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[Leyi Loh](https://orcid.org/0000-0002-6315-7545), [Yi Wei Ho](https://orcid.org/0000-0002-5487-4948), [Fengyuan Xuan](https://orcid.org/0000-0002-0624-882X), Andrés Granados del Águila, [Yuan Chen](https://orcid.org/0009-0009-0835-3680), See Yoong Wong, Jingda Zhang, [Zhe Wang](https://orcid.org/0000-0001-6485-1523), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Paul J. Pigram](https://orcid.org/0000-0002-7972-492X), Michel Bosman, [Su Ying Quek](https://orcid.org/0000-0003-4223-2953), [Maciej Koperski](https://orcid.org/0000-0002-8301-914X), [Goki Eda](https://orcid.org/0000-0002-1575-8020)

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[Nb impurity-bound excitons as quantum emitters in monolayer WS2](https://mdr.nims.go.jp/datasets/1414b237-1840-44da-b2fd-9e4325f57980)

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Nb impurity-bound excitons as quantum emitters in monolayer WS2Article https://doi.org/10.1038/s41467-024-54360-5Nb impurity-bound excitons as quantumemitters in monolayer WS2Leyi Loh 1,2,11, Yi Wei Ho 1,3,11, Fengyuan Xuan 4,11,Andrés Granados del Águila3, Yuan Chen 5, See Yoong Wong6, Jingda Zhang1,Zhe Wang 5, Kenji Watanabe 7, Takashi Taniguchi 8, Paul J. Pigram 6,Michel Bosman2, Su Ying Quek 1,2,4,9,10 , Maciej Koperski 2,3 &Goki Eda 1,4,5Point defects in crystalline solids behave as optically addressable individualquantum systems when present in sufficiently low concentrations. In two-dimensional (2D) semiconductors, such quantum defects hold potential asversatile single photon sources. Here, we report the synthesis and opticalproperties of Nb-doped monolayer WS2 in the dilute limit where the averagespacing between individual dopants exceeds the optical diffraction limit,allowing the emission spectrum to be studied at the single-dopant level. Weshow that these individual dopants exhibit common features of quantumemitters, including narrow emission lines (with linewidths <1meV), strongspatial confinement, and photon antibunching. These emitters consistentlyoccur within a narrow spectral range across multiple samples, distinct fromcommon quantum emitters in van der Waals (vdW) materials that show largeensemble broadening. Analysis of theZeeman splitting reveals that they canbeattributed to bound exciton complexes comprising dark excitons and nega-tively charged Nb.Defects in crystalline semiconductors are quantum systems thatpossess unique local electronic structures. When sufficiently iso-lated from one another, these defect-derived states can be indivi-dually addressed by optical means. The quantum nature of suchisolated defects manifests in non-classical statistics of emittedphotons, which is of fundamental importance to quantumtechnologies1. Intentional incorporation of dilute impurities is apromising approach to achieving single photon emission as pre-viously shown in various wide-bandgap materials2,3 and conven-tional semiconductors4,5.Two-dimensional (2D) semiconductors, such as monolayer tran-sition metal dichalcogenides (TMDs), are an attractive platform torealize single-photon sources by quantum defect engineering due totheir versatility and ease of integration into on-chip photonics6. Whilesingle photon emission inmonolayer semiconductors has been widelyreported, these emitters typically depend on naturally occurringdefects whose origins remain unclear7. The emitters therefore oftenlack spectrally deterministic character, displaying variability in theirenergy over tens of millielectronvolts (meV). This variability, some-times referred to as ensemble broadening, describes the energyReceived: 28 May 2024Accepted: 8 November 2024Check for updates1Department of Physics, National University of Singapore, Singapore, Singapore. 2Department of Materials Science and Engineering, National University ofSingapore, Singapore, Singapore. 3Institute for Functional IntelligentMaterials, National University of Singapore, Singapore, Singapore. 4Centre for Advanced2D Materials, National University of Singapore, Singapore, Singapore. 5Department of Chemistry, National University of Singapore, Singapore, Singapore.6Centre forMaterials andSurfaceScience, andDepartment ofMathematical andPhysical Sciences, La TrobeUniversityMelbourne,Melbourne, VIC, Australia.7Research Centre for Functional Materials, National Institute for Materials Science, Tsukuba, Japan. 8International Centre for Materials Nanoarchitectronics,National Institute for Materials Science, Tsukuba, Japan. 9NUS Graduate School, Integrative Sciences and Engineering Programme, National University ofSingapore, Singapore, Singapore. 10NUS College, National University of Singapore, Singapore, Singapore. 11These authors contributed equally: Leyi Loh, YiWei Ho, Fengyuan Xuan. e-mail: phyqsy@nus.edu.sg; msemaci@nus.edu.sg; g.eda@nus.edu.sgNature Communications |        (2024) 15:10035 11234567890():,;1234567890():,;http://orcid.org/0000-0002-6315-7545http://orcid.org/0000-0002-6315-7545http://orcid.org/0000-0002-6315-7545http://orcid.org/0000-0002-6315-7545http://orcid.org/0000-0002-6315-7545http://orcid.org/0000-0002-5487-4948http://orcid.org/0000-0002-5487-4948http://orcid.org/0000-0002-5487-4948http://orcid.org/0000-0002-5487-4948http://orcid.org/0000-0002-5487-4948http://orcid.org/0000-0002-0624-882Xhttp://orcid.org/0000-0002-0624-882Xhttp://orcid.org/0000-0002-0624-882Xhttp://orcid.org/0000-0002-0624-882Xhttp://orcid.org/0000-0002-0624-882Xhttp://orcid.org/0009-0009-0835-3680http://orcid.org/0009-0009-0835-3680http://orcid.org/0009-0009-0835-3680http://orcid.org/0009-0009-0835-3680http://orcid.org/0009-0009-0835-3680http://orcid.org/0000-0001-6485-1523http://orcid.org/0000-0001-6485-1523http://orcid.org/0000-0001-6485-1523http://orcid.org/0000-0001-6485-1523http://orcid.org/0000-0001-6485-1523http://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/0000-0002-7972-492Xhttp://orcid.org/0000-0002-7972-492Xhttp://orcid.org/0000-0002-7972-492Xhttp://orcid.org/0000-0002-7972-492Xhttp://orcid.org/0000-0002-7972-492Xhttp://orcid.org/0000-0003-4223-2953http://orcid.org/0000-0003-4223-2953http://orcid.org/0000-0003-4223-2953http://orcid.org/0000-0003-4223-2953http://orcid.org/0000-0003-4223-2953http://orcid.org/0000-0002-8301-914Xhttp://orcid.org/0000-0002-8301-914Xhttp://orcid.org/0000-0002-8301-914Xhttp://orcid.org/0000-0002-8301-914Xhttp://orcid.org/0000-0002-8301-914Xhttp://orcid.org/0000-0002-1575-8020http://orcid.org/0000-0002-1575-8020http://orcid.org/0000-0002-1575-8020http://orcid.org/0000-0002-1575-8020http://orcid.org/0000-0002-1575-8020http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54360-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54360-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54360-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-54360-5&domain=pdfmailto:phyqsy@nus.edu.sgmailto:msemaci@nus.edu.sgmailto:g.eda@nus.edu.sgwww.nature.com/naturecommunicationsdistribution of individually addressable emitters. It arises from non-uniform strain, dielectric environment, and electrical potential acrossthe sample. Recently, defect engineering by ion beam irradiation hasbeen shown to reduce the ensemble broadening of the emitters tosomeextent8,9. Impurity doping is an alternative approach to achievingvirtually identical emitters. However, maintaining precise control overimpurity concentrations within the parts-per-million (ppm) range,where quantum emission characteristics are expected, remains achallenge10,11.Here, we demonstrate the synthesis of Nb-dopedmonolayerWS2 indilute dopant concentrations and investigate its optical response as itapproaches the single impurity limit. We show that Nb dopantsmanifestas an intense, inhomogeneously broadened emission peak below thefree exciton lines at high concentrations. In contrast, at concentrationsapproaching a few ppm, they manifest as a single, spectral-resolution-limited peak. In this dilute limit, the emitters exhibit photon antibunch-ing and ensemble broadening below 5meV, which ismore than an orderof magnitude smaller than that of strain-induced emitters. Further, weshow that these quantum emitters can be best described as boundexciton complexes with partially free dark exciton character.ResultsSynthesis of WS2 monolayers with tunable Nb dopingNb is known to be an acceptor dopant in group six TMDs, char-acterized by its high solubility up to alloying limits12,13. While Nbdoping in monolayer TMDs has been demonstrated previously13,14,dilute doping at levels below 1011 cm−2 remains largelyunexplored11,15. In this study, we prepare Nb-doped WS2 by chemicalvapor deposition (CVD) in vapour-liquid-solid mode using liquid-phase metal precursors as established in our previous works12,16,17.To achieve controlled doping in the dilute limit, we apply serialdilutions of the Nb precursor solution across five orders of magni-tude prior to its mixing with the W host precursor solution. Themixture is then drop-cast onto a SiO2/Si substrate and reactedwith Svapor at 850 oC to yield monolayer WS2 crystals with Nb con-centrations ranging from 1013 cm−2 down to 108 cm−2 (see Supple-mentary Fig. 1 and Methods for detailed synthesis protocols). Thesynthesized monolayer crystals are lifted off from the growth sub-strate and encapsulated between hBN layers to minimize extrinsicdisorder (Fig. 1a, see Supplementary Fig. 2 for fabrication details).To ensure the absence of local strain, which can yield unintentionallocalized emitters18, the encapsulated samples are flattened with anatomic force microscope (AFM) tip. The flattened regions of thesample show a smooth surface with sub-nanometer roughness overseveral micrometer lengths (Fig. 1b).Atomic-resolution Z-contrast imaging ofmonolayer samples usinghigh-angle annular dark field-scanning transmission electron micro-scopy (HAADF-STEM) shows that all Nb atoms are substitutional at theWposition (Fig. 1c). The Nb concentration, as determined from a seriesof scanning transmission electronmicroscopy (STEM) images (Fig. 1d),104 ppm Nb1000 ppm Nb10 ppm Nba c 107 108 109 1010 1011 1012 1013 (cm-2)Ar + H2S powderW S2 NbII) Drop cast10,000-fold dilutionW solution with ultra-dilute NbSiO2/Si substrateIII) CVD reactionIV) Encapsulation + AFM tip cleaninghBN top and bottom layersbsample Height (nm)010I) Solution preparationscan0 1 2 3 4-0.8-0.40.00.40.81.2)mn(thgieHDistance (µm)Nb solution0.0 0.5 1.0 1.5 2.00.00.40.8)stinu.bra(ytisnetnIPosition (nm)NbdFig. 1 | Dilution of Nb dopants in WS2 monolayers. a Schematic illustrationdepicting the preparation of WS2 monolayers with ultra-dilute Nb dopants. CVDdenotes chemical vapour deposition andAFMrepresents atomic forcemicroscopy.bAFMheight imageof the encapsulated sample after tip cleaning. Shownbelow theimage is the height profile along a line crossing the sample, with its position indi-cated on the image. Scale bar is 1 µm. c Magnified high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) image of Nb dopant intheWS2, accompanied by the corresponding intensity profile integrated across therow of W atoms where the Nb is situated. d A series of HAADF-STEM imagesacquired on Nb-doped WS2 samples at different doping concentrations. Scale baris 1 nm.Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 2www.nature.com/naturecommunicationsexhibits a linear relationship with the nominal Nb concentration in theprecursor mixture (Supplementary Fig. 3).Emitter distributionRepresentative photoluminescence (PL) spectra of the samples areshown in Fig. 2a. Nb-doped samples exhibit low energy emission fea-tures below 1.95 eV that are absent in undoped samples. The intensityof the broad low-energy emitter (NbXG) scales with the Nb con-centrations, indicating that these emitters arise from transitionsinvolving a large number of Nb centers (Supplementary Fig. 4). In thedilute doping regime of 5 ppm and below, the intensity of the sharplow-energy peaks (NbXL) remains largely constant but their occur-rence decreases with dopant concentration (Fig. 2c). This observationsuggests that each spatially isolated NbXL peak is associated with oneor a few emissive dopants within the excitation spot.Samples with Nb concentrations equal to or exceeding 50 ppmpredominantly display broad emission features with linewidths ofapproximately 20meV at 4 K. The peaks can be fitted with a fewGaussian functions, indicating that inhomogeneous broadeningdefines their line shape (Fig. 2b). The appearance of multiple peaksmay be attributed to various Nb defect configurations such as Nb-S-vacancy pairs (Supplementary Fig. 5) and Nb-dimers (SupplementaryFig. 6), which become appreciable at higher Nb concentrations. Con-sequently, the Nb-derived emission is more prone to disorder broad-ening with increasing Nb-doping (see Supplementary Note 1 fordetails). In contrast, samples with estimated Nb concentrations of 5and 0.1 ppm exhibit sharp emission features with linewidths around310 µeV. These peaks exhibit Lorentzian line shapewith an asymmetrictail, indicating negligible inhomogeneous broadening contributions.Confocal PLmapping shows that the NbXG peaks appear uniformlyacross the samplewhereas theNbXL peaks are observed only at selectedspots (Fig. 2c). This trend is generally consistent with the expectedreduction in the number of Nb atoms within the laser spot withdecreasing concentration, approaching the limit of single emitters.Single photon characteristicsThe narrow emission peak in the 0.1 ppm sample (NbXL) can beattributed to individual Nb, given that the expected average distancebetween the impurities exceeds the diffraction limit of the excitationlaser. This peak displays blinking and spectral jittering (Fig. 3a), whichare common features of quantum emitters located close to the mate-rial surface. Under non-resonant continuous-wave (CW) laser excita-tion, the emitter saturates quickly with increasing laser power (Fig. 3b,Supplementary Fig. 7), in line with the relation for excitons bound to asmall number of defects that can be described as a two-level system19.This saturationbehavior is well describedby I = 2Isat=ð1 +Psat=PÞ, whereI (Isat) is the (saturated) PL intensity and P ðPsatÞ is the (saturating)excitation power. The extracted Psat is 0.5 µW, which is almost threetimes lower than the values reported for dilute chalcogen defects at adensity of 1010 cm−2 (i.e., 10 ppm) under similar excitationconditions20,21.The PL decay transient of the emitter (Fig. 3c) can be described bya triexponential decay function comprising fast (0.6 ns), moderate(80 ns), and long (1600ns) decay components. From the intensityratios, we attribute the long decay component to the broad back-ground emission and the shorter-lived components to the sharp Nbpeak (see Supplementary Note 2 and Supplementary Fig. 8 for moredetails). A delay time of 0.5 ns in the intensity peak relative to theexcitation pulse indicates the timebetween the excitongeneration andits capture by the Nb centers.We investigate the quantum nature of the emitter by collectingphotons in the spectral window of 10meV around the 1.92 eV peak andexamining their second-order autocorrelation function (g(2)(t)) with aHanbury Brown and Twist (HBT) interferometer. Due to the spectraloverlap of the long-lived broad background emission (see Supplemen-tary Note 3 for its origin), which is only weakly non-classical, and thesharppeakof interest, wedifferentiate their photon statistics byutilizingpulsed laser excitation and deconvoluting the g(2)(t) function accordingto the known lifetimes of the components. Specifically, we bin thecoincidence counts in 32 ns intervals alignedwith the excitation pulse tocapture thephoton statistics of the localizedNb-peak as shown in Fig. 3d(see Supplementary Note 4, Supplementary Fig. 9 and 10 for details).Comparisonof thezero-delaydipwith the integratedcounts atdelaysupto 200 µs yields g(2)(0) =0.27 ±0.22, revealing the single-photon natureof the NbXL peak, with an estimated quantum yield of ~10−5 (see Sup-plementary Note 5 and Supplementary Fig. 11).a b cX0NbXGpristine 0.1 ppm 5 ppm 50 ppm 500 ppm1.80 1.84 1.88 1.92 1.9603006009001200Exp01x(ytisnetnI3)stinu.braPhoton energy (eV)G1G2G3  G4FitNbXG1.910 1.915 1.920 1.9250306090120150 Exp)stinu.bra(ytisnetnIPhoton energy (eV)NbXL L1 L2 BG Fit NbXL1.90 1.95 2.00 2.051.90 1.95 2.00 2.05)stinu.bra(ytisnetniLPPhoton energy (eV)X0XXDX0D/DX0Dpristine0.1 ppm5 ppm50 ppm500 ppmNbXLNbXG10NormalizedintensityFig. 2 | Evolution of emission features as a function of Nb-doping. a Typicalphotoluminescence (PL) spectrum of WS2 monolayers with varying Nb-dopinglevels, with sharp Nb peak (NbXL) and broad Nb peak (NbXG) identified. Peakpositions related to neutral excitons (X0), negative trions (X�), dark trions (X�D),and dark excitons either in phonon replica form or bound to native defects(X0D/DX0D) are shown for reference. b Two distinct Nb-induced emissions—a NbXGpeak and a NbXL peak—each fitted with different functions. c PL intensity maps ofX0, NbXG and NbXL peaks in samples doped at different concentrations. Eachcolumn shows PL maps for different peak energies for the same sample. Thecontours of themonolayers are shown by white dashed lines. Black and grey pixelsdenote areas where the respective peaks were not detected: black for areas withinthe sample region and grey for areas outside the sample. The detection thresholdsfor X0 and bothNbpeaks (i.e., NbXG andNbXL) are set to 5% and 20%of the highestintensity in the map, respectively. Scale bar is 5 µm. Spectra in (a and c) wereobtained with a 473 nm continuous -wave (CW) laser with a power of 5 µW. Spectrain (b) were obtained with a 532 nm CW laser with a power of 0.5 µW. All measure-ments were conducted at a temperature of 4 K.Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 3www.nature.com/naturecommunicationsOrigin of the Nb-induced single photon emittersSubstitutional Nb impurities are known to be p-type dopants in group6TMDs10,12. Our gate-dependent PLmeasurements show that the diluteimpurities are not sufficient to compensate for the natural n-doping ofthe host, suggesting that all Nb atoms are negatively charged (Sup-plementary Figs. 12, 13). Such negatively charged acceptors are pre-dicted to trap free excitonswith a large binding energy, resulting in theformationof boundexciton complexes22.Weperformmagneto-opticalspectroscopy to verify the exciton character of the NbXL peak.Polarization-resolved PL spectra are obtained by exciting the samplewith linearly polarized light in the presence of an out-of-plane mag-netic field (B⊥) up to 9 T (Faraday configuration). Figure 4a shows thatthe NbXL peak exhibits a clear Zeeman splitting, resembling thatof spin-forbidden dark trion peak (XD-). The distinct splitting with the“cross” pattern (Fig. 4b) is consistent with the behavior of spin-forbidden dark excitons23–25. The g-factor of the NbXL is determined tobe ~ −10.4, comparable to that of X�D (g ~ −12.3) (Fig. 4c, SupplementaryFig. 14). This g-factor is similar to that of common quantum emitters inW-based TMDs (g = −8 ~ −13)26–28. Unlike the native and strain-inducedquantum defects in W-based systems, NbXL exhibits negligible zero-field splitting, which is a defining feature of neutral excitons trapped ina symmetric confining potential29. The negligible linear polarizationanisotropy from these emitters (Supplementary Fig. 15) is consistentwith the nonpolar nature of an isolated substitutional Nb defect.To further verify the origin of the NbXL peak, we analyze variousrecombination pathways involving Nb acceptors by comparing themeasured g-factorswith thoseobtained by first principles calculations.Our density functional theory (DFT) band structure with spin−orbitcoupling (SOC) for a 10 × 10 supercell with one Nb−1 ion substituting aW atom indicates that Nb-induced bands lie just below the valenceband maximum (VBM), hybridizing strongly with the valence bandstates (Fig. 4d). We compute the single-band g-factors for the VBM,conduction bandminimum (CBM), and theNb defect level (gVBM, gCBMand gNb, respectively). The Nb state predominantly comprises dz2orbitals and the corresponding g factor is small (gNb ~ −1.0 for spin upand 1.0 for spin downNb states, respectively). The total g-factor for thespin-allowed transition, involving an electron in the CBM recombiningradiatively with a hole at the Nb site amounts to ~ 7.0 for spin-up and ~7.6 for spin-down states, respectively. On the contrary, the g-factor forthe calculated spin-forbidden transition, which is ~ −9.4, largely agreeswith the experimental observation (Fig. 4e).We thus conclude that neutral dark excitons bound to ionizedNb, which may be denoted as Nb�X0D, best describes the origin ofthe NbXL peak. The brightening of dark excitons bound to Nbcenters can be ascribed to the hybridization of VBM with the Nbstates, breaking the valley selectivity and leading to an enhancedradiative recombination efficiency of the dark excitons7. Addition-ally, phonon-emitter coupling can also facilitate the formation of anadmixture of dark and bright excitons within the same valley30. Theenergy separation between X0D and NbX, which is the binding energyof the complex, is ~100meV. This large binding energy, distinctlygreater than that of dark trions (~20meV), agrees with the expec-tation that stationary charges are more effective in trapping exci-tons than free carriers22,31 (Fig. 4f).bc da 1.920 1.935 2.030 2.06501020304050Energy (eV))s(emiT10 Normalizedintensity050100150Coincidence- background (count)0 1 2 Exp. data               Lorentz fitg(2)(0) = 0.27 ± 0.220.00.51.0g(2)0.3 0.6 0.9 1.2 1.5 1.8 2.160090012001500180021002400)stinu.bra(y tis ne tn iLPLaser power (µW)Psat = 0.5 µW ± 0.2 )stinu.bra(ytisnetnIX0NbXLXTXSFig. 3 | Optical characteristics of theNb-induced singlephotonemitters. aTimeevolution of PL spectra highlighting the region of NbXL as well as free trions andneutral exciton peaks over 60 s. b Power dependence of the integrated PL signal.Error bars represent standard deviation of the fitted curves. Psat denotes thesaturating laser power of NbXL. c Time-resolved PL data fitted to a triexponentialfunction, revealing three distinct lifetime components: τ1, τ2, and τ3.The longcomponent (light grey curve) corresponds to the broadbackground (BG) feature inthebottompanel of 2b (i.e., the grey area underneath the sharpNbpeak). The sharpNb peak represents the single photon emitter (SPE). The instrumental responsefunction (IRF) of ~0.2 ns is also shown. The timedifference τ0 between the rise timeof the IRF and the emitter is indicated. d Second-order photon correlation of thetwo faster-decaying components marked with light and dark orange lines in (c).Intensity correlation shows antibunchingwith0.27 ±0.22 at zerodelay. Uncertaintyis obtained from the standard deviation of 390 peaks for t ≠0. A 532 nmCW laser isused in (a,b),whilst a pulsed laser tuned to theA-exciton resonance is used in (c,d).All measurements were conducted at 4 K.Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 4www.nature.com/naturecommunicationsEnsemble broadening of single emittersWe evaluate the spectral reproducibility of the NbXL in 0.1 ppm sam-ples in comparison with the state-of-the-art quantum emitters in rela-ted van der Waals (vdW) materials. In our study, NbXL peaks acrossmultiple samples consistently fall within an energy range of 20meV(Supplementary Fig. 16). Figure 5a shows the histogramdescribing thedistribution of 83 NbXL energies surveyed across four different sam-ples. Two distinct emitter clusters centred around 1.92 eV and 1.93 eVexhibit an ensemble broadening of 1.8 ± 0.7meV and ~3.5 ± 1meV,respectively. We speculate that these cluster originate from Nb indifferent chemical environment such as nearby surface functionalgroups and chalcogen-site defects.Figure 5b presents a comparison of the spectral reproducibility ofquantum emitters in various vdW materials, characterized by ensem-ble broadening at cryogenic temperatures (a more comprehensivesurvey is presented in Supplementary Table 1 and SupplementaryFig. 17). The comparison is made against different methods used toinduce emitters, such as strain32–35, beam irradiation9,36,37 and ionimplantation38. Notably, the ensemble broadening of NbXL is at leastone order of magnitude smaller than those of other emitters in 2DTMD systems9,32–34 and is comparable to state-of-the-art emitters inhBN, including those derived from known defect structures38,39 andproduced under refined synthetic conditions36,37. Moreover, our valuesare similar to those found in non-vdW systems with known impuritystructures, such as Cl-doped ZnSe quantum wells40, diamond hostingSiV centers41, and NV centers42. The overall trends suggest that dilutesubstitutional doping is a promising approach for generating energe-tically well-defined quantum emitters.DiscussionWe have demonstrated the bottom-up growth of monolayer WS2 withultra-dilute Nb dopants. In this concentration limit, individual Nb-derived states can be optically excited one at a time using a focusedlaser beam, resulting in single photon emission. Unlike point defects ininsulators, the excited Nb states are more accurately described asa trion-like bound exciton complex with partial free-exciton character.The binding energy of these complexes are few times greater than thatof trions, possibly due to their larger reduced mass.Our study represents the initial steps towards realizing a broadpalette of reliable and robust 2D quantum emitters. It is predicted1.920 1.925 1.930 1.935Photon energy (eV))stinu.bra(ytisnetniLP9 T4.5 T0 T-4.5 T-9 TNbXL0 2 4 6 8 10-6-5-4-3-2-10)Vem(gnittilpsnameeZB  (T)g = -10.4 ± 0.3 1.920 1.932 2.024 2.070-8-6-4-202468Photon energy (eV)B (T)10Normalizedintensitya b c= 1.0= 7.2= 2.5= 4.8ExcitonenergyNbd f80 meV20 meVDistance= 4.6= -1.0e-1.0-0.50.00.51.01.5)Ve(ygrenEW totalNbtotalNb )stinu.bra(ytisnetnINbXLXGXDX0DXSXTX0Fig. 4 | Origin of the localized Nb emitters. a Colour plot of the polarization-resolvedmagneto-PL spectra of a dilute Nb-doped samplemeasured in the Faradayconfiguration. The spectrum in the upper panel shows the PL spectrum at 0 T.b PLspectra of NbXL at selected fields (B⊥), with the splitting of NbXL tracked withdashed lines. c Zeeman splitting of NbXL as a function of B⊥, where the g-factor isderived from the linear fit (red line).Magneto-PLmeasurements were conducted ata temperature of 1.6 K with a 532 nm CW laser. d Density functional theory (DFT)band structure with spin-orbit coupling (SOC) for a 10 × 10 supercell of WS2 withone Nb−1-substituted W atom, is shown on the left panel. The corresponding pro-jected density of states (pDOS) of the total orbital and orbital contributions of Nb−1which are overlayedover the total density of states (DOS) ingrey shade, is shownonthe right panel. e Schematic of the band structure at K’ with the single-band g-factors. g"ð#ÞCBM represent the spin-up (spin-down) g-factor of conduction bandminimum (CBM) bands, g"ð#ÞVBM represents the spin-up (spin-down) g-factorof valencebandmaximum(VBM)bands, and g"ð#ÞNb represents the g-factor of spin-up(spin-down) Nb defect bands. The optical transition responsible for NbXL is alsoshown. f Schematic illustration of the excitons diffusing (denoted by the dashedarrows) and eventually binding to a mobile electron or a single Nb ion to emit atenergies redshifted by the respective binding energies, indicated by the horizontaldashed lines.Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 5www.nature.com/naturecommunicationsthat excitons form a variety of stable bound complexes with dif-ferent emission characteristics depending on the defect species.While Nb-doped WS2 is identified as an attractive system in thisstudy, these emitters require significant enhancements in bright-ness, purity, and operational temperature to be viable for practicalapplications. Notably, classical background emission from commondefects poses significant challenges. Exploring different impuritiesin high-quality host crystals may provide critical insights into thedesign principles necessary for optimizing the characteristics ofthese impurity-induced emitters.MethodsGrowth of dilute Nb-doped WS2 monolayersAn initial solution was prepared by dissolving 1mg niobium (V)oxalate (C10H5Nb20.H2O, Alfa Aesar) in 40mL H2O, which approx-imates to 1 at% Nb when mixed with 50mg of W precursor. Theinitial solution was then subjected to a series of 10:1 dilution toachieve the desired dilute concentration, governed by theC1V 1 =C2V 2 relationship where C1(V1) represents the initial con-centration (volume) and C2V2 represents the concentration(volume) of the Nb precursor. After a series of necessary dilutions,50mg sodium tungstate dihydrate (Na2WO4·2H2O, Sigma–Aldrich)was added to the dilute Nb volume with addition of H2O to bring tothe total water volume to 40mL, forming the dilute Nb in W pre-cursor mixture. The metal precursor mixture was then drop-cast onSiO2/Si substrate, followed by a blow-dry with a N2 gun. A furnacewith a 1 in. diameter horizontal fused quartz tube was used for thechemical vapour deposition (CVD) growth. Throughout the growthprocess, a mixture of 25 sccm of hydrogen/argon (5% H2/95% Ar)and 25 sccm Ar gas was used as carrier gas; ∼10mg of S powder wasintroduced in the upstream region, which reached ∼300 °C duringthe growth. Before reaching the growth temperature of 850 °C, thefurnace was stabilized at 200 °C for 5min and ramped up at a rate of20 °C/min, followed by 10min of annealing at 850 °C. After 10minof annealing, the furnace was slid to the upstream region tovaporize the sulfur, and the reaction lasted for 5min. After thereaction, the furnace lid was opened, and the gas flowwas increasedto 500 sccm to allow for rapid cooling.STEM sample transfer, imaging and analysesThe STEM samples were prepared with the polycarbonate transfermethod as in our previous work17. HAADF- and MAADF-STEM imageswere acquired with an aberration-corrected JEM-ARM200F (JEOL)instrument equipped with a cold-field emission gun and an ASCORprobe corrector, which was operated at 80 kV. HAADF- and MAADF-STEM images were collected at semi-angles ranging between68–280mrad and 30–120mrad, respectively, with a convergencesemi-angle of 31 mrad.Peak detection and filtering in PL mapsFor the emitter distribution analyses, the photoluminescencehyperspectral data, in the energy range of 1.90 eV to 2.07 eV with aresolution of 1014 steps per pixel, were imported into MATLABR2023a (v9.14) for further data processing and analysis. Back-ground pixels with low total intensity (i.e., below 0.02 of totalnormalized background) were removed from the dataset toenhance visualization and focus solely on relevant features. Sub-sequently, the data from all samples were concatenated to facilitatedirect comparisons. A script was developed to remove cosmic sig-nal interference within the photoluminescence spectra. This algo-rithm employed a peak search methodology to identify cosmicpeaks characterized by their intensity (minimum peak prominenceof 500) and narrowness (limited to a maximum of 5 data points).Once identified, these cosmic peaks were replaced by the average ofthe three data points located on both the left-hand side (LHS) andright-hand side (RHS) of the peak. The normalized combined data-set, ranging between 0 and 1 for peak detection, was subjected tofurther analysis.A tailored MATLAB script was formulated to execute peakdetection and filtering across all pixels in the photoluminescencehyperspectral data. For each pixel, the script applied peak detectionalgorithms using the ‘islocalmax’ and ‘islocalmin’ functions toidentify local maxima and minima in the PL spectra within thespecified energy range. Identified peaks were subjected to a set ofcriteria to confirm the validity of their selection. These criteriaencompassed evaluating peak height to discard saturated signals,assessing the distance from neighbouring minima to filter out noiseand alleviate broaden peaks, and checking the height differencefrom the closest minimum to eliminate low-intensity peaks. Thescript recorded the positions of peaks and intensities of peaks thatsatisfied all criteria for every pixel.First, the lowest (Xmin) and highest intensities (Xmax) in eachmap were identified. The as-acquired intensity (X ) of each featurewas then normalized using Min-Max normalization, expressed asXnorm = ðX � XminÞ=ðXmax � XminÞ. This process rescales all datapoints in the photoluminescence map from 0 (representing the1.915 1.920 1.925 1.930 1.935 1.94002468101214161820ecneruccOEnergy (eV)0.1 ppm Nb83 emittersBin size = 1.2 meV1.8 meV3.5 meVa b1234100)Vem(gnineda orbelbme snE2D quantum emittersGaSe [35]WSe2 [33]WS2 [32]MoS2 [9]MoTe2 [34]hBN [36-38]WS2[This Work]StrainIon beam (vacancy)Implant (dimer)e-beamImpurityFig. 5 | Ensemble broadening of 2D quantum emitters. aHistogram showing thelocalized Nb emitter distribution (NbXL) surveyed across various positions inmultiple samples nominally doped at 0.1 ppm. Fitted Gaussian curves for the twomain emitter clusters, alongside their full-width-at-half-maximums (FWHM), areshown. Spectra surveyed were acquired with a 473 nm and 532 nm CW laser at 4 K.b Comparison of the ensemble broadening of the 0.1 ppm sample with thatof various other two-dimensional (2D) materials, namely strained GaSe35, strainedmonolayer MoTe234, strained WS2 and WSe232,33, He-ion bombarded MoS29, beam-treated hBN grown under high-pressure high-temperature36,37, and annealedC-implanted hBN38. All the data correspond to measurements conducted at cryo-genic temperatures. Note: Open symbols represent emitters of unknown structuralorigin, while solid symbols represent emitters whose structural origin has beenidentified. Red denotes single-layer chalcogenide semiconductors and blue repre-sent ultrathin hBN (less than 100 nm thick).Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 6www.nature.com/naturecommunicationsbackground) to 1 (representing the maximum signal). Specifically,for the X0 peak, peaks within the range of 2.05–2.07 eV with anintensity greater than 0.05 of the normalized background wereselected. Further analysis was conducted for the Nb signal in the lowenergy range, specifically below 1.95 eV. Peaks with an intensitygreater than 0.2 of the normalized background and a widthexceeding 15 data points, classified as NbXG signals, were selected.Similarly, for NbXL, peaks that showed an intensity above 0.2 of thenormalized background but have awidth smaller than 15 data pointswere selected.Optical spectroscopyLow temperature photoluminescence measurements and mapping(presented in Fig. 2) were performed using a home-built opticalsystem on the cryostat (Quantum Design PPMS and attocubeattoCFM). A 473 nm CW laser (spot diameter ~1 μm2) was used togenerate the PL maps by raster scanning the xy piezo stage. The PLspectra were recorded on Andor Kymera 328i spectrometerequipped with Andor iDus CCD.Time-resolved photoluminescence was acquired in a closed-cyclecryostat (attocube attoDRY1000) coupled with a home-built opticalsetup. For the lifetime measurement, a pulsed laser (NKT PhotonicsSuperK FIANIUM) with repetition rate tunable between 1.95 to78.2MHz, set to 600 nm was cleaned by a band-pass filter and shoneonto the sample through a cold objective lens (f = 2.87mm, 0.82 NA).The reflected PL signalwas collectedby the same lens, separatedwith anon-polarizing beam splitter (NPBS, Thorlabs BS013), filtered by a pairof tunable filters (Semrock Versachrome) and a long-pass filter(Thorlabs FELH0600), before detected by a single photon detector(SPD, Excelitas SPCM-AQRH-16) and a time-correlated single photoncounting (TCSPC) module (PicoHarp 300). The integrating spectralwindow was verified with a spectrometer (Andor IsoPlane320,Kuro2048B, 1800 g/mm 500nm) by diverting the signal with a remo-vablemirror. For the g(2)(t)measurement, a NPBS (Thorlabs BS014) wasused to split the signal and detect together with another SPD of thesame model. A short-pass filter (Thorlabs FESH0700) was installedbetween the twoSPDs to eliminate crosstalk. TheTCSPCwasoperatingin the time-tagged time-resolved (TTTR) mode and the data was post-processed to construct the g(2)(t) curve.In polarization-resolved measurements, a 532 nm CW laser(Laser Quantum gem 532) was shone onto the sample with the samesetup, with an additional polarizer and analyzer placed before andafter the laser entering and exiting the NPBS. Their transmissionaxes are aligned parallel to each other for co-polarization. A half-waveplate (HWP, Thorlabs AHWP10M-580) mounted on a motor-ized rotational mount (Thorlabs PRM/M1Z8) was installed betweenthe NPBS and the objective lens. The spectrum was collected as afunction of the HWP angle.Magneto-PL measurements were obtained with a 532 nm line-arly polarized laser focused onto the sample positioned on a x-y-z-piezo stage in a cryostat (attocube attoDRY2100) filled with Heexchange gas cooled to 1.6 K. The magnetic field was applied per-pendicular to the sample plane (Faraday configuration) up to 9 Twith superconducting coils. The σ+ and σ− circular polarizationcomponents were resolved by reversing the polarity of the mag-netic field whilst collecting the signal through a fixed configurationof a linear polarizer and a λ/4-waveplate.Device fabrication and gate dependent PL spectroscopyThe sample was coated with LOR 3 A resist and baked for 5min.Then, a second layer of S1805 photoresist was deposited and bakedfor 1 min. Laser lithography (Heidelberg Instruments μMLA) wasused to deposit the electrodes. Cr and Au electrodes with thick-nesses of 3 and 50 nm, respectively, were deposited on the FLGusing a standard thermal evaporator. The sample was immersed inPG remover for 1 h and kept at 60 °C to remove the photoresist andlift off the metal. For the measurements, the sample was mountedon a chip carrier positioned on a set of x/y piezo positioners. Thesample was excited with a pulsed laser set at 78.2 MHz repetitionrate and wavelength of 600 nm. The gate voltage on the sample wasregulated with a Keithley source meter.First-principles calculationsThedensity functional theory calculations in thisworkwereconductedwithin the VASP code43 using the Perdew, Becke and Ernzerhofapproximation for the exchange-correlation functional44. Theprojected-augmented wave with an energy cut-off 450eV were used.The Nb−1-doped 10 × 10 supercell (1 at% Nb) was fully relaxed with asingle Γ-point until the total energy changes less than 10−5eV betweentwo consecutive iterations, and all forces are converged to less than0.02 eV/Å. Spin-orbit coupling was included in the non-self-consistentcalculation to obtain the band structure for the 10 × 10 supercell Nb−1-WS2. The g-factors of theWS2 CBM and VBMwere computed using thenumerical approach in Quantum ESPRESSO package45 described inref. 46 and ref. 47The g-factor for theflatdefectbandwasestimatedbyassuming that the valley contribution is negligible. The orbital con-tribution of the defect band is also taken to be zero because the bandarises from dz2 orbitals.Data availabilityAdditional data that support the findings of this study are availablefrom the corresponding authors on request.Code availabilityThe code used for the findings of this study is available from the cor-responding authors on request.References1. Aharonovich, I., Englund, D. & Toth, M. Solid-state single-photonemitters. Nat. Photonics 10, 631–641 (2016).2. Brouri, R., Beveratos, A., Poizat, J.-P. & Grangier, P. Photon anti-bunching in the fluorescence of individual color centers in dia-mond. Opt. Lett. 25, 1294–1296 (2000).3. Kurtsiefer, C., Mayer, S., Zarda, P. &Weinfurter, H. Stable solid-statesource of single photons. Phys. Rev. Lett. 85, 290–293 (2000).4. Castelletto, S. & Boretti, A. Silicon carbide color centers for quan-tum applications. J. Phys. Photonics 2, 22001 (2020).5. 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Valley-filling instability and critical magneticfield for interaction-enhanced Zeeman response in doped WSe2monolayers. npj Comput. Mater. 7, 198 (2021).AcknowledgementsThe authors acknowledge support from theMinistry of Education (MOE),Singapore, under AcRF Tier 3 (MOE2018-T3-1-005) and the SingaporeNational Research Foundation for funding the research under medium-sized centre programme. This project was supported by the Ministry ofEducation (Singapore) through the Research Centre of Excellence pro-gram (grant EDUNC-33-18-279-V12, I-FIM). Thismaterial wasbased uponwork supportedby theAir Force EuropeanOfficeof AerospaceResearchand Development Office of Scientific Research and the Office of NavalResearch Global under award number FA8655-21-1-7026. This researchis supported by the Ministry of Education, Singapore, under its Aca-demic Research Fund Tier 2 (T2EP50122-0012). The work was supportedby the National Science Centre, Poland (grant no. 2022/46/E/ST3/00166). S.Y.Q. acknowledges computational resources at the CA2DMcluster and at the National Supercomputing Centre (NSCC) in Singa-pore, and funding from the National University of Singapore and MOE.L.L. and M.B. acknowledge support fromMOE’s AcRF Tier 1 (R-284-000-179−133). This work was performed in part at the Australian NationalFabrication Facility (ANFF), a company established under the NationalCollaborative Research Infrastructure Strategy, through the La TrobeUniversity Centre for Materials and Surface Science. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grant Numbers 19H05790,20H00354 and 21H05233).Author contributionsL.L. and G.E. conceived the work. L.L. devised the growth strategy,fabricated the samples and conducted the structural characterizations.Y.W.H. conducted the optical measurements, g(2)(t) measurements andanalyses. F.X. conducted the first principles calculationswith input fromJ.Z. under the supervision of S.Y.Q. d.-Á.A.G. conducted themagneto-PLand preliminary PL measurements. Y.C. assisted Y.W.H. with the opticalsetup, measurements and fabricated the gate-dependent devices.S.Y.W. conducted the PL peak search and filtering analyses of themapping data under the supervision of P.J.P. Z.W. devised the sche-matics and advised on the manuscript structure. K.W. and T.T. suppliedthe bulk hBNcrystals.M.B. supervised the STEMexperiments anddefectanalyses. M.K. supervised and advised on the optical measurements.G.E. supervised theproject. L.L. andG.E.wrote thepaperwith input fromY.W.H. All authors contributed to the scientific discussions and manu-script revisions.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 8www.nature.com/naturecommunicationsAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-54360-5.Correspondence and requests for materials should be addressed toSu Ying Quek, Maciej Koperski or Goki Eda.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-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-54360-5Nature Communications |        (2024) 15:10035 9https://doi.org/10.1038/s41467-024-54360-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Nb impurity-bound excitons as quantum emitters in monolayer WS2 Results Synthesis of WS2 monolayers with tunable Nb doping Emitter distribution Single photon characteristics Origin of the Nb-induced single photon emitters Ensemble broadening of single emitters Discussion Methods Growth of dilute Nb-doped WS2 monolayers STEM sample transfer, imaging and analyses Peak detection and filtering in PL maps Optical spectroscopy Device fabrication and gate dependent PL spectroscopy First-principles calculations Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information