A.; Shah, M.; Schneider, L. M.; Kang, K.; Koch, M.;Yang, E.-H.; Rahimi-Iman, A. Radiative Pattern of Intralayer andInterlayer Excitons in Two-Dimensional WS2/WSe2 Heterostructure.Sci. Rep. 2022, 12, 6939.(40) Sortino, L.; Zotev, P. G.; Mignuzzi, S.; Cambiasso, J.; Schmidt,D.; Genco, A.; Aßmann, M.; Bayer, M.; Maier, S. A.; Sapienza, R.;Tartakovskii, A. I. Enhanced Light-Matter Interaction in anAtomically Thin Semiconductor Coupled with Dielectric Nano-Antennas. Nat. Commun. 2019, 10, 5119.(41) Luo, Y.; Shepard, G. D.; Ardelean, J. V.; Rhodes, D. A.; Kim, B.;Barmak, K.; Hone, J. C.; Strauf, S. Deterministic Coupling of Site-Controlled Quantum Emitters in Monolayer WSe2 to PlasmonicNanocavities. Nat. Nanotechnol. 2018, 13, 1137−1142.(42) Akselrod, G. M.; Argyropoulos, C.; Hoang, T. B.; Ciracì, C.;Fang, C.; Huang, J.; Smith, D. R.; Mikkelsen, M. H. Probing theMechanisms of Large Purcell Enhancement in Plasmonic Nano-antennas. Nat. Photonics 2014, 8, 835−840.(43) Choi, J.; Florian, M.; Steinhoff, A.; Erben, D.; Tran, K.; Kim, D.S.; Sun, L.; Quan, J.; Claassen, R.; Majumder, S.; Hollingsworth, J. A.;Taniguchi, T.; Watanabe, K.; Ueno, K.; Singh, A.; Moody, G.; Jahnke,F.; Li, X. Twist Angle-Dependent Interlayer Exciton Lifetimes in VanDer Waals Heterostructures. Phys. Rev. Lett. 2021, 126, No. 047401.(44) Oliaei Motlagh, S. A.; Apalkov, V.; Stockman, M. I. TransitionMetal Dichalcogenide Monolayers in an Ultrashort Optical Pulse:Femtosecond Currents and Anisotropic Electron Dynamics. Phys. Rev.B 2021, 103, 155416.(45) Beversluis, M. R.; Bouhelier, A.; Novotny, L. ContinuumGeneration from Single Gold Nanostructures through near-FieldMediated Intraband Transitions. Phys. Rev. B 2003, 68, 115433.(46) Zhou, W.; Dridi, M.; Suh, J. Y.; Kim, C. H.; Co, D. T.;Wasielewski, M. R.; Schatz, G. C.; Odom, T. W. Lasing Action inStrongly Coupled Plasmonic Nanocavity Arrays. Nat. Nanotechnol.2013, 8, 506−511.(47) Pelton, M. Modified Spontaneous Emission in NanophotonicStructures. Nat. Photonics 2015, 9, 427−435.(48) Wu, Y.; Xu, J.; Poh, E. T.; Liang, L.; Liu, H.; Yang, J. K. W.;Qiu, C.-W.; Vallée, R. A. L.; Liu, X. Upconversion Superburst withSub-2 μs Lifetime. Nat. Nanotechnol. 2019, 14, 1110−1115.(49) Akselrod, G. M.; Ming, T.; Argyropoulos, C.; Hoang, T. B.; Lin,Y. X.; Ling, X.; Smith, D. R.; Kong, J.; Mikkelsen, M. H. LeveragingNanocavity Harmonics for Control of Optical Processes in 2DSemiconductors. Nano Lett. 2015, 15, 3578−3584.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.5c02703Nano Lett. 2025, 25, 14800−1480714807https://doi.org/10.1038/s41567-018-0123-yhttps://doi.org/10.1038/s41567-018-0123-yhttps://doi.org/10.1038/s41567-018-0123-yhttps://doi.org/10.1038/s41598-022-10851-3https://doi.org/10.1038/s41598-022-10851-3https://doi.org/10.1038/s41467-019-12963-3https://doi.org/10.1038/s41467-019-12963-3https://doi.org/10.1038/s41467-019-12963-3https://doi.org/10.1038/s41565-018-0275-zhttps://doi.org/10.1038/s41565-018-0275-zhttps://doi.org/10.1038/s41565-018-0275-zhttps://doi.org/10.1038/nphoton.2014.228https://doi.org/10.1038/nphoton.2014.228https://doi.org/10.1038/nphoton.2014.228https://doi.org/10.1103/PhysRevLett.126.047401https://doi.org/10.1103/PhysRevLett.126.047401https://doi.org/10.1103/PhysRevB.103.155416https://doi.org/10.1103/PhysRevB.103.155416https://doi.org/10.1103/PhysRevB.103.155416https://doi.org/10.1103/PhysRevB.68.115433https://doi.org/10.1103/PhysRevB.68.115433https://doi.org/10.1103/PhysRevB.68.115433https://doi.org/10.1038/nnano.2013.99https://doi.org/10.1038/nnano.2013.99https://doi.org/10.1038/nphoton.2015.103https://doi.org/10.1038/nphoton.2015.103https://doi.org/10.1038/s41565-019-0560-5https://doi.org/10.1038/s41565-019-0560-5https://doi.org/10.1021/acs.nanolett.5b01062?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b01062?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b01062?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aspubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.5c02703?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as