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Hangyong Shan, Ivan Iorsh, Bo Han, Christoph Rupprecht, Heiko Knopf, Falk Eilenberger, Martin Esmann, Kentaro Yumigeta, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Sebastian Klembt, Sven Höfling, Sefaattin Tongay, Carlos Antón-Solanas, Ivan A. Shelykh, Christian Schneider

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[Brightening of a dark monolayer semiconductor via strong light-matter coupling in a cavity](https://mdr.nims.go.jp/datasets/0869e246-7012-4c39-a986-84afd3b1eff4)

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Brightening of a dark monolayer semiconductor via strong light-matter coupling in a cavityARTICLEBrightening of a dark monolayer semiconductor viastrong light-matter coupling in a cavityHangyong Shan 1, Ivan Iorsh2, Bo Han1, Christoph Rupprecht3, Heiko Knopf4,5,6, Falk Eilenberger 4,5,6,Martin Esmann 1,7, Kentaro Yumigeta8, Kenji Watanabe 9, Takashi Taniguchi 10, Sebastian Klembt3,Sven Höfling3, Sefaattin Tongay 8, Carlos Antón-Solanas 1, Ivan A. Shelykh2,11 & Christian Schneider 1,7✉Engineering the properties of quantum materials via strong light-matter coupling is a com-pelling research direction with a multiplicity of modern applications. Those range frommodifying charge transport in organic molecules, steering particle correlation and interac-tions, and even controlling chemical reactions. Here, we study the modification of thematerial properties via strong coupling and demonstrate an effective inversion of the exci-tonic band-ordering in a monolayer of WSe2 with spin-forbidden, optically dark ground state.In our experiments, we harness the strong light-matter coupling between cavity photon andthe high energy, spin-allowed bright exciton, and thus creating two bright polaritonic modesin the optical bandgap with the lower polariton mode pushed below the WSe2 dark state. Wedemonstrate that in this regime the commonly observed luminescence quenching stemmingfrom the fast relaxation to the dark ground state is prevented, which results in the brighteningof this intrinsically dark material. We probe this effective brightening by temperature-dependent photoluminescence, and we find an excellent agreement with a theoretical modelaccounting for the inversion of the band ordering and phonon-assisted polariton relaxation.https://doi.org/10.1038/s41467-022-30645-5 OPEN1 Institute of Physics, Carl von Ossietzky University, Oldenburg 26129, Germany. 2 Faculty of Physics, ITMO University, Saint-Petersburg 197101, Russia.3 Technische Physik, Universität Würzburg, Am Hubland, Würzburg D-97074, Germany. 4 Institute of Applied Physics, Abbe Center of Photonics, FriedrichSchiller University, Jena 07745, Germany. 5 Fraunhofer-Institute for Applied Optics and Precision Engineering IOF, Jena 07745, Germany. 6Max PlanckSchool of Photonics, Jena 07745, Germany. 7 Center for Nanoscale Dynamics (CeNaD), Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26129 Oldenburg, Germany. 8 School for Engineering of Matter, Transport, and Energy, Arizona State University, Tempe 85287 AZ, USA.9 Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 10 International Center forMaterials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 11 Science Institute, University of Iceland,Dunhagi 3, Reykjavik IS-107, Iceland. ✉email: christian.schneider@uni-oldenburg.deNATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 |www.nature.com/naturecommunications 11234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-30645-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-30645-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-30645-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-30645-5&domain=pdfhttp://orcid.org/0000-0003-3988-4870http://orcid.org/0000-0003-3988-4870http://orcid.org/0000-0003-3988-4870http://orcid.org/0000-0003-3988-4870http://orcid.org/0000-0003-3988-4870http://orcid.org/0000-0002-4646-2484http://orcid.org/0000-0002-4646-2484http://orcid.org/0000-0002-4646-2484http://orcid.org/0000-0002-4646-2484http://orcid.org/0000-0002-4646-2484http://orcid.org/0000-0002-2329-9696http://orcid.org/0000-0002-2329-9696http://orcid.org/0000-0002-2329-9696http://orcid.org/0000-0002-2329-9696http://orcid.org/0000-0002-2329-9696http://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/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0002-9316-4340http://orcid.org/0000-0002-9316-4340http://orcid.org/0000-0002-9316-4340http://orcid.org/0000-0002-9316-4340http://orcid.org/0000-0002-9316-4340http://orcid.org/0000-0002-2268-471Xhttp://orcid.org/0000-0002-2268-471Xhttp://orcid.org/0000-0002-2268-471Xhttp://orcid.org/0000-0002-2268-471Xhttp://orcid.org/0000-0002-2268-471Xmailto:christian.schneider@uni-oldenburg.dewww.nature.com/naturecommunicationswww.nature.com/naturecommunicationsAtomically thin transition metal dichalcogenides (TMDCs)represent an emerging class of functional materials thatare of particular interest in photonics due to theirremarkable capability of efficient light emission andabsorption1–3. In contrast to the vast majority of conventionalsemiconductors, their truly two dimensional (2D) nature resultsin the strong enhancement of the electron-hole Coulombattraction, which makes their optical response to be dominated byexciton transitions even at room temperature4–6.Since both the valence and the conduction bands emerge from thep-orbitals of the transition metals, the effects of spin-orbit couplingare of central importance in excitonic ordering. Specifically, theoptical selection rules allow the excitation of the lowest energyexciton in monolayers of MoSe2 andMoTe27,8, whereas inWSe2 andWS2 it is spin-forbidden, and thus the exciton transition remainsoptically dark9. As a consequence, at low temperatures, the lumi-nescence of these dark materials is intrinsically quenched due to thefast relaxation of excitons into the dark ground state, and needs to bethermally ’activated’10. This creates a serious obstacle for optoelec-tronic applications which require maximized quantum efficiency,such as light-emitting diodes2,11,12, and conventional13–15—as wellas polariton lasers16,17.A number of methods to enhance the luminescence efficiency ofoptically dark 2D materials have already been investigated. Theseinclude the band-structure shaping by spin-orbit engineering9, theapplication of an in-plane magnetic field7,18,19, and the direct cou-pling of out-of-plane optical dipole moment of dark excitons withstrongly localized electric fields in nanoantenna tips20, or a TMpolarized optical mode at an oblique incidence21. However, therelevance of these approaches relying on high magnetic fields ornanoantenna tips is certainly limited for wide-spread use inapplications.In the present work, we follow an alternative approach to reacheffective brightening, which is based on the idea that the nature ofthe exciton ground state of the system can be qualitativelychanged in the strong light-matter coupling regime22, whenoptically active excitons are effectively hybridized with a spatiallyconfined photonic mode of a microcavity, giving rise to compo-site elementary excitations known as exciton-polaritons17,23,24.Attempts to engineer the emission properties of organic mole-cules via the inversion of the singlet-triplet state configuration bystrong light-matter coupling were reported recently25,26. How-ever, for the cases studied thus far, the detailed analyses revealedthat the reverse intersystem crossing rates mostly remain invar-iant even as the lower polariton energy is pushed below the tripletenergy26, calling for further engineering efforts. We demonstratethe phenomena of the brightening by analyzing the temperaturedependence of the photoluminescence (PL) from a WSe2monolayer, showing that the trend of the rapid decrease of PLintensity with decreasing temperature is inverted if a WSe2monolayer is placed inside a high finesse optical cavity. Wesupport this remarkable experimental finding by theoreticalmodelling of the dynamics of the mode occupancies in bothregimes.ResultsExperimental geometry and brightening mechanism. In Fig. 1a,we show the experimental system consisting of two distributedBragg reflectors (DBRs) with a WSe2 monolayer flake situated inthe antinode of the confined electromagnetic mode. The flake ofWSe2 is mechanically exfoliated from a bulk crystal and it iscapped with hexagonal boron nitrite (h-BN) via a deterministicdry-transfer method. Both DBRs are composed of SiO2/TiO2, thecorresponding Bragg wavelength is 750 nm. An optical micro-scope image of the sample is displayed in Fig. 1b. The WSe2monolayer flake, indicated with a dashed yellow line, forms afinite-size trap for exciton-polaritons, with a size of ~10 × 7 μm2.The brightening mechanism in WSe2 monolayers in the stronglight-matter coupling regime is illustrated in Fig. 1c. Thesequence of the two lowest dark Dj i and bright Xj i excitonstates at the K-point is given in the left panel. The spins of anelectron and a hole in the ground state (brown line) areantiparallel to each other, and direct optical excitation of thissinglet configuration is forbidden in the electric dipole approx-imation, making the ground state optically dark. The energy ofthe optically active triplet state (orange line) is ~40 meVhigher21,27.If a WSe2 monolayer is placed inside an optical microcavity,the strong light-matter coupling can dramatically reshape theenergy spectrum of the system, as it is illustrated in the rightpanel of Fig. 1c. Indeed, bright excitons interact with cavityphotons, giving rise to upper and lower polariton (UP and LP)modes. The Rabi splitting between these two hybrid modes ΩR,depends on the excitonic oscillator strength and cavity qualityfactor. If ΩR is sufficiently large, one can push the LP energybelow the dark exciton energy, reversing the energy levelordering: From one characteristic for an optically dark material,to a corresponding bright one. Note, that the LP energy can betuned not only by changing the Rabi splitting but also bychanging the relative detuning between the bare photon andexciton modes.We use angle-resolved photoluminescence spectroscopy tostudy the optical properties of the coupled monolayer-microcavity system. The distribution of the PL intensity inenergy and momentum is shown in Fig. 2a. The finite size of theflake results in the discretization of the energy levels of lowerpolaritons28, which yields a dispersion-less ground state at1.610 eV. It furthermore yields a first excited state at 1.618 eV,with emission maxima at finite k-values, and finally a continuousemission band at ∣k∥∣ > 2 μm−1. The full quantitative descriptionof the modes in connection with the precise shape of themonolayer is derived in ref. 29 by accounting the energy spectrumof polaritons in the presence of an external potential V(r) vianumerically solving a Schrödinger equation for polaritons. Theslightly asymmetric distribution of PL intensity at high energyresults from the irregular geometry of WSe2 flake, as discussed indetail in ref. 29.We notice, that the model which we apply in Supplementarysection 2 is a simplified and less technical, yet analogous approachbased on the discretization of the photon field as prior to thecoupling to the excitons. In the model, the discretization isconsidered first in the photon field: due to the lateral confinementof the cavity and the flake, the photonic modes are essentiallydiscretized. This discretization of photon modes then translatesinto the discretized polariton spectrum. Hence, this model is areduced version of the full solution to the Schrödinger equation.It is important to point out, that these two formulations areequivalent and yield the same polaritonic ground and first excitedstates.To fit experimental data, we use the two coupled oscillatormodel, with parameters extracted from the experimental data.The energies of the bright exciton (X) and cavity photon (C) are1.660 eV and 1.614 eV, respectively, the Rabi splitting is 41 meV.Due to the red-detuned conditions of our microcavity, and thefact that polaritons efficiently populate the ground-state of thepolariton trap, a direct verification of strong coupling conditionsvia mapping of the Rabi-splitting is difficult. However, it is stillpossible to directly verify the strong coupling conditions of ourTMDC-cavity system unambiguously by resorting to magneticfield measurements: in atomically thin TMDCs, the valleypseudospin is associated with magnetic moments30,31. SinceARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30645-52 NATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsFig. 1 Sample structure and brightening mechanism. a Schematic illustration of sample structure with a WSe2 monolayer, capped with h-BN, andembedded between two dielectric DBRs. Two arrows represent the Rabi oscillation between excitons and microcavity photons. b Optical microscopicimage of the sample. The WSe2 monolayer and h-BN boundaries are indicated with yellow and white dashed lines, respectively. c Scheme of WSe2 groundstate brightening via strong coupling. In pristine WSe2 monolayers, the optically dark exciton Dj i (brown line) is the lowest transition at the K-point, whichlies ~40meV below the bright exciton Xj i (orange line). Exciton-polaritons are formed when optically bright excitons strongly couple to microcavityphotons, the corresponding energy diagram is enclosed in a dashed box. The energy level of the resulting lower polaritons LPj i can be located below thedark exciton state Dj i, as long as the Rabi splitting ΩR is sufficiently large. The lower polariton branch, which inherits the spin character from the brightexciton, becomes the ground state of the coherently dressed system. Thus, the band ordering is reversed, and the intrinsically dark 2D semiconductor iseffectively brightened via the strong coupling with microcavity photons.Fig. 2 Polariton dispersion relation and valley-Zeeman effect. a Dispersion relation of exciton-polaritons at ambient conditions. The exciton (X) andmicrocavity photon (C) are represented by dotted and dashed lines, respectively. The dark exciton is marked as D. The upper and lower polariton (UP andLP) branches are plotted as solid lines. The discrete energy modes of LP are a typical dispersion relation of polaritons confined at a finite-size trap.b Normalized circularly polarized PL intensity spectra of exciton-polaritons under a magnetic field at room temperature. These spectra are extracted fromthe dispersion relations at zero in-plane momentum k∥= 0. From top to bottom panels, the applied magnetic field is +9, 0 and −9 T, respectively. σ+ (σ−)denotes the emission of light with right (left)-hand circular polarization. An energy splitting is observed under the application of magnetic fields.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30645-5 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 |www.nature.com/naturecommunications 3www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsexciton-polaritons inherit the spin from excitons, they alsoexperience the valley-Zeeman effect, similar to bare excitons. Incontrast, the effect is obsolete for cavity photons32, renderingmagnetic measurement a powerful and elegant tool to distinguishhybrid exciton-polaritons from pure photonic modes.In Fig. 2b, we plot circularly polarized components of the PLrecorded in the external magnetic field. For the sake of clarity,both components have been normalized in their intensity. Theslight energy offset between the two panels is induced by thereduction of air pressure in our experimental apparatus whichrenormalizes the cavity energy (see Supplementary Fig. S2 formore details). One clearly sees the energy splitting of ~0.5 meVbetween σ+ and σ− polarized components in the magnetic field of+9 T (top panel), which unambiguously indicates the presence ofthe excitonic component. As expected, the sign of the Zeeman-splitting is changed if the direction of magnetic field is inverted(−9 T, bottom panel). It is worth noting, that the effect persistsfor weak pump powers, as shown in Supplementary Fig. S3. Wehave demonstrated that our sample exhibits macroscopic phasecoherence29, which rules out the purely excitonic behaviour.Considering the sample simultaneously presents the Zeemansplitting and macroscopic phase coherence, its polaritonic originis unambiguously proved.Manifestation of the ground state brightening. To demonstratethe brightening effect in the regime of the strong light-mattercoupling, we compare the temperature-dependent PL for theisolated WSe2 flake and the flake placed inside the microcavity.The characteristic temperature-dependent exciton response hasbeen employed previously to verify the conduction band inver-sion in MoWSe2 alloy monolayers9.We first turn our attention to the investigation of the bareexciton response of a pristine WSe2. To warrant a validcomparison, the WSe2 monolayer is exfoliated from the samecrystal and transferred on an identical DBR as that used in ourpolariton sample. Again, the monolayer is capped by a thin h-BNlayer. Throughout our experiments, we used a non-resonantcontinuous-wave laser at 532 nm focused on a spot of ~3 μmdiameter to excite the sample (see more details of the setup in the“Methods” section).Figure 3a–c shows the PL intensity distribution of the pristineWSe2 monolayer for three temperatures, 150, 50 and 10 K. Thepump power is kept at 30 μW (see more details in “Methods”section). At 150 K, one clearly sees a strong PL signal from theflake region at the energy corresponding to the bright excitonwith a broad emission tail at lower energies, which is probablyassociated with trions and spectrally broad defect-induced PL. Asthe temperature is reduced down to 50 K and finally 10 K, theexciton energy is blue-shifted by tens of meV33, and thecorresponding emission intensity is reduced by a factor of 20due to the fast non-radiative relaxation to the spin-forbidden darkground state10. Note that also the dark exciton substantially blue-shifts upon temperature reduction.The angle-resolved PL spectra for the WSe2 flake inside themicrocavity at the same temperatures are presented in Fig. 3d–f.To show the polaritonic data clearly, the photon energy scale iszoomed-in in panels g–i. The LP energy position is mainlydefined by the cavity mode, which is unaffected by thetemperature changes, and thus the thermal blueshift of LP isseverely reduced with respect to that of the bare exciton. Thedetailed analysis of the peak corresponding to the ground state ispresented in Supplementary Fig. S4. Most interestingly, the LPphotoluminescence strongly increases in intensity with decreasingtemperatures: The maximal emission intensity of the polaritonground state at 10 K is four times larger than that at 150 K, whileit is enhanced by seven times for the first excited polariton state inthe trap. This opposite temperature dependence of PL clearlyindicates that the ground state of our hybrid system becomesoptically bright.In Fig. 4a, we present the integrated PL intensity from bareexcitons in a pristine WSe2 flake as a function of temperature.The integrated areas are displayed as dashed boxes in Fig. 3a–c.As the temperature is reduced from 200 to 10 K, the PL intensity(green circles) experiences an exponential drop, stemming fromthe fast relaxation towards the dark ground state10. As shown inthe left inset of Fig. 4a, the presence of dark excitons at energiesthat lie below bright excitons, suggests preferential population ofthe dark state with the reduction of temperature. The quenchedlight emission at low temperatures can be thermally activatedfollowing the Boltzman distribution10. The slight intensityreduction in the region from 200 to 270 K was previouslyreported in flux-grown samples34, and was attributed to phonon-induced non-radiative channels. The schematic is displayed as theright inset of Fig. 4a. With the increase of temperature, acousticphonons start to participate in the scattering with bright excitons,yielding final states that are dark due to the momentum-forbidden condition. It is worth noting, that the precise trend isslightly dependent on the integration area, and there could besample-to-sample differences, depending on the method ofsample growth, exfoliation, etc, but the general phenomenon ofa generic intensity reduction is universally present10,34.We modelled this temperature dependence of the bare excitonPL by solving the system of rate equations corresponding to thephonon-assisted population relaxation in a pristine WSe2monolayer (see details in the Supplementary section 1). In thismodel, two kinetic equations are considered, which representexciton occupancies of the bright and dark states. The brightexciton scatters into dark exciton by emitting a phonon, with arate that depends on the bare exciton-phonon scattering rate W0.The model fit is shown as a solid curve in Fig. 4a, closelyreproducing the experimental trend. One clearly sees the thermalactivation of the PL in the range from 10 to 200 K. Above thistemperature, due to the relaxation into momentum-forbiddendark states that lie outside the light cone, the depletion of bright-exciton starts to play a role, which results in the slow decrease ofPL in the range between 200 and 270 K.The temperature dependence of the PL intensity in the strongcoupling regime is presented in Fig. 4b, and clearly displays theopposite trend. The data for both trapped polariton states, groundstate (blue squares) and the first excited state (red diamonds), aresimilarly analyzed and plotted. These polariton states showsimultaneously a small intensity peak at around 225 K, whichreproduces the behaviour of bare excitons. Below 150 K thepolariton PL dramatically enhances with reduced temperature,clearly demonstrating the brightening effect of the polaritonground state. Furthermore, we analyze the intensity of higherenergy states that range from 1.64 to 1.66 eV in SupplementaryFig. S6. Its temperature dependence exhibits the same result as theground and first excited states in Fig. 4b. Those higher energystates lie below the dark exciton, and polaritons relax into theground state in a dynamic, cascaded manner. As such, it is naturalto encounter increase of luminescence intensity of higherpolariton states.The results of the theoretical modelling based on a system ofrate equations are shown by solid curves in Fig. 4b (see the detailsin the Supplementary section 2) and are in good quantitativeagreement with the experimental data. In the simulations, weaccount for the ground and first excited cavity modes, and thusconsider three polariton states. The resulting system contains fourequations describing the transitions between dark exciton andpolariton branches (Supplementary section 2). The equation forARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30645-54 NATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 | www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsFig. 3 Temperature-dependent PL of bare excitons and exciton-polaritons. a–c Real-space resolved PL intensity distribution of a pristine WSe2 monolayerflake as a function of energy at temperatures 150, 50 and 10 K, respectively. The emission of bare excitons becomes dimmer as temperature decreases: thehallmark of a dark exciton ground-state. d–f Polariton dispersion relations recorded at 150, 50 and 10 K. In contrast to bare excitons, the LP luminescencesignificantly increases at low temperatures, behaving in the same manner as that of a bright material. g–i The zoom-in images of panels (d–f) in energy.The highlighted boxes are analysis regions of integrated intensity in Fig. 4.Fig. 4 Integrated PL intensity of bare excitons and exciton-polaritons as a function of temperature. a Temperature-dependent emission intensity of bareexcitons in pristine WSe2 monolayer. The experimental data are shown as green circles, and the corresponding integration regions are marked as dashedboxes in Fig. 3a–c. The solid curve represents the result of a theoretical modelling (see main text). The mechanism of PL intensity for different temperatureranges is shown as insets: thermal activation (10–200 K) and relaxation into momentum-forbidden dark states (200–270 K). b Temperature-dependent PLemission intensity of exciton-polaritons. The experimental data of the ground state and first excited state are shown as blue squares and red diamonds,respectively. The integration region of the ground state (first excited state) is indicated with a dashed (dotted) box in Fig. 3g–i. The solid curves are fits ofthe theory model. The strong PL intensity at low temperatures evidences the brightening effect of intrinsically dark exciton. The error bars are obtained bycomparing the signal intensity to the standard deviation of the background noise.NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30645-5 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 |www.nature.com/naturecommunications 5www.nature.com/naturecommunicationswww.nature.com/naturecommunicationsthe ground state occupancey reads:_nL ¼ �nL=τL þ X2LPeff �WL!DðnD þ 1ÞnL þWD!LðnL þ 1ÞnDð1Þwhere τ�1L ¼ X2Lτ�1nr þ C12Lτ�1c1 þ C22Lτ�1c2 , XL, C1L, C2L are thecorresponding Hopfield coefficients, and W are the phonon-assisted inelastic scattering rates, the expressions for which arepresented in the Supplementary section 2.To account for the fast thermalization of non-resonantlypumped excitons, which leads to the decrease of the fraction ofthe thermal excitons lying within the light cone and formingpolaritons with temperature, we introduce the effective pumpingPeff which is expressed as:Peff � PϵlckBT; ð2Þwhere ϵlc is the energy of the excitons corresponding to thewavevector of light in the material,ϵlc ¼_22MexcεTiO2ðωx=cÞ2 � 58 μ eV � 0:6K: ð3ÞThis approximation holds for T≫ 0.6 K.As lower polariton states at around k∥= 0 have energies farbelow the dark exciton energy, LP can be effectively populated byinelastic processes of phonon emission. Thus, differently from thecase of bare excitons, most of the bright excitons contribute to thePL signal via polariton emission at low temperatures, whichexplains the rapid increase of PL intensity with the decreasingtemperature. In this work, we study temperature-dependentpolariton emission while the Rabi-splitting remains approxi-mately constant. Similarly, we believe that tuning of the Rabi-splitting, e.g., using an open-cavity35 at constant temperaturecould be an alternative method to probe the brightening effect.In strongly coupled organic microcavities, the reverse inter-system crossing rates are unchanged because of the delocalizationnature of polaritons26,36. In this work, however, we find thestrong coupling is a feasible approach. Two possible reasons maybe attributed: (1) the spatial confinement of polaritons, whichfacilitates polaritonic relaxation to the ground state via phonons,(2) the high-quality factor of optical cavity, which prolongslifetimes of polaritons.DiscussionIn summary, we demonstrate the possibility to effectivelybrighten an intrinsically dark semiconductor monolayer by pla-cing it inside a resonantly tuned optical microcavity in the regimeof strong light-matter coupling.In our experiments, we utilize a WSe2 monolayer flake, whichfeatures the spin-forbidden dark exciton ground state, separatedfrom the bright state by an energy of ~40 meV. This splitting iscomparable with the vacuum Rabi-splitting characteristic to theresonant coupling of bright excitons with cavity photons, whichallows to push the energy of the lower polariton below the energyof the dark exciton. As a consequence, the ground state of thesystem becomes bright, and instead of showing a PL quenching,characteristic for pristine WSe2 monolayers, we observe a strongPL enhancement with decreasing temperature, due to the fast andefficient phonon-assisted energy relaxation.In a broader scale, our approach for band-structure engineer-ing aligns with contemporary efforts to tune transport, topolo-gical and magnetic properties of low dimensional materials usingthe fundaments of cavity quantum electrodynamics.MethodsSample fabrication. The bottom DBR, composed of 10 pairs of SiO2/TiO2 layers,is obtained commercially from Laseroptics GmbH. The mechanically exfoliatedWSe2 monolayer is capped by a ~5 nm h-BN multilayer via the deterministic dry-transfer method. The top DBR is evaporated by an ion-assisted physical vapourdeposition process37, consisting of 9 pairs of SiO2/TiO2 layers: the SiO2 layer incontact with h-BN is 105 nm in thickness, and the thickness of each repetitive pairis 129 and 83 nm, respectively (more details are described in ref. 29). The controlsample constituted by a pristine WSe2 monolayer is also mechanically exfoliatedfrom a bulk crystal. It is dry-transferred onto another identical DBR. An h-BNmultilayer with similar thickness ends the final capping.Experimental setup. A standard back Fourier plane imaging setup is utilized toperform angle-resolved PL measurements. The excitation source is a continuous-wave (CW) 532 nm laser, and it is focused on the sample by a long working-distance objective (Mitutoyo M Plan Apo NIR 50×, NA= 0.42). The charge-coupled device (CCD) of Andor (iDus 416) is attached to a spectrometer (Sham-rock 500i). Its sensor is operated at −80 ∘C. A 600 nm longpass filter of Thorlabs(FELH0600) is used to block the green laser from reaching the CCD. In themeasurements of Fig. 3a–c, the pump power is kept at 30 μW, and the exposuretime is 2 s. In the measurements of Fig. 3d–f, the pump power is 30 μW and theexposure time is increased to 10 s, to compensate for the less efficient light-collection in the back-fourier plane imaging configuration. To carry outtemperature-dependent experiments, the sample is mounted on a motorized XYstage of a customized low-vibration cryostat from ColdEdge. The available lowesttemperature is 10 K, and the temperature of the sample is adjusted by a Lakeshoretemperature controller (Model 335). The magnetic measurements are performed atroom temperature using an attoDRY2100. A CW 532 nm laser excites the sample,and a set of quarter waveplate, half waveplate as well as linear polarizer in thecollection path is used to detect circularly polarized PL emission. In magnetic fieldmeasurements, the used pump power is 100 μW and the exposure time is 120 s.Data availabilityThe data that support the findings of this study are available from the correspondingauthors upon reasonable request.Received: 26 December 2021; Accepted: 11 May 2022;References1. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: anew direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).2. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductortransition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).3. Xia, F., Wang, H., Xiao, D., Dubey, M. & Ramasubramaniam, A. Two-dimensional material nanophotonics. Nat. Photonics 8, 899–907 (2014).4. Chernikov, A. et al. Exciton binding energy and nonhydrogenic rydberg seriesin monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).5. Wang, G. et al. Colloquium: Excitons in atomically thin transition metaldichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).6. Novoselov, K. 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Integration of atomically thin layers of transition metaldichalcogenides into high-Q, monolithic bragg-cavities: an experimentalplatform for the enhancement of the optical interaction in 2D-materials.Optical Mater. Express 9, 598–610 (2019).AcknowledgementsThe authors gratefully acknowledge funding by the State of Lower Saxony. Fundingprovided by the European Research Council (ERC project 679288, unlimit-2D) isacknowledged. C.S. and B.H. acknowledge financial support by The German ResearchFoundation (DFG) (SCHN1376/14-1, SPP 2244). S.H. acknowledges financial support bythe DFG (HO 5194/16-1) and INST 93/932-1 FUGG. H.S. acknowledges the Sino-Germany (CSC-DAAD) Postdoctoral Scholarship Program from China ScholarshipCouncil and German Academic Exchange Service. I.I. and I.A.S. acknowledge the sup-port from the joint RFBR-DFG project No. 21-52-12038. I.I. acknowledges the supportMinistry of Science and Higher Education of Russian Federation, goszadanie no. 2019-1246. S.T acknowledges support from DOE-SC0020653 (materials synthesis), AppliedMaterials Inc., NSF CMMI 1825594 (NMR and TEM studies), NSF DMR-1955889(magnetic measurements), NSF CMMI-1933214, NSF 1904716, NSF 1935994, NSF ECCS2052527, DMR 2111812, and CMMI 2129412. K.W. and T.T. acknowledge support fromthe Elemental Strategy Initiative conducted by the MEXT, Japan (Grant NumberJPMXP0112101001) and JSPS KAKENHI (Grant Numbers JP19H05790 andJP20H00354). M.E. acknowledges funding by the University of Oldenburg through aCarl-von-Ossietzky fellowship. F.E. and H.K. are supported by the Federal Ministry ofEducation and Science of Germany under Grant ID 13XP5053A.Author contributionsThis work was initialized and guided by C.S. The experiments were conducted by H.S.,B.H. and C.A.-S. The magnetic field measurements were carried out by H.S. and C.A.-S.,supervised by S.K. and S.H. The data analysis was performed by H.S., C.S., M.E. andC.A.-S. The TMDC [h-BN] crystals were produced by K.Y. and S.T. [K.W. and T.T.]. Thesample was fabricated by C.R., and further processed by H.K. and F.E. The theory andsimulations were performed by I.I., under the supervision of I.A.S. The manuscript waswritten by C.S., H.S., I.I., I.A.S. and C.A.-S., with input from all the co-authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41467-022-30645-5.Correspondence and requests for materials should be addressed to Christian Schneider.Peer review information Nature Communications thanks Vasil Saroka and the other,anonymous, reviewer(s) for their contribution to the peer review of this workReprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-022-30645-5 ARTICLENATURE COMMUNICATIONS |         (2022) 13:3001 | https://doi.org/10.1038/s41467-022-30645-5 |www.nature.com/naturecommunications 7https://doi.org/10.1038/s41467-022-30645-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunicationswww.nature.com/naturecommunications Brightening of a dark monolayer semiconductor via strong light-matter coupling in a cavity Results Experimental geometry and brightening mechanism Manifestation of the ground state brightening Discussion Methods Sample fabrication Experimental setup Data availability References References Acknowledgements Author contributions Competing interests Additional information