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Yue Luo, Dapeng Ding, Andres M. Mier Valdivia, Daniel T. Larson, Song Liu, Hong Kuan Ng, Jing Wu, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Efthimios Kaxiras, Hongkun Park, Philip Kim, William L. Wilson

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[Observation of hyperbolic intersubband polaritons in native-dielectric-doped van der Waals semiconductor quantum wells](https://mdr.nims.go.jp/datasets/e3e9571d-d352-4eb7-8fb3-0348169a7443)

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Observation of hyperbolic intersubband polaritons in native-dielectric-doped van der Waals semiconductor quantum wellsArticle https://doi.org/10.1038/s41467-025-65196-yObservation of hyperbolic intersubbandpolaritons in native-dielectric-doped van derWaals semiconductor quantum wellsYue Luo 1,2,3 , Dapeng Ding3,4, Andres M. Mier Valdivia3, Daniel T. Larson 3,Song Liu5, Hong Kuan Ng3, JingWu 1, Kenji Watanabe 6, Takashi Taniguchi 7,Efthimios Kaxiras3, Hongkun Park 4, Philip Kim 3 & William L. Wilson 2Highly doped semiconductor quantum wells (QWs) exhibit strong intersub-band transitions resulting from nanoscale electron confinement. Couplingphotons to these collective dipoles in this anisotropic quantum structureenables intersubband polaritons with strong nonlinear optical response andhyperbolicity. Analogous to epitaxially grown multi-quantum wells, two-dimensional (2D) van der Waals (vdW) semiconductor heterostructures pro-vide a compelling alternative platform, offering additional degrees of freedomand exceptional optoelectronic properties. Here we report intersubbandpolaritons in multilayer vdW WSe2 QWs with broadband tunability. By oxi-dizing the top WSe2 layer into a self-limiting native oxide, we activate chargetransfer–induced efficient, high-density doping, enabling strong intersubbandtransitions and directly visualized polariton propagation. Lithographicallydefined nanostructures reveal their hyperbolic nature and sub-diffractionalconfinement, while electrostatic gating offers dynamic dispersion control.These results position vdW multilayers as a highly adaptable platform fortunable mid-infrared nanophotonics and integrated polaritonic circuits,detectors, and light sources.The quantum confinement of charge carriers in low-dimensionalmaterials leads to emergenceof quantized energy states,mappedontothe edges of the systems conduction and valence bands. Intersubbandtransitions represent a particular set of absorption or emission pro-cess, whereby electrons (or holes) in a doped semiconductor undergotransitions between distinct subbands confined within the conductionor valence bands1,2. These transitions are observed and exploited insemiconductor quantum wells (QWs) where one-dimensional con-straint is imposed on their free carriermotion3–5. The harnessing of theintersubband transitions oscillator strength has been crucial for theconceptualization and fabrication of an array of optoelectronicdevices, including quantum cascade lasers6 (QCLs) and infraredphotodetectors7. Strong coupling and ultra-strong coupling betweencavity photons and individual intersubband transitions have beendemonstrated as cavity intersubband polaritons (ISPs) using a varietyof different photonic cavity structures containingmulti-QWswith highcarrier density8–10. By engineering the design of theQWsemiconductorheterostructures, both transition energies and dipole momentsbetween the subbands can be tailored. Consequently, these ISPs areelectrically tunable through the terahertz and mid-infrared spectrumrange, with collective properties, such as hyperbolicity11 andnonlinearity12. A wide array of device applications have beenReceived: 10 June 2025Accepted: 9 October 2025Check for updates1School of Electronic Science and Engineering, Southeast University, Nanjing, Jiangsu, China. 2Center forNanoscale Systems,HarvardUniversity,Cambridge,MA,USA. 3Departmentof Physics, HarvardUniversity,Cambridge,MA,USA. 4Department ofChemistry andChemical Biology,HarvardUniversity, Cambridge,MA, USA. 5Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China. 6International Center for Materials Nanoarchitectonics, NationalInstitute for Materials Science, Ibaraki, Japan. 7Research Center for Functional Materials Science, National Institute for Materials Science, Ibaraki, Japan.e-mail: yueluo@seu.edu.cn; wwilson@cns.fas.harvard.eduNature Communications |        (2025) 16:10158 11234567890():,;1234567890():,;http://orcid.org/0000-0002-2757-5395http://orcid.org/0000-0002-2757-5395http://orcid.org/0000-0002-2757-5395http://orcid.org/0000-0002-2757-5395http://orcid.org/0000-0002-2757-5395http://orcid.org/0000-0001-8528-0280http://orcid.org/0000-0001-8528-0280http://orcid.org/0000-0001-8528-0280http://orcid.org/0000-0001-8528-0280http://orcid.org/0000-0001-8528-0280http://orcid.org/0000-0002-4182-6701http://orcid.org/0000-0002-4182-6701http://orcid.org/0000-0002-4182-6701http://orcid.org/0000-0002-4182-6701http://orcid.org/0000-0002-4182-6701http://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/0000-0001-9576-8829http://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://orcid.org/0000-0003-2755-7610http://orcid.org/0000-0003-2755-7610http://orcid.org/0000-0003-2755-7610http://orcid.org/0000-0003-2755-7610http://orcid.org/0000-0003-2755-7610http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65196-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65196-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65196-y&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65196-y&domain=pdfmailto:yueluo@seu.edu.cnmailto:wwilson@cns.fas.harvard.eduwww.nature.com/naturecommunicationsdemonstrated such as realizing unconventional light sources13,14,inversionless polariton laser15, ultrafast terahertz saturable absorber16and optical switches17.Emerging 2D van der Waals materials, such as transition metaldichalcogenides (TMDs), are an alternative platform that form nat-ural QWs where charge carriers are quantum confined within theatomically thin layers18–20. In addition, the energy separation betweenthe quantized states in few-layer TMDs is governed by the interlayercoupling and can be controlled via engineering the multi-layerstructure, geometry, and composition. For instance, the valenceband and conduction band splitting in few layers of tungsten dis-elenide (WSe2) are about few hundred meV at Γ and K valley18,21,22,where intersubband transitions are within the mid-infrared to fewTHz energy range. These TMD layers with atomically smooth inter-faces can be further assembled into heterostructures with othertypes of TMDs, leading to controlled band realignment and anextended range of intersubband transition energies23. Additionally,forming heterostructures with metals or semi-metals providespathways for electrically contacting the vdW QWs, enabling activetuning of the resonance energies through carrier injection. Theintersubband transitions in these vdW QWs have garnered growinginterest and have been investigated using techniques such as infra-red nano-imaging18, photoluminescence excitation24, magneto-transport20 and resonant tunneling25,26 techniques.In spite of their unique spectral properties, the coupling of theintersubband transitions in vdW QWs with free-space photons hasproven challenging, due to the mismatch between the out-of-planepolarization of the intersubband optical transitions and the in-planepolarization of the normal incident free-space photons12,22. To over-come the momentum mismatch, photonic cavities such as planarresonators8 or metasurfaces12 are often employed, but their use sig-nificantly increases device fabrication complexity. The bulky structureof these devices poses challenges for integration with other opticalcomponents on the chip. Furthermore, the weak oscillator strengthbetween the lower subbands induced by typical electrostatic dopinghas rendered the observation of ISP propagation elusive18,27. Achievinghigh carrier dopingwithin the quantumwell, alongwith the use of out-of-plane optical probes, is essential for advancing the study of ISPs invdW QWs.Recently, tungsten oxyselenide, the native-dielectric created byoxidizing the top-most monolayer of WSe228, has been shown to pro-vide efficient charge transfer to graphene when a direct contact isformed29. This oxidation process is self-limiting, providing an efficientand controllable doping method that yields a carrier density nearly anorder of magnitude higher than that achievable by electrostaticgating28–30. This approach has been demonstrated to efficiently mod-ulate the carrier density in graphene and thereby allow engineering ofplasmon polaritons31. Although promising for carrier density control,its application to the formation and study of ISPs remains unexplored.Herein, we report that by utilizing this native transition metal oxide(TMO) charge transfer strategy on few-layerWSe2, we can substantiallypopulate the higher energy subbands with carriers resulting in inter-subband transitions with sufficient oscillator strength, suitable forreaching a polaritonic regime. With this system improvement, weexperimentally demonstrate that the ISP propagation inWOx/4L-WSe2heterostructure can be imaged optically, readily in real-space, withnano-scale resolution scattering-type scanning near-field opticalmicroscopy (s-SNOM). We quantify the dispersion of the observedhyperbolic modes and demonstrate the electrical tunability of the ISPsby further applying gate bias to the heterostructure device. Finally, wein addition fabricate lithographically patterned oxide transfer dopinglayers to further provide an additional lateral quantum confinement tothe ISPs. Within these nanoresonators, we demonstrate that devicesexhibit hyperbolic rays traveling along conical trajectories and have anegative dispersion relation in the highly confined ISPs.ResultsIntersubband transition and native-dielectric-dopingThe intersubband transition energies in the WSe2 QWs can beapproximated with an infinite square well potential with well widthL =Nd, where N is number of layers and d is the monolayer thickness(Fig. 1a). The dispersion near the band edge at the Γ point can beobtained fromEΓ kz ,k� � � � ℏ2k2z2mv, z� ℏ2k22mv, xyð1 + ζk2z Þ ð1Þwhere mv, z and mv, xy are the out-of-plane and in-plane effectivemasses, ζ is the nonlinearity parameter and kz � πndðN + 2vÞ22. The inter-subband transition energies can be expressed asE1 � E2�� ��= 3π2ℏ22mv, zd2 N + 2vð Þ2ð2ÞandE2 � E3�� ��= 5π2ℏ22mv, zd2 N +2vð Þ2ð3ÞWe compare the intersubband transition energies calculatedwith this modified infinite square well model with density functiontheory (DFT) and find a good agreement with experimental values21(Fig. 1b). The intersubband transition energies inmultilayerWSe2 canbe tuned from 636meV to 39meVby control of the number of layers.To engineer optical access to the intersubband states in the mid-infrared energy range, typical of a QCL source, we specifically choosea platform of a five-layer (5 L) 2H-WSe2 homostructure to create ahighly doped vdW multi-QW with accessible, partially occupiedsubbands. Figure 1c illustrates the fabrication process of WOx-dopedWSe2 multilayers. In our method, the electronic band structure is, inessence, adjusted through the self-limiting oxidation of the topWSe2layer. We subject a dry-transferred WSe2 flake to a UV-Ozone treat-ment, designed to convert the top layer into a TMO layer which has ahigh work function, while maintaining the atomic integrity of theunderlying layers (see Methods and Supplementary Note 1). Thesignificant work function difference between WOₓ and WSe2 inducesa surface charge transfer32, promoting strong hole doping in theWSe2 layers. The hole density in these p-doped WSe2 multilayers ismeasured under ambient conditions using standard four-probemeasurements (Supplementary Note 2). We find a hole density ofp = 0.93 × 1013 cm−2 at VGS = 0 V, aligning with prior reports of dopingin the 1013cm−2 range29. By applying a back gate voltage, VGS, to theheavily doped Si substrate separated by the 300 nm silicon oxidelayer, we can further increase this density to p = 1.11 × 1013cm−2 atVGS = −25 V. The doping level achieved through the TMO layer pro-cess surpasses most electrostatic gating methods using soliddielectrics by an order of magnitude. Electrostatic approaches gen-erally yield densities in the 1011 to 1012cm−2 range33.We calculated the expected electronic band structure mod-ification from the top WOx layer onto the WSe2 layers underneath,using density functional theory (DFT) incorporating spin-orbitcoupling effects (Supplementary Note 2). Figure 1d, e presentsthe band structure of WOx/4L-WSe2 heterostructure calculatedusing this approach. These calculations elucidate the splitting ofthe highest valence band into multiple subbands at the Γ point inthe Brillouin zone, corresponding to the interlayer coupling.Upon p-doping, free holes partially occupy these subbands fromthe subband base to the Fermi energy (EF), transitions can occurwithin the |k| ≤ kF range between a subband and a higher unoc-cupied subband. This is manifested as an absorption peak. Toinvestigate the influence from the WOx layer, selenium atoms inArticle https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 2www.nature.com/naturecommunicationsthe topmost layer were substituted with oxygen, and the ionicpositions subsequently re-optimized. As depicted in Fig. 1d, e,this modification of the electronic states results in an alteredband structure at the Γ point, displaying distinct subband split-ting at mid-IR energies. Our calculation suggests that when thetop layer (L5) is oxidized, the symmetry is broken and the topvalence subband comes almost exclusively from the L5. The 2ndvalence subband then comes mostly from L4 and L3 while the 3rdvalence subband from L2. In order to maximize the coupling oflight to intersubband transitions, it is desirable to populate holesin the second subbands in a few-layer WSe2, which requires car-rier density more than ~1013 cm−2 and has been challenging toreach by electrostatic gating alone. In contrast, using the TMOlayer we can easily generate the sufficient carrier density with EFpositioned within the valence band. As illustrated in Fig. 1f, whenthe heterostructure is excited by photon with the out-of-planepolarization whose energy is resonant with the transition energybetween the subbands, an intersubband transition between thesecond and third subbands can be observed.Near-field imaging of the intersubband polaritonsAn s-SNOM equipped with a broadband pulsed laser is utilized tocarry out the nano-Fourier-transform infrared spectroscopy (nano-FTIR). The infrared excitation laser beam is focused on themetallizedtip of the atomic force microscope (AFM), generating an enhancedoptical field that interacts with the heterostructure sample beneath.With that configuration, we are able to characterize the intersubbandtransitions in WOx/4L-WSe2 at near-field with out-of-plane excitationpolarization. The scattered light from the tip is collected, and thenear-field amplitude and phase are recorded from the sample flake.This data is calibrated against a gold substrate to eliminate anyinstrumental responses. The near-field results provide insights intothe sample’s complex permittivity, optical conductivity, and itsabsorption characteristics under the excitation energy Eph (Fig. 1g).Notably, while the dielectric response of WSe2 remains featurelessfrom 120meV to 160meV34, WOx/4L-WSe2 heterostructure exhibits adistinct absorption peak, clearly indicative of the predicted inter-subband transition. To avoid interference from SiO2 phonons, typi-cally prominent around 140meV, an Au/Si substrate without an SiO2Energy (eV)21.510.50-0.5-1-1.52 4 6 8 100.00.20.40.60.8EISB (eV)N DFT  AnalyticalcUVOzone5L WSe24L WSe21L WOxdM K Γ MeM K Γ ML5L4L3L2L1fEFIntersubbandtransitionEphECEVWOx WSe2eha bN=2 N=3 N=4 N=5 zEFig. 1 | Intersubband transition in WSe2 andWOx heterostructure. a Schematicillustration of subbands in the van der Waals (vdW) material quantum wells withdifferent thickness defined by the number of layers N. Black dashed lines illustratethe subband energy positions. b Theoretical calculation of the intersubband tran-sition energy of the first and second subband as a function of N for holes in thevalence band using density function theory (DFT) (green circles) and modifiedinfinite quantum well model, respectively. Red shaded area indicates the energycoverage of ourmid-infrared laser. c Schematics of the doping process. Ultraviolet-ozone oxidation transforms the topmost layer of the 5L-WSe2 into transitionmetaloxides (TMOs) resulting in WOx/4L-WSe2. The oxidation process effectively dopedthe underneath WSe2 layers. DFT calculated band structure for WOx/4L-WSe2heterostructure showing contribution from4L-WSe2 ingreen (d) and topWOx layerin blue (e). Red dashed lines indicate the Fermi energy EF. Red solid arrows indi-cated the optical transition. f Illustration of charge transfer betweenWOx andWSe2as the result of the work-function mismatch. EC is conduction band edge and EV isvalence band edge;Excitation light with out-of-plane polarization can excite thecharge carriers from the lower state to the upper excited state if excitation photonenergy Eph is in resonant with the E23 intersubband transition energy. g NanoFourier transform infrared spectrum of theWOx/4L-WSe2 near-field amplitude s(ω)andphaseφ(ω).h Phase contrast between the sample and substrate as a function ofgate voltage Vg.Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 3www.nature.com/naturecommunicationslayer was utilized. We further explore the nano-FTIR result by fittingthe data with modulated scattered field where tip-sample interactionand complex permittivity described as Lorentz model are taken intoconsideration (Supplementary Note 4). We then demonstrate inter-subband absorption control by analyzing the phase contrast betweenthe sample and the substrate φsample-φsub while changing the carrierdensity using a gate bias. The interferometric detection of the near-field optical response can decouple the amplitude and phase com-ponents from the scattered field as Escat ∝ Seiφ Ein, where S is therelative amplitude andφ is the phase shift35. Hence, the relative phaseshift is a measurement of absorption at the near-field. As shown inFig. 1h, we can clearly see that the absorption decreases when weinject electron into the sample to decrease the hole carrier density.(Note the electrostatic bias cannot tune the carrier density to thecharge neutrality point due to the high doping level from the chargetransfer of the WOx).According to the nano-FTIR spectrum, the εimag should exhibitstrong resonant-like features along the out-of-plane crystal direction,implying the anisotropic dielectric permittivity should satisfyεreal, i × εreal, j≠i <0, since the real and imaginary parts of the dielectricfunction are connected through the Kramers–Kroing relation36. Due tothe different value of the effective masses and dielectric screening inthe in-plane and out-of-plane directions, the highly doped WOx/4L-WSe2 heterostructure exhibits strong anisotropy in the frequencyrange (Fig. 2a). The heterostructure behaves like a dielectric in-plane,where εx, y >0. For the out-of-plane direction, the heterostructurebehaves likemetal under thehigh carrier density conditions, showing astrong intersubband absorption with εz <0 at the mid-IR frequency.We note that this phenomenon is fundamentally different fromrecently demonstrated bound carrier excitation in bulk WSe2 near theinterband optical transition energy37. In the bulk WSe2 crystal, thesubbands remain degenerate, and hyperbolic behavior emerges onlyunder non-equilibrium conditions, in contrast to the ISPs studied here.To effectively couple intersubband transitions to free-spacephotons and excite ISPs in the WSe2 quantum wells, we employeds-SNOM with both a continuous-wave QCL and a pulsed optical para-metric oscillator laser to sweep across the transition energies. Thisconfiguration introduces an out-of-plane light component that drivesthe intersubband transitions within the heterostructure, thereby giv-ing rise to ISPs. In order to reveal the ISP propagation in the hetero-structure, we now investigate the polariton dispersive dynamicsinterferometrically using the real-space near-field nano-imaging tech-nique. Figure 2b, c presents data collected at different excitationenergies, Eph = 144meV and Eph = 149meV, respectively. Oscillations ofthe near-field amplitude s(ω) are observable at the flake edge. Thesefringes arise from the interference between the tip-launched polaritonand the propagated polariton reflected at the sample edge. By exam-ining the cross-sectional profile perpendicular to the sample edge, wecan extract the periodicity of the bright-dark fringes, which corre-sponds to half of the polariton wavelength (λISP/2). As the excitationenergy increases from 144meV to 149meV, the polariton wavelengthincreases from 317 ± 10 nm to 453 ± 12 nm (Fig. 2d). The propagationlength of the ISP is fitted to be 0.8 μm (Supplementary Note 5). Thelifetime of the ISP is calculated as τISP =Lvg=0:4ps (SupplementaryNote 10). Using the same method, we systematically extract thepolariton wavelengths at various tuned excitation energies from the100 120 140 160 180 200-20-100102030� �Energy (meV)�WSe2,xx�WSe2,zz�xx�zzkxkzkykxkzky144 meV147 meV149 meVIm(rp )(arb.units)MinMaxa de f gcbEph = 144 meVEph = 149 meVMaxMins(ω)(arb.units)MaxMins(ω)(arb.units)0.4 0.8 1.2 1.6 21.61.82q(107m-1)n (1013 cm-2)Eph = 144 meV Eph = 270 meVEph = 98 meVWOx/5L-WSe2WOx/3L-WSe20.2 0.40123s(�) (arb.units)Position (�m)MaxMins(ω)(arb.units)Fig. 2 | Nano-imaging of intersubband transition and hyperbolic plasmonpolariton inWOx/4L-WSe2. a Permittivity of theWSe2 (dashed lines) andwith highcarrier density under charge transfer (solid lines). Inset: the isofrequency surfacemodified from ellipse to a hyperboloid in the red-shaded region. Images of near-field scattering amplitude s(ω) for WOx/4L-WSe2 with excitation energyEph = 144meV (b) and Eph = 149meV (c). The layer thickness is d ~ 4.5 nm. Scale bar:500 nm. d Line traces of the interference pattern from the edge-reflected plasmonpolariton taken from the near-field scattering amplitude image as illustrated in (b)and (c) (whitedashed lines). Blackdashed linemarks theedgeof the sample and reddashed line marks the peak position. e Dispersion of the intersubband polariton(ISP) in WOx/4L-WSe2. Color plot is calculated using the Fresnel reflection coeffi-cients Im(rp). Yellow squares are experimental data. The error bars are determinedfrom the fitting uncertainties of the fringe periodicities. f The extracted real part ofmomentum q as a function of carrier density n for WOx/4L-WSe2. The red solid lineis the fit to the data using the relation q � 1=n. The error bars are determined fromthe fitting uncertainties of the fringe periodicities. g Images of near-field scatteringamplitude s(ω) for WOx/3L-WSe2 and WOx/5L-WSe2 with excitation energiesEph = 270meV and Eph = 98meV, respectively. Scale bar: 250 nm.Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 4www.nature.com/naturecommunicationsnano-imaging data. The confinement factor λ0=λISP reaches up to 27,comparable to that of plasmon polaritons in graphene and phononpolaritons in h-BN, while still smaller than the acoustic plasmon ingraphene38. We visualize the dispersion relations with a false colormapping of the imaginary part of the reflection coefficients Im (rp),representing the photonic density of states as a function of wavevector q=2π=λISP (Fig. 2e and Supplementary Note 6). This inverserelationship between energy and momentum confirms the Type Ihyperbolic polariton dispersion, where εz <0 and εx, y >0.As noted, in addition to the charge transfer process via TMO layer,the carrier density can be further tuned.We demonstrate the electricalcontrol of the polaritons by systematically tuning of the intersubbandtransitions in the valence band via back-gating. Since the chargetransfer method between the TMO layer and WSe2 drives a muchhigher carrier density than that possible via tuning by electrostaticgating, we can vary the carrier density modestly in the p-type dopingregime. Figure 2f shows the ISPmomentum q as a function of the back-gate voltage Vg at a representative energy Eph = 144meV. The magni-tude of q is approximately proportional to n−1, where higher holedensity leads to increased negative permittivity39. The evolution of qwithVg further confirms thehole doping in theWOₓ/4L-WSe2 structureand the observed negative dispersion relation (SupplementaryNote 8). Such active tunability is generally absent in the naturalhyperbolic materials such as h-BN40 and MoO341. The intersubbandtransition energy can be controlled with the thickness of the vdWlayers.We alsodemonstrated thenano-imaging of the ISP in bothWOx/3L-WSe2 and WOx/5L-WSe2 heterostructure at excitation wavelengthEph = 270meV and Eph = 98meV, respectively (Fig. 2g). This findingaligns well with the theoretical calculation shown in Fig. 1b.Measurement of the hyperbolic propagationWe explore the presence of hyperbolic ISP by positioning theWOx/4L-WSe2 heterostructure on the 50nm Au disk (Fig. 3b). The conical-shaped rays launched by the edge of the Au disk will reach the topsurface of the heterostructure forming bright rings separated by theedge (Fig. 3a). The distance between the bright ring and theelectrostatic edge, denoted as ΔR, is modulated by the isotropiccomponents of the dielectric tensor, with the relationshipΔR=d = tanθ�� ��= i ffiffiffiffiffiffiffiεxyp=ffiffiffiffiffiεzp, where d represents the heterostructure’sthickness, and θ is the angle from the surface normal42,43. Directionalpropagation of the hyperbolic ISP along the resonance cone isobserved at Eph = 145meV (Fig. 3c). The line-profiles taken from thes-SNOM amplitude image reveal that the radial distance ΔR is sig-nificantly smaller than that observed in bulk hyperbolic materials, dueto the thickness of the heterostructure as thin as d ~ 4.5 nm (Fig. 3d).We further verify the hot-ring feature for different layer numbersamples by transferring the heterostructure with different thicknessonto the same Au disk. When the excitation energy matches the E23transition energy of theWOx/6L-WSe2 at Eph = 114meV,we can see onlythe bottom half lights up (Fig. 3e). When we increase the excitationenergy to Eph = 146meV, the upper half lights up as the intersubbandtransition energy increases with the fewer layer numbers (Fig. 3f). Thelayer-dependent hyperbolicity highlights ISPs as a promising additionto the family of hyperbolic polaritons, complementing other recentlydemonstrated phenomena such as topological transitions44, negativerefraction45,46, and low-loss propagation47.Intersubband polaritons in nanoresonatorsWe further manipulate the hyperbolic ISP by fabricate the WOₓ/4L-WSe2 heterostructure into nanoresonators where the polaritonmodes are confined by the circular boundaries. Figure 4a illustratesthe schematic of an s-SNOM measurement conducted on focus ionbeam (FIB) patterned WOₓ/4L-WSe2 nanoresonators with an under-lying gold mirror. By eliminating the need for a polymer mask in theetching process, direct FIB fabrication keeps the heterostructuresurface uncontaminated, minimizing the risk of residue depositionor chemical interaction commonly associated with mask-basedtechniques, thereby preserving the material’s intrinsic propertiesand optimizing the quality of subsequent device performance.Additionally, a gold mirror is deposited on the substrate to minimizeradiative decay into the silicon substrate, thereby resulting in lowerloss and longer lifetime (Supplementary Notes 9 and 10). To exploreEph = 145 meVAFM heightbadcΔR-200 -100 0 100 20000.050.1 1s(�) (arb.unitsPosition (nm)MaxMins(ω) (arb.units)MaxMins(ω) (arb.units)ΔRWOx/WSe2Au diskaFig. 3 |Hyperbolic ISP revealedbynano-imagingonAunanodisk. a Schematicofhyperbolic polaritons launched at the edge of the Au nanodisk, which travel alongconical trajectories and form a bright ring. The distance between the ring and theedge of the Au nanodisk is ΔR. Topography (b) and near-field scattering amplitudes(ω) image of WOx/4L-WSe2 plasmonic cavity with diameter D = 300nm and exci-tation energy Eph = 145meV (c). Scale bar: 300nm. d Line profile of the measurednear-field amplitude taken at the dashed line in (c). Near-field scattering amplitudes(ω) image of sample on the Au nanodisk that is partially covered by WOx/4L-WSe2and WOx/6L-WSe2 simultaneously and excited with Eph = 114meV (e) andEph = 146meV (f), respectively. Red dashed lines indicate the boundary. Scalebar: 150 nm.Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 5www.nature.com/naturecommunicationsthe relation between the resonant energy and the diameters of thenanoresonators, we patterned disk nanoresonators with diametersranging from 100 nm to 800 nm. The propagation of the ISP in thenanoresonators can be described by the wave equationρðiωÞ2 =∇2ρv2pðωÞ, where ρ denotes the integrated two-dimensionalcharge density and vp is the group velocity48. For a disk-shapedresonator, the solution of ρ can be expressed in terms of Besselfunctions, with the eigenvalues ksn determined by the disk diameter.Consequently, because the ISP can resonate only with resonators ofspecific sizes at a given excitation photon energy, tuning the Ephenables the systematic mapping of the relationship between diskdiameter and the ISP resonant modes (Fig. 4b).To quantitatively study the confined mode in the resonators,we analyzed each disk resonator at different excitation energies.The near-field amplitude image of a representative nanoresonatorwith a diameter of D = 500 nm is shown in Fig. 4c, where astanding-wave pattern with multiple fringes emerges49,50. Fig-ure 4d presents the Fourier transform |s(kx, ky)| of the near-fieldamplitude image from Fig. 4c, revealing the iso-frequency con-tours for the ISP at 146meV. The in-plane permittivity of the WOₓ/4L-WSe2 heterostructure is isotropic. We then extract the near-field amplitude response from the standing wave in the resonatorat different excitation energies (Fig. 4e). The signal was normal-ized to the background at the surrounding gold surface to com-pensate for variations in the laser power and optical alignment ineach measurement. At Eph = 139meV, the near-field amplitudeshows a peak D = 300 nm. The size of the resonator imposes aconstraint on the ISP wavelength confined in the resonator. Withincreasing Eph, disk diameter exhibiting a stronger scattered near-field response also increases due to the longer polariton wave-length, aligning with the hyperbolic dispersion relation observedin the unpatterned heterostructures. We then investigate the fieldconcentration and the resonance behavior of the confined ISP byanalyzing a resonator with D = 600 nm under various excitationenergies. Figure 4f shows the near-field optical response as afunction of the excitation energy. The signal is normalized to thesubstrate background to eliminate the influence from the powerstability and detection efficiency. We fit the peak with Gaussianfunction with center energy at 147meV and FWHM= 3.2 ± 0.3meV. The quality factor is then calculated as Q = ω/FWHM = 45.9,where ω is the resonant frequency48,51.We finally conducted a numerical simulation for the resonatorwith same diameter of D = 600nm to further explore the polaritonspropagation in WOₓ/4L-WSe2 nanoresonators. The z-component elec-tric field distribution, mapped at various excitation energies in Fig. 4f,shows that as the Eph increases from 144meV to 148meV, the distancebetween the bright maxima widens, following the negative dispersionrelation. At an Eph = 151meV, the polariton wavelength λISP = 478 nmexceeds the nanoresonator’s radius, precluding effective ISP modeconfinement. Our FDTD simulations show that the highly confinedmodes have an effective mode volume V of 2 × 10�6=λ30, respective tothe free space photon wavelength λ0, which quantifies the strongcbadWOxWSe2AuSiO2SiMaxMins(ω)(arb.units)kxkyMaxMaxs(kx ,ky )(arb.units)Eph = 146 meVEph = 148 meVEph = 151 meVEph = 144 meV MaxAuMinEz (arb.units)WOx/4L-WSe2zzx5.5 nm139147151158161MaxMins(ω)(arb.units)Eph (meV)D (nm)008001ge f140 145 150 1551.21.62 D=600 nm Gaussian fits/)retnec(s)bus(Eph (meV)0 200 400 600 8001.21.41.611.21.411.21.4Diameter (nm)139 meVdezilamroN)stinu.bra( 144 meV151 meVFig. 4 | Intersubband polariton confined in WOx/4L-WSe2/Au nanoresonators.a Schematics of WOx/4L-WSe2/Au nanoresonators fabricated by focused ion beamongold substrate.bNear-field scattering amplitude s(ω) images of an array ofWOx/4L-WSe2/Au nanoresonators with different diameters (100nm to 800 nm) anddifferent shapes. The images are measured at a series of excitation energies from139meV to 161meV. Scale bar: 1μm. cNear-field scattering amplitude s(ω) image ofWOx/4L-WSe2/Au nanoresonator with diameter D = 600nm. The excitation energyis Eph = 146meV. Scale bar: 250nm. d The corresponding Fourier transform imageof (c). kx and ky arewavevectors in x and ydirection. Scale bar: 40 k0, where k0 is themomentum of light in free space. eNormalized near-field scattering amplitude as afunction of diameters of the resonatorswith excitation energy at Eph = 151meV (toppanel), Eph = 144meV (middle panel) and Eph = 139meV (bottom panel). Red arrowshelp to identify the peak value of s(ω). f Normalized amplitude as a function ofexcitation energy for the WOx/4L-WSe2/Au nanoresonator with diameterD = 600nm (green circles). Gray solid line is the Gaussianfitting.g Finite-differencetime-domain simulation of the out-of-plane field Ez in WOx/4L-WSe2/Au nanor-esonator with different excitation energies of Eph = 144meV, Eph = 146meV,Eph = 148meVand Eph = 151meV, respectively. Thediameter of the nanoresonator isD = 600nm.Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 6www.nature.com/naturecommunicationsspatial confinement of light in the disk nanoresonators52. Theseobservations highlight that the structural refinement of nanor-esonators via FIB patterning facilitates enhanced control over polar-iton modes, resulting in a higher quality factor and improved modeconfinement. Importantly, there remains potential to further optimizethe cavity design to achieve even greater polariton confinement with asignificantly reduced mode volume53.DiscussionWe report the creation and experimental observation of ISPs in high-density p-type doped WOₓ/WSe2 QW heterostructures. These widelytunable ISPs are systematically studied using spatially and spectrallyresolved near-field microscopy. Unlike phonon-polaritons in h-BN40 ormolybdenum oxide (MoO3)41, where the polariton properties are fixedby the atomic arrangement of the crystal structure, the ISPs in atom-ically thin vdW QW heterostructures can be actively tuned by varyingthe carrier density with electrostatic doping in addition to the passiveband structure engineering via doping using self-limited oxidationlayers. Intersubband transitions are observed in other 2D semi-conductormaterials such asMoS218,19 and themonolayer TMOstrategyis transferable to othermaterials with lowerwork function to provide apath to high-density p-type doping31. We note that the ISPs excited canexist in much broader energy ranges than other types of polaritons,potentially from near IR to THz, due to the various subband spacingenergies possible (Fig. 2g and Supplementary Note 7). Furthermore,with high-quality wafer-scale TMD crystals becoming available, this 2DvdW QW platform potentially allows for a wide variety of applicationsfeaturing tunable hyperbolic polaritonic devices.MethodsSample fabricationWe exfoliated thin WSe2 flakes onto SiO2 substrates using Scotchtape from a bulk commercial source (HQ Graphene). Suitable five-layer flakes were identified via optical contrast, using a “staircase”flake on the same chip to reliably distinguish between crystals ofvarious thicknesses. We subsequently dry-transferred the flakesonto a separate SiO2 substrate coated in Ti/Au (5 nm/50 nm). Devi-ces with contacts were transferred onto a bare SiO2 substrate with aheavily doped Si back gate for density control. The contacts con-sisted of 20 nm/70 nm of Pd/Au deposited directly on top of theWSe2 flake patterned via electron beam lithography with a polymermask, following the recipe in ref. 1. For all devices, we oxidized thetop TMD surface as the very last step just before measurements toensure a high-quality oxide and clean off any residues. Oxidationwas performed in a Samco UV & Ozone Stripper with a plate tem-perature of 100 °C for 1 h. All measurements were carried out atroom temperature.Carrier density measurementWe fabricated a separate device with various electrodes to elec-trically characterize the induced properties from the top oxide layer.We applied a constant voltage bias of 0.25 V and swept the Si gate VSiwith Keithley 2400 sourcemeters. We measured the 4-terminal (4t)voltage V4t between source and drain with an Agilent 34401A 6½Digit Multimeter. We extract the field-effect mobility μFE of the WOx/4L-WSe2 to be 0.9 ± 0.1 cm2/Vs by using μFE =L4tCWV4tdIdVSi, where L4t isthe separation between the 4t voltage probes, C is the 285 nm SiO2dielectric gate capacitance,W is the estimated channel width, and I isthe source-drain current. We calculated dIdVSifrom the linear regime ofthe field effect transistor. To calculate the hole density, we use therelation p V Si� �= ICedIdVSi� ��1, where e is the elementary charge.Near-field optical measurementThe nano-imaging experiments were performed using commercials-SNOM (Attocube systems AG). The system is equipped with QCLlaser and OPO for the nano-imaging within mid-IR range andbroadband DFG laser for nano-FTIR measurement. Platinum siliconcoated AFM tips were used in the s-SNOM with a typical radius of20 nm. The s-SNOM was operated under the tapping mode with atapping frequency around 240 kHz. We use pseudo-heterodyneinterferometric detection module to extract the near-field amplitudeand phase signals. The background signal is suppressed by demo-dulation of the near-field signal at the third harmonics of the tappingfrequency. All the near-field optical measurements are done at room-temperature.Numerical simulationsThe numerical simulations of the propagation of ISPs and nanor-esonators were carried out by the FDTD simulation software (FDTDsolutions). The dipole sources are used to excite the polariton andperfect metal layer boundary condition is used to simulate the near-field modes.Data availabilityThe Source Data underlying the figures of this study are available athttps://doi.org/10.5281/zenodo.17288925. All raw data generated dur-ing the current study are available from the corresponding authorsupon request.References1. West, L. C. & Eglash, S. J. First observation of an extremely large-dipole infrared transition within the conduction band of a GaAsquantum well. Appl. Phys. Lett. 46, 1156–1158 (1985).2. Weber, E. R., Willardson, R. K., Liu, H. & Capasso, F. IntersubbandTransitions in Quantum Wells: Physics and Device Applications. 62(Academic Press, 1999).3. Delteil, A. et al. 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Y.L. was supported by the South-east University Interdisciplinary Research Program for YoungScholars (Fundamental Research Funds for the Central Universities,2242025F10008). Y.L acknowledges the support from NationalNatural Science Foundation of China (Grant No.9247710104). Y.Land J.W. acknowledge the support from Center for Fundamentaland Interdisciplinary Sciences. D.D. acknowledges the supportfrom Samsung Electronics. A.M.V. is supported by AFOSR (FA2386-21−1-4086). P.K. and E.K. acknowledges the support from ARO MURI(W911NF-21-2-0147). D.T.L is supported by NSF Award No. DMR-1922172. E.K. acknowledges the support from ARO (W911NF-21-1-0184). Calculations were performed on the FASRC Cannon clustersupported by the FAS Division of Science Research ComputingGroup at Harvard University. Authors thank Wei Li and WeikangWang for the help on nano-FTIR measurements as well as GabrielSchleder and Daniel Bennett for helpful discussions.Author contributionsY.L., H.P., P.K., and W.L.W. conceived the experiment. S.L. carriedout the crystal growth. D.D., A.M.M.V., S.L. fabricated the devicesamples. H.K.N. and J.W. fabricated the Au disk samples. K.W. andT.T. provided the h-BN crystal. D.T.L. and E.K. performed the DFTcalculation. Y.L. carried out the s-SNOM experiments and analyzedthe data with P.K. and W.L.W. and Y.L. performed theoretical cal-culations and FDTD simulations for the polariton. All authors dis-cussed results and wrote the manuscript.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 8www.nature.com/naturecommunicationsAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65196-y.Correspondence and requests for materials should be addressed toYue Luo or William L. Wilson.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-65196-yNature Communications |        (2025) 16:10158 9https://doi.org/10.1038/s41467-025-65196-yhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Observation of hyperbolic intersubband polaritons in native-dielectric-doped van der Waals semiconductor quantum wells Results Intersubband transition and native-dielectric-doping Near-field imaging of the intersubband polaritons Measurement of the hyperbolic propagation Intersubband polaritons in nanoresonators Discussion Methods Sample fabrication Carrier density measurement Near-field optical measurement Numerical simulations Data availability References Acknowledgements Author contributions Competing interests Additional information