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A. Hötger, T. Amit, J. Klein, K. Barthelmi, T. Pelini, A. Delhomme, S. Rey, M. Potemski, C. Faugeras, G. Cohen, D. Hernangómez-Pérez, [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), [K. Watanabe](https://orcid.org/0000-0003-3701-8119), C. Kastl, J. J. Finley, S. Refaely-Abramson, A. W. Holleitner, A. V. Stier

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[Spin-defect characteristics of single sulfur vacancies in monolayer MoS2](https://mdr.nims.go.jp/datasets/cbf309a5-d498-4c4e-8212-b4f3c85fc5d6)

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Spin-defect characteristics of single sulfur vacancies in monolayer MoS2ARTICLE OPENSpin-defect characteristics of single sulfur vacancies inmonolayer MoS2A. Hötger1, T. Amit2, J. Klein3, K. Barthelmi1, T. Pelini4, A. Delhomme4, S. Rey5, M. Potemski 4,6, C. Faugeras 4, G. Cohen 2,D. Hernangómez-Pérez 2, T. Taniguchi 7, K. Watanabe 8, C. Kastl 1, J. J. Finley 1, S. Refaely-Abramson 2, A. W. Holleitner1 andA. V. Stier 1✉Single spin-defects in 2D transition-metal dichalcogenides are natural spin-photon interfaces for quantum applications. Here wereport high-field magneto-photoluminescence spectroscopy from three emission lines (Q1, Q2, and Q*) of He-ion induced sulfurvacancies in monolayer MoS2. Analysis of the asymmetric PL lineshapes in combination with the diamagnetic shift of Q1 and Q2yields a consistent picture of localized emitters with a wave function extent of ~3.5 nm. The distinct valley-Zeeman splitting in out-of-plane B-fields and the brightening of dark states through in-plane B-fields necessitates spin-valley selectivity of the defect statesand lifted spin-degeneracy at zero field. Comparing our results to ab initio calculations identifies the nature of Q1 and Q2 andsuggests that Q* is the emission from a chemically functionalized defect. Analysis of the optical degree of circular polarizationreveals that the Fermi level is a parameter that enables the tunability of the emitter. These results show that defects in 2Dsemiconductors may be utilized for quantum technologies.npj 2D Materials and Applications            (2023) 7:30 ; https://doi.org/10.1038/s41699-023-00392-2INTRODUCTIONSpin-defects in host crystals can be fundamental building blocksfor quantum technologies, such as computing, sensing orcommunication1–4. For instance, color centers in diamond havebeen investigated since the early 1980s, of which the nitrogenvacancy (NV) center is the most prominent example5,6. In thisdefect, the crystal field splitting lifts the ground state spindegeneracy and provides the required unique quantum degree offreedom to form an addressable two-level system7–10. In addition,NV centers are single photon sources11–13 and therefore constituteexcellent building blocks for future quantum photonic circuits.However, a key prerequisite for such applications is the ability toposition defects deterministically. This is a challenge for defects in3D crystals, such as single NV centers, as they can be positionedeither vertically or laterally with high precision, but not bothsimulateneously14–17. This disadvantage can be overcome bycreating optically addressable spin-defects in 2D host crystals.Localized single photon emission in 2D materials was firstdiscovered in monolayer WSe2, a prototypical member of thesemiconducting 2D transition metal dichalcogenides (TMDs)18–22.Subsequently, single photon emitters were discovered in hex-agonal boron nitride (hBN)23. Contrasted with hBN, TMDs havestrong light-matter coupling24 and locked spin-valley physics25,which provides a natural spin-photon interface. Moreover, the 2Dsemiconducting host crystal has enabled new possibilities toengineer and manipulate these defects19,26–28, which led tofurther advances in quantum devices, such as quantum lightemitting diodes29–31.First approaches for the deterministic creation of quantumemitters in 2D materials made use of strain potentials, for instanceinduced by a textured substrate32–38. This results in a localbandstructure modulation in the host crystal, limited by thebending radius of the material, yet the latter approach intrinsicallylacks reproducibility. Furthermore, the confining potential oftenbreaks crystal symmetries, leading to the loss of valley opticalselection rules. A higher degree of spatial resolution andreproducibility can be achieved by using the accuracy ofelectron-beam or focused ion beam irradiation39–43. Specifically,He-ions can be precisely focused and create optically active pointdefects in monolayer MoS241 with a precision better than 10 nm44.In photoluminescence (PL) spectroscopy, spectrally narrow emis-sion lines appear about 200 meV red-shifted from the neutralexciton of He-ion irradiated MoS241. Second order correlationmeasurements unambiguously showed single photon emissionfrom single He-ion irradiation sites, which in turn could be relatedto the generated point defects45,46. A specific advantage is thatthese defects can be implanted into more complex, electronicdevice heterostructures, allowing for the electrical control ofquantum emission28.The microscopic origin of various localized emission centers iscurrently a matter of debate. One specific defect complex, which ispredominant in He-ion irradiated MoS2, is the chalcogen vacancy,where one sulfur atom has been removed from the host lattice44.Sub-gap quantum emission from this defect47 was suggested tooriginate from a relaxation cascade where an optical interbandexcitation creates a bound electron-hole pair that subsequentlylocalizes into the defect and radiatively recombines48. However,pristine defect states have been predicted to be essentially spindegenerate47,49. Moreover, other relaxation pathways, such asdefect-to-band transitions are in principle possible, and, due to the1Walter Schottky Institute and Physics Department, TU Munich, 85748 Garching, Germany. 2Department of Molecular Chemistry and Materials Science, Weizmann Institute ofScience, Rehovot, Israel. 3Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 4Laboratoire National des ChampsMagnetiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 38042 Grenoble, France. 5Department of Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark.6Institute of Experimental Physics, Faculty of Physics, University of Warsaw, 02-093 Warszawa, Poland. 7International Center for Materials Nanoarchitectonics, National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 8Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.✉email: andreas.stier@wsi.tum.dewww.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRS1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00392-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00392-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00392-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41699-023-00392-2&domain=pdfhttp://orcid.org/0000-0001-8881-6618http://orcid.org/0000-0001-8881-6618http://orcid.org/0000-0001-8881-6618http://orcid.org/0000-0001-8881-6618http://orcid.org/0000-0001-8881-6618http://orcid.org/0000-0002-9615-8739http://orcid.org/0000-0002-9615-8739http://orcid.org/0000-0002-9615-8739http://orcid.org/0000-0002-9615-8739http://orcid.org/0000-0002-9615-8739http://orcid.org/0000-0001-6727-5023http://orcid.org/0000-0001-6727-5023http://orcid.org/0000-0001-6727-5023http://orcid.org/0000-0001-6727-5023http://orcid.org/0000-0001-6727-5023http://orcid.org/0000-0002-4277-0236http://orcid.org/0000-0002-4277-0236http://orcid.org/0000-0002-4277-0236http://orcid.org/0000-0002-4277-0236http://orcid.org/0000-0002-4277-0236http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0001-5309-618Xhttp://orcid.org/0000-0001-5309-618Xhttp://orcid.org/0000-0001-5309-618Xhttp://orcid.org/0000-0001-5309-618Xhttp://orcid.org/0000-0001-5309-618Xhttp://orcid.org/0000-0003-3036-529Xhttp://orcid.org/0000-0003-3036-529Xhttp://orcid.org/0000-0003-3036-529Xhttp://orcid.org/0000-0003-3036-529Xhttp://orcid.org/0000-0003-3036-529Xhttp://orcid.org/0000-0002-7031-8327http://orcid.org/0000-0002-7031-8327http://orcid.org/0000-0002-7031-8327http://orcid.org/0000-0002-7031-8327http://orcid.org/0000-0002-7031-8327http://orcid.org/0000-0002-5476-1919http://orcid.org/0000-0002-5476-1919http://orcid.org/0000-0002-5476-1919http://orcid.org/0000-0002-5476-1919http://orcid.org/0000-0002-5476-1919https://doi.org/10.1038/s41699-023-00392-2mailto:andreas.stier@wsi.tum.dewww.nature.com/npj2dmaterialsstrong spin-orbit interaction in the host MoS2, considerations withrespect to spin-valley physics have yet to be taken into account. Inthis manuscript, we investigate three distinct emission lines of He-ion induced sulfur vacancies created in monolayer MoS2 by high-field magneto-optical spectroscopy, which has previously beenshown to be an important tool to investigate the excitonic spin-valley physics in 2D TMDs50–52. We identify the bands involved inthe optical quantum emission and show that an energy-dependent degree of hybridization between atom-like defectstates and the MoS2 bandstructure leads to varying degree ofvalley selectivity for the distinct electron-hole transitions. Ourresults display that sulfur vacancies in monolayer MoS2 are spin-defects that can be tailored to specific quantum applications.RESULTSPhotoluminescence from sulfur vacancies in monolayer MoS2The left hand side of Fig. 1a shows the schematic of the sampleunder investigation. A monolayer MoS2 is encapsulated in hBN,fabricated by standard dry viscoelastic stamping methods (seeMethods for details). Subsequently, a focused He-ion beam isscanned across the sample, creating predominantly sulfurvacancies in the MoS244. Our sample is He-ion irradiated with apitch of ~2 μm, which allows us to selectively investigateindividual irradiated locations (see Supplementary Fig. 1a). Typicaldefect PL spectra at 1.7 K and zero magnetic field are shown inFig. 1b. The dominant feature at 1.75 eV, labeled Q1, haspreviously been identified as a single photon emitter45,46associated with an unpassivated sulfur vacancy48. In this manu-script, we discuss only those locations which contained a singleQ1 line, generally the case for the sample under investigation. Thelow energy tail of Q1 is attributed to the coupling of a localizedstate to acoustic phonons in MoS2. Analysis of the lineshape withan independent boson model allowed the determination of theeffective Bohr radius of this localized state to be ≈2–3 nm41. Aweak secondary feature about 30 meV red-shifted from the zerophonon line (ZPL) of Q1, can be assigned to a phonon replica dueto a local phonon mode (LPM) of this defect center46. Emissionline Q2 forms in a distinct energy band ≈ 75 meV red-shifted fromQ1, while another emission line Q* appears ≈50 meV blue-shifted.Both lines generally appear fainter as compared to Q1, while thelineshape of all features are similar. The statistical evaluation of allemission lines investigated throughout the sample clearlyindicates these three inhomogeneously broadened, yet distinct,emission bands (see Supplementary Fig. 1c). Our zero B-fieldspectroscopy therefore establishes the observed emission lines tooriginate from localized defect centers. This is consistent withpredictions of six spinor wave functions due to an atomistic defectassociated with a sulfur vacancy resulting from its C3v symmetry,where two spin-split bands are above the Fermi energy and one isbelow it (see Supplementary Fig. 10). As sketched in Fig. 1c anddiscussed in detail below, we unambiguously identify Q1 as anexcitonic transition predominantly between defect induced states(cD1/cD2↔ vD) at the Γ point, with significant hybridization acrossthe Brillouin zone and specifically at the K=K 0 points47. This spreadFig. 1 Defect luminescence of He-ion irradiated monolayer MoS2. a Sketch of the monolayer MoS2 encapsulated in hexagonal boron nitride(hBN) illustrating the He-ion irradiation and the out-of-plane magneto-spectroscopy scheme. b Typical low-temperature photoluminescence(PL) spectra of the quantum emission Q1, Q2, and the local phonon mode (LPM) of Q1. c Illustration of the MoS2 bandstructure at the K and Γvalleys including the defect states of a sulfur vacancy. The modified bandstructure shows flat defect-related levels vD, cD2, and cD1. The red(blue) color represents the spin-up (spin-down) eigenstate of the associated band. A small spin splitting of the defect states is observed in ourcalculations at the K/K 0 valleys, as discussed in the main text. At B⊥= 0 T, the Fermi energy EF lies below the unoccupied defect states. Solidcircles mark significant defect states. d Degree of circular polarization (DCP) versus B⊥for Q1 and Q2. The blue shaded area highlights the±10% experimental uncertainty. The oscillations in the DCP below ~15 T are predominantly due to fringe field induced Faraday rotation in thelow temperature objective. The solid lines are fits to the data with Eq. (1) for Q1 and a Boltzmann statistics fit for Q2 (see Supplementary Fig. 5).A. Hötger et al.2npj 2D Materials and Applications (2023)    30 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;in momentum-space originates from the localized character of thesulfur vacancy, as shown by the calculated wave functiondistributions associated with the electronic defect levels cD1,cD2 and vD (see Supplementary Fig. 10). The wave functions areprimarily composed of transition metal d-orbitals and thereforecontain the spin-valley physics of monolayer MoS2 throughout theBrillouin zone47. For the energetically lower lying emission Q2, weidentify the superposition of transitions between both spin-up/down defect induced conduction band states (cD1) and the MoS2valence band (VB) at the K=K 0-points in the Brillouin zone.Although Q2 is also excitonic, the transitions are confined to theK=K 0-points. We further demonstrate that Q* originates from achemically functionalized sulfur vacancy and the emission is ofcharacter Q2. One of the central aspects of this manuscript is theobservation of the valley dichroism of all emission lines throughthe valley Zeeman splitting and optical degree of circularpolarization (DCP) in high magnetic fields. We note that valleyselectivity stems from contributions at the K=K 0-points to theexcitonic transitions, which we probe via circular polarizationresolved magneto-spectroscopy. As an example, the DCP of Q1and Q2 are shown in Fig. 1d, which, for Q1 reveals essentially nopolarization in the B-field range below 15 T, and a rapid rise of theDCP, tending towards unity at the highest fields. Q2 polarizesalready at low fields. The observation that these emission linesshow valley dichroism at finite magnetic field necessitates thelifting of the spin degeneracy, and we further proof in detail belowthat the spin degeneracy of the defect states in the K=K 0 valleys isalready lifted at zero magnetic field. Thus, the sulfur vacancy inMoS2 can be considered as a spin-defect.Out-of-plane magnetic field measurements on defects in MoS2In order to investigate the nature of the observed emission bands,we employ magneto-PL spectroscopy, where the magnetic fieldB⊥up to 27 T is applied perpendicular to the 2D sample plane andparallel to the optical beam path (Faraday geometry). The samplewas mounted in a He-exchange gas cryostat with a bathtemperature of TBath = 4.2 K. The sample was excited with alinearly polarized continuous wave (CW) laser at a wavelength of515 nm and power of ~10 μW, focused to a beam spot of ~1 μm.The linear polarization excites interband transitions in both K=K 0valleys of the host MoS2. At each positive magnetic field, we probethe circular dichroism by detecting the PL for σ−and σ+polariza-tion, which we calibrate with the well known valley Zeemansplitting of the neutral exciton in MoS2 (see Supplementary Fig. 2).As such, we minimize the impact of positional sample drift withrespect to the beam path in very high magnetic fields. From thefaint appearance of the negatively charged trion in the PL spectraand the value of the valley Zeeman splitting for the neutralexciton (μ⊥=−2.8 ± 0.1μB), we conclude that our MoS2 crystal isweakly electron doped n ≈ 5 × 1011 cm−253. Figure 2a depictstypical polarization resolved PL spectra of Q1 and the LPM at B⊥=0 T. Unlike strain induced quantum emitters in monolayerTMDs32,36,54, the He-ion-induced defects show no valley dichroismat zero magnetic field (Fig. 1d)48. This is expected for the C3vsymmetry of an unperturbed sulfur vacancy with defect-to-defecttransitions at the Γ-point47,49. The left (right) panel of Fig. 2b showsthe normalized PL of Q1 versus B⊥for σ−(σ+) polarized detection.The position of the ZPL exhibits a monotonic blue-shift withincreasing magnetic field for both polarizations. We plot the PLpeak position in Fig. 2c and find that the average peak position forFig. 2 Out-of-plane magnetic field B⊥dependent photoluminescence of defect luminescence Q1. a Low-temperature photoluminescence(PL) spectra of defect luminescence Q1 at zero out-of-plane magnetic field (B⊥) for σ+(red) and σ−(blue) polarized detection. The zero-phononline (ZPL) of Q1 occurs at 1.752 eV with a red-shifted (30 meV) local phonon mode (LPM, see inset). b PL versus B⊥for Q1. The left (right) panelshows the σ−(σ+) polarized signal. The spectra were normalized to their maximum intensity. c The fitted position of the ZPL of Q1 shows adiamagnetic shift of 1.0 ± 0.1 μeV T−2. d Valley Zeeman splitting of Q1 versus B⊥. The black dashed line shows a fit to the data with a Zeemansplitting of μ⊥,Q1=+ 0.1 ± 0.1μB. e Bandstructure of MoS2 with a periodic sulfur-vacancy extracted from DFT calculations. The color codedenotes the total magnetic moment at each k-point. f Density of states (DOS) plot of the Brillouin zone, showing energetically narrowdensities at the defect levels. g Illustration of the two spin-split electron states in the K=K 0 valley and possible optical transitions of Q1 for zeroand finite magnetic field.A. Hötger et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    30 σ+ and σ−detection 12 ðEσþ þ Eσ�Þ can be fitted with a quadraticfunction (~B⊥2) with a prefactor of σ= 1.0 ± 0.1 μeV T−2. Thequadratic-in-B⊥blueshift is consistent with the expected diamag-netic shift of a bound particle in 2D, ΔEdia ¼ e2hr2iB2?=8mr50,51.The root mean square radius in the plane of the 2D material isexpressed as rrms ¼ffiffiffiffiffiffiffiffiffiffiffi8mrσp=e, where mr is the reduced mass ofthe particle and e the elementary charge, respectively. Theobserved diamagnetic shift coefficient of Q1 is roughly 5 × largerthan that of the neutral MoS2 exciton50,51. Assuming thereduced mass for the neutral exciton and Q1 are the same,(mr= 0.275m051), the observed diamagnetic shift yields a particlesize rrms = 3.5 nm, consistent with the findings of the independentboson model discussed above. The valley Zeeman splitting,defined from the difference Eσþ � Eσ� ¼ μ?B is shown in Fig. 2d.In contrast to other quantum emitters in 2D materials18–21,36,55,56,the Q1 emission shows little, but experimentally detectable,positive valley Zeeman splitting of μ⊥,Q1=+ 0.1 ± 0.1μB. Such avanishing Zeeman splitting has recently been observed on aquantum emission and was attributed to a quasiparticle transitionbetween pristine conduction band and in-gap defect state57.However, the latter study does not provide a full evaluation on theexcitonic effects, which are crucial for magneto-spectroscopy inTMDs. In order to get a first insight into the nature of the Q1emission line, Fig. 2e shows the DFT bandstructure of MoS2 with a2% sulfur vacancy density. The pristine bandstructure of MoS2 isessentially unaffected by the presence of the sulfur vacancies.However, additional electronic states lie within the bandgap (cD1,cD2), as well as in the valence band (vD) of MoS2. These states arerelatively flat in k-space, which yields a high joint density of statesfor defect-to-defect transitions in this system (Fig. 2f), particularlyat the Γ-point. For a pure defect-to-defect transition at the Γ-point,we expect exactly zero valley Zeeman splitting due to thevanishing of the valley selectivity. In turn, the finite valley Zeemansplitting is consistent with a Q1 emission dominated by defect-to-defect transitions at the Γ-point and its hybridization with defect-to-band transitions at the K=K 0-points, which we discuss in detailbelow.Although we find μ⊥,Q1 ≈ 0, we measure a large degree ofcircular polarization (Fig. 1d) at high magnetic fields, calculatedfrom the integrated PL intensities of both helicitiesðIσþ � Iσ�Þ=ðIσþ þ Iσ�Þ. This B-field induced circular polarizationrequires spin polarized states to participate in the opticaltransition. The measured DCP at B⊥= 0 T is within theexperimental uncertainty of ±10% (indicated by the shaded areain Fig. 1d). The uncertainty originates from spectral jitter as well asuncompensated Faraday rotation of the linearly polarized excita-tion light combined with imperfectly aligned λ/4 and linearpolarizers in the detection path. In our understanding, theintensities of the σ+- and σ−-polarized transition in either the Kor the K 0-valley are weighted with the probability of the defectlevel at EcD2 to be occupied by an electron of the Fermi sea usingthe Fermi-Dirac fFD distribution. In turn, we assume followingexpression to fit the DCP as a function of the applied magneticfield.DCPðBÞ ¼¼ f FDðEcD2;0þμcD2�BÞ�f FDðEcD2;0�μcD2 �BÞf FDðEcD2;0þμcD2�BÞþf FDðEcD2;0�μcD2 �BÞ ;(1)with the Zeeman shift of the cD2 states in the K=K 0 valleys to beμcD2 ⋅ B and EcD2,0 the energy of state cD2 at zero field. Fitting thedata of Q1 in Fig. 1d with Eq. (1) (see line in Fig. 1d) yieldsμcD2= 2.6 ± 0.5μB, with the error given by the systematic error ofour polarization alignment in the high-magnetic field setup.Moreover, the fit assigns cD2 to be above the Fermi energy EF atB⊥= 0 T, with EcD2− EF= 3.2 ± 0.7 meV. We note that the ab initiocalculations as in Fig. 2e determine μcD2 to be 0.86μB, which isagain clearly positive. For the experimental (ab initio) value, theZeeman shift of cD2 at 22.5 T equals ~3.4 meV (1.12 meV), which islarger than the thermal energy of ~0.7 meV at 4.2 K. In ourunderstanding, this explains that the DCP can be detected at highmagnetic fields at the given temperature. We note that thisinterpretation is corroborated by a gate-tunable device where theDCP changes sign by reversing the polarity of B⊥(see Supplemen-tary Fig. 4). As a consequence, an applied magnetic field lifts thespin degeneracy of Q1. Moreover, a characteristic blue-shift of thequantum emission with increasing charge carrier density suggeststhe defects to be charge neutral (see Supplementary Fig. 4). Basedon these findings, Fig. 2g summarizes the interpreted bandstruc-ture at K=K 0 and Γ for zero and finite B⊥. With increasing magneticfields, the spin-up state of cD2 in the K valley (lowest defect statein the bandgap at the K-point) is pushed away from the Fermiedge, which decreases the possibility for it to be occupied with anelectron from the Fermi edge. This increases the part ofσ+polarized light emitted at the K-point and eventually polarizesthe overall emission. Conversely, at the K 0-point, the spin-downdefect state is the lowest defect state in the bandgap and ispushed towards the Fermi edge. Therefore, the intensity ofσ−polarized light subsequently diminishes. From the combinedexperimental observations of small valley Zeeman splitting andstrongly B⊥-dependent DCP, we identify Q1 as an excitonicemission of a neutral sulfur vacancy in MoS2 between hybridizeddefect-to-defect and defect-to-band transitions and relate theobserved DCP to a combination of magnetic field inducedZeeman shifts and occupation effects.The B⊥-dependence of the LPM emission mirrors that of Q1, asexpected, with a diamagnetic shift of σ= 1.00 ± 0.04 μeV T−2, anegligible μ⊥ and the same DCP trend as Q1 (see SupplementaryFig. 3). The similar magnetic field dependence of Q1 and LPMfirmly supports the claim that the LPM emission is a replica of thesame optical transition as Q1 with the additional emission of aphonon related to a local mode of the defect center46,58.We now turn to the magneto-spectroscopy of the emission lineQ2. Figure 3a shows polarization resolved spectra of the quantumFig. 3 Out-of-plane magnetic field B⊥dependent photolumines-cence of defect luminescence Q2. a PL of Q2 versus B⊥for σ−(leftpanel) and σ+polarized detection (right panel). b The Zeemansplitting of Q2 shows a Zeeman splitting of μ⊥=+ 1.3 ± 0.1μB.c Position of the ZPL of Q2 versus the applied magnetic field (B⊥),showing a diamagnetic shift of σ= 1.1 ± 0.2 μeV T−2.A. Hötger et al.4npj 2D Materials and Applications (2023)    30 Published in partnership with FCT NOVA with the support of E-MRSemission Q2 as a function of magnetic field. We focus on thedominant peak at 1.677 eV, and note that fainter peaks observedat this particular spot on the sample shift equally with B⊥(seeSupplementary Fig. 6 for magneto-spectroscopy of more loca-tions). Unlike Q1, we observe a sizeable valley Zeeman shift. Thisobservation necessitates the lifting of valley degeneracy withincreasing magnetic field and points towards optical transitions atthe K=K 0-points. The extracted valley Zeeman splitting is depictedin Fig. 3b and yields a positive magnetic momentμ⊥=+ 1.3 ± 0.1μB, a sign that is opposite to the neutral excitonof the host MoS2. Furthermore, similar to Q1, we observe adiamagnetic shift with σ= 1.1 ± 0.2 μeV T−2 (Fig. 3c), indicatingagain that this emission originates from a bound state. Themagnetic field dependent DCP of Q2 shows a different behavioras Q1 and can be fit with the usual equation using Boltzmannstatistics of the involved spin-split defect states of cD1 (see Fig. 1dand Supplementary Fig. 5). The diamagnetic shift of Q* isnegligible (see Supplementary Figs. 7–9). In turn we interpret itsemission to stem from a wave function of chemically functiona-lized defects.In-plane magnetic field measurements on defects in MoS2To further investigate the details of the electronic states involvedin the emission lines Q1 and Q2, we turn to magneto-spectroscopy in the Voigt configuration for which the magneticfield (B∥) is applied parallel to the sample plane and perpendicularto the optical beam path (see Fig. 4a and Supplementary Note 3for data on Q*). In monolayer TMDs, strong spin-orbit couplingleads to out-of plane spin eigenstates particularly at the K=K 0points in the Brillouin zone. In principle, an in-plane magnetic fieldB∥induces a precession of the out-of-plane spins, leading to anincreased mixing of the spin-eigenstates with increasing B∥. Thismixing results in a magnetic-field dependent brightening of spin-forbidden transitions at K=K 0 with the intensity of the darktransitions increasing relative to the bright transitions withB∥259–61, similar to dark-bright mixing of interband transitions insemiconductor quantum dots with C3v symmetry62. Figure 4bshows a colormap of the PL versus B∥for Q1. We observe amonotonous redshift of the emission line, which is accompaniedwith spectral jitter with increasing magnetic field. Importantly, nobrightening of a lower lying emission line is observed. The dashedwhite line in Fig. 4b is a guide to the eye that shows a redshift ofQ1 with an in-plane magnetic moment μ∥=− 1μB.The in-plane magneto-PL of a typical Q2 quantum emitter isshown in Fig. 4c. At B∥ = 0 T, one emission line is observed at1.696 eV. This line diminishes with increasing B∥, while a new peak,1.4 meV red-shifted from the original Q2 emission line, quicklyappears above 3 T. Figure 4d shows the integrated PL ratio of thetwo lines together with a quadratic-in-B fit, consistently describingthe brightening of a dark transition. The low energy peakcontinues to red-shift with increasing B∥. This behavior can bedescribed with the magnetic field induced splitting of a dark andbright emission branch63ΔðBkÞ ¼ ðΔDB ±ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiΔ2DB þ ðμk � BkÞ2qÞ; (2)where ΔDB is the dark-bright splitting at B∥ = 0 T and ∣μ∥∣ is themagnitude of the in-plane magnetic moment. The white dashedline in Fig. 4c depicts Eq. (2) with ΔDB= 1.4 meV and ∣μ∥∣= 1μB.The excellent agreement between data and fit together with thequadratic dependence of the relative intensities of dark and brightemission branch (Fig. 4d) shows the brightening of a darktransition. This observation necessitates the involvement of twospin states in Q2, while the observation of the valley Zeemansplitting shown above requires the breaking of valley degeneracy.As such, we conclude that Q2 must be a superposition oftransitions involving both cD1 states and the valence band of thehost MoS2 (Fig. 4e). For neutral excitons in TMDs, a redshift withincreasing B∥was explained with the average valley Zeeman shiftof a bright and dark state (∣μ⊥,dark∣− ∣μ⊥,bright∣= 2∣μ∥∣)59,60,63. Ourobserved shift is in very good agreement with the calculateddifference of the bright and dark transition of Q2, which is simplygiven by the Zeeman splitting of the cD1 band (ΔμcD1= 2.2μB),extracted from Fig. 2e. Finally, the combined magneto-spectroscopy in the Faraday and Voigt geometry unambiguouslyidentifies Q2 as a spin conserving transition from the cD1 state tothe respective MoS2 valence band in the K=K 0 valley.The fact that the emission line Q1 is energetically higher thanQ2, while the diamagnetic shift, and therefore the binding energyof Q1 and Q2 are essentially the same, requires the defect bandvD to be located below the valence band edge of MoS2, assketched in Fig. 4e47–49.First-principles calculations on monolayer MoS2 withembedded sulfur vacanciesTo deepen the insight into the nature of Q1 and Q2, wetheoretically investigate exciton transitions in monolayer MoS2with embedded sulfur vacancies using ab initio calculations.Details about the calculation can be found in the SupplementaryNote 4 as well as the Methods section of refs. 47,48,64. In brief, weuse many-body perturbation theory within the GW-Bethe Salpeterapproximation with explicit spin-orbit coupling and spinor wavefunctions and compute the many-body Zeeman splitting follow-ing ref. 65. Figure 5a shows the mean calculated Zeeman splittingfor an excitonic absorption as a function of excitation energy. Linecolors represent the calculated absorption strength forFig. 4 In-plane magnetic field B∥measurements on the photo-luminescence of defect luminescence Q1 and Q2. a Sketch of thein-plane magnetic field B∥configuration (Voigt Geometry). Nopolarization optics were used in the detection path. b Emission ofQ1 remains bright for all fields. c The in-plane field reveals a secondstate Q2D energetically below Q2. The white dashed lines are guidesto the eye for the expected in-plane Zeeman shift of Q1 and thedark-bright-splitting of Q2. The dark-bright splitting ΔDB = 1.4 meVfor Q2 is calculated with Eq. (2). d The quadratic dependence of theemission ratio between Q2D and Q2 indicates the brightening of adark ground state. e Sketch of the defect levels with the possibleoptical transitions for Q1 and Q2 at finite B∥.A. Hötger et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    30 σ+polarized light. The mean Zeeman splitting at each energy iscalculated by averaging the Zeeman splitting of all discreteexcitons composing the overall optical absorption in a narrowenergy band. The transitions are broadened with a Gaussian andweighted by the oscillator strength of the respective excitons,which is calculated with the mentioned first-principles methods,accounting for the coupling between the associated electron andhole wave functions upon interaction with light (see Supplemen-tary Fig. 10). It has previously been shown47,48,64, that theenergetically lowest interband transitions are mainly composedof pristine MoS2 valence band to defect band transitions. Thestrongly varying average exciton Zeeman splitting is testament ofapproximately conserved valley selectivity in this energy range,which sensitively depends on the distinct electron-hole transitionsin a specific energy interval. We observe strong variations of theexciton Zeeman splitting in the energy range below ~1.70 eV,originating from the hybridization of the BSE excitations, whichmix electron-hole transitions from defect and non-defect bands.Specifically in the range of ~1.64–1.68 eV we observe a significantincrease of the Zeeman splitting, consistent with our observationfor the Q2 emission. This is a result of allowed transitions to in-gapdefect states of both spin components (Fig. 1c) In Fig. 5b, c and dwe show the normalized contributions of electron-hole transitionscomposing the excitons in this energy range (magenta shadedarea in Fig. 5a) at three representative points in the Brillouin zone(K, Γ, and K 0). The height of each bar corresponds to the relativecontribution of transitions from an occupied state (x-axis) to anunoccupied state (y-axis) upon excitation with σ+polarized light.At the K=K 0 points, we find strong contributions for electron-holetransitions between the pristine-like MoS2 valence band and bothspin states of cD1. As a result, in the region of positive averageZeeman splitting, the contribution is highest for transitions fromthe upper MoS2 valence band to the defect state cD1, ascontributions at the Γ-point are comparatively reduced. For Q1,the energy range between ~1.74 and 1.79 eV is selected. In thisenergy range, the absorption strength dominates, which isconsistent with the dominating PL of Q1 as compared to theother defect emission bands. Furthermore, a slightly positiveexciton Zeeman splitting is calculated, which again is consistentwith our observations in Fig. 2d. Figure 5e, f and g shows thecontributions of electron-hole transitions composing the excitonin the corresponding energy range. At the K=K 0-points, only band-to-defect transitions are contributing, whereas at the Γ-point,defect-to-defect transitions are dominating. Specifically, we findcontributions from the lower valence band to defect band cD2 atthe K=K 0-points in absorption. Unlike Q1, the calculations suggestthat the Q2 emission is only comprised of band-to-defecttransitions at the K=K 0-points. The hybridization of Q1 with theenergetically lower Q2 emission can be deduced from the band-to-defect contributions at the K=K 0-points.DISCUSSIONIn order to characterize the defect luminescence, Q1 and Q2 ofHe-ion irradiated monolayer MoS2 towards spin-defect properties,we combine our experimental observations with theoreticalinsight. He-ions create sulfur vacancies, which induce flat defectbands throughout the pristine bandstructure of monolayer MoS2.As a result, a high joint DOS for defect-to-defect transitions iscreated. At the K=K 0-points however, the defect vD lies below thevalence band maximum of MoS2, such that defect-to-bandtransitions are more likely. In high-field magneto-spectroscopy,we observe a diamagnetic shift of the defect luminescence Q1and Q2, which is consistent with a bound particle of ~3.5 nm. Thislocalized character will result in optical transitions covering asignificant momentum-space. Thus, the GW-Bethe-Salpeter equa-tion is useful for gaining deeper understanding into the defect-induced transitions. Here we find that the nature of Q1 and Q2 canFig. 5 GW-BSE results for optical absorption, exciton Zeeman splitting, and transition contributions. a Mean exciton Zeeman splitting as afunction of excitation energy. The colorcode on the line represents the absorption strength at each energy. b–d Electron-hole transitionscontributing to excitons in the energy range associated with Q2, namely in the magenta shaded area in a. The electron bands (cD1 and cD2),as well as the hole bands (vD and VB) are illustrated in energetic order under the consideration of the lifted spin degeneracy at theK=K 0-points. e–g Electron-hole transitions contributing to excitons in the energy range associated with Q1, namely in the gray shaded area ina. The transitions are shown for three selective k-points, K (b, e), Γ (c, f), and K 0 (d, g).A. Hötger et al.6npj 2D Materials and Applications (2023)    30 Published in partnership with FCT NOVA with the support of E-MRSbe viewed as mixed states of defect-to-defect and defect-to-bandtransitions. The level of this admixture determines the magneticmoment and valley selectivity of these hybridized transitions47,64.We find a dominant contribution of band-to-defect transitions atthe K=K 0-points for the energy interval of Q2, whereas Q1additionally acquires sizeable defect-to-defect character from theΓ-point. These contributions at the Γ-point induce a breaking ofthe valley selectivity, reflected in the small valley Zeeman splittingof this transition. For both Q1 and Q2, however, we find amagnetic-field dependent DCP, which necessitates spin conser-ving optical transitions. The distinct behavior of the DCP isexplained by the defect-to-band transitions at the K=K 0-pointscontributing to Q1 and Q2. The in-plane magneto-spectroscopyreveals a spin-forbidden dark ground state for Q2, whichunambiguously proofs the lifted spin degeneracy of the defectbands at the K=K 0-points even at zero magnetic field. In contrast,the absence of a dark state for Q1 can be explained by thesignificant portion of transitions happening at the Γ-point, wherethe defect bands are spin degenerate due to Kramers’ theorem.In conclusion, the combination of in-plane and out-of-planemagneto-spectroscopy identifies the Q1 emission as a defect-to-defect transition with admixture of Q2, which is dominated bytransitions from in-gap defect states to the pristine valence bandof MoS2. This outcome suggests tailored modification of thedefect luminescence through either charging or chemicalmodification (Q*, see Supplementary Note 2 and 3). We showthat the defect states at K=K 0 are split at zero magnetic field, aproperty that characterizes the sulfur vacancy in MoS2 as a spindefect with desirable features for possible quantum technologicalapplications.METHODSSample preparationMoS2 bulk crystals were purchased from HQGraphene, and thehBN crystals were provided by Takashi Taniguchi and KenjiWatanabe from NIMS, Japan. Monolayers of MoS2 and few-layerhBN were obtained by mechanical cleavage of bulk crystals. Thethin crystals were stacked with the viscoelastic transfer methodonto a Si substrate with 285 nm of thermal SiO2. After theassembly of the desired heterostructure, namely the MoS2encapsulated in hBN, the helium ion microscope (HIM) OrionNanoFab from Zeiss was used to precisely irradiate the samplewith He-ions at 30 kV in an array pattern with a pitch of 2 μm. Thedose was chosen to get a high yield of single sharp emitter linesfor Q1. For the photoluminescence measurements in Fig. 1b anexcitation wavelength of 639 nm and a power of 550 nW at a bathtemperature of 1.7 K was used. The photoluminesence signal wasguided on a nitrogen cooled CCD via a 300 grooves/mmdispersive grating. A long pass filter was used to extinguish thedirectly reflected excitation laser emission.Magneto-spectroscopyThe magneto-photoluminescence measurements were performedin a cryostat cooled to 4.2 K surrounded by a resistive magnet. Forexcitation, a laser diode with an emission wavelength of 515 nmwas used. For the measurements in Faraday configuration (B-fieldperpendicular to the sample plane and parallel to the opticalbeam path), the linearly polarized excitation was focused on thesample with an objective with NA = 0.81. The reflected light wascollected with the same objective and guided through a λ/4-platefollowed by a linear polarizer to select the σ+(σ−) polarized light inthe detection. A long pass filter was used to extinguish the directlyreflected excitation laser emission. The collected light wasanalyzed in a spectrometer equipped with a liquid nitrogencooled CCD and a 600 grooves/mm dispersive grating. Formeasurements in Voigt configuration (B-field parallel to thesample plane and perpendicular to the optical beam path) thesample was mounted vertically and the detection was unpolar-ized. A mirror tilted by 45∘ was used to guide incident lightperpendicular to the sample plane. A large working distanceobjective with NA = 0.35 was used to focus the excitation laser viathe tilted mirror onto the sample and collect the reflected light.Ab initio calculationsState-of-the-art ab initio ground-state and excited-state calcula-tions were carried out in a 5 × 5 × 1 supercell of monolayer MoS2composed of 74 atoms and a single sulfur vacancy. Ground stateDFT calculations were performed using the Quantum Espressopackage66,67 for assessing the atomic structure, spinor wavefunctions and single-particle magnetization, with an energy cutoffof 75 Ry. These properties were used as a starting point for a GW68calculation of the quasi-particle energies, including spin-orbitcoupling within the BerkeleyGW69 software, with summation over3998 bands on a 3 × 3 × 1 k-grid and an energy cutoff of 25 Ry forthe dielectric matrix. Electron-hole coupling and exciton energieswere calculated using BerkeleyGW by solving the Bethe-Salpeterequation (BSE)70,71 by interpolating the GW results to a k-grid of6 × 6 × 1 with a dielectric matrix which was calculated with a 5 Rycutoff and summation over 1798 bands. Quasi-particle magnetiza-tion corrections and many-body excitonic Zeeman splitting wereevaluated from the GW-BSE results following recently derivedmethods65,72. 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K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers19H05790, 20H00354 and 21H05233). T.A, G.C., D.H., and S.R-A. acknowledge supportfrom the David Lopatie Fellows Program and the ERC Starting grant 101041159. S.R.acknowledges support from the Independent Research Fund Denmark.A. Hötger et al.8npj 2D Materials and Applications (2023)    30 Published in partnership with FCT NOVA with the support of E-MRSAUTHOR CONTRIBUTIONSA.H., J.K., J.J.F., A.W.H., and A.S. conceived and designed the experiments. T.A, G.C.,D.H., and S.R-A. performed the DFT-GW and BSE calculations. S.R. and J.K. preparedthe sample. K.W. and T.T. provided high-quality hBN bulk crystals. A.H., A.S., T.P., A.D.,C.F., J.K., and K.B. performed the optical measurements. A.H. analyzed the data. C.K.,M.P., and C.F. contributed interpreting the data. A.H. and A.S. wrote the manuscriptwith input from all coauthors.FUNDINGOpen Access funding enabled and organized by Projekt DEAL.COMPETING INTERESTSThe authors declare no competing interests.ADDITIONAL INFORMATIONSupplementary information The online version contains supplementary materialavailable at https://doi.org/10.1038/s41699-023-00392-2.Correspondence and requests for materials should be addressed to A. V. Stier.Reprints and permission information is available at http://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jurisdictional claimsin published 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 anymedium 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. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023A. Hötger et al.9Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2023)    30 https://doi.org/10.1038/s41699-023-00392-2http://www.nature.com/reprintshttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Spin-defect characteristics of single sulfur vacancies in monolayer MoS2 Introduction Results Photoluminescence from sulfur vacancies in monolayer MoS2 Out-of-plane magnetic field measurements on defects in MoS2 In-plane magnetic field measurements on defects in MoS2 First-principles calculations on monolayer MoS2 with embedded sulfur vacancies Discussion Methods Sample preparation Magneto-spectroscopy Ab initio calculations DATA AVAILABILITY References Acknowledgements Author contributions Funding Competing interests ADDITIONAL INFORMATION