## Introduction

Point defects are important for a variety of physical phenonema in semiconductors. For example, they provide a means to engineer the equilibrium free-carrier density, they can serve as quantum emitters capable of hosting discrete quantum spin systems that can be optically addressed1. A major challenge in several of these applications is that the defects need to be precisely positioned, which is particularly difficult for conventional three-dimensional semiconductors where defects are often buried deep within the bulk structure. One route to remedy this challenge is to reduce the physical dimensionality of the material. Over the last decade it became possible to fabricate and manipulate atomically thin two-dimensional (2D) materials that offer intriguing electronic and optoelectronic properties2,3. In particular, the hexagonal transition metal dichalcogenides (TMDCs), such as MoS2, MoSe2, WS2, and WSe2, are excellent candidates for photonic applications due to their exceptionally strong light-matter interaction resulting from weak non-local dielectric screening4,5,6. The strong Coulomb coupling manifests itself in an exciton dominated spectral response and very large exciton binding energies4,5,7,8,9.

Beyond the response of mobile excitons, also quantum dot-like emission from localized excitons was recently demonstrated in WSe210,11,12,13,14, GaSe15, MoSe216, and WS217 and the nature of the potential, which localizes the excitons is still not fully understood. The origin of such quantum emitters was hitherto considered to be caused by uncontrolled strain potentials that locally reduce the band gap, thus, funneling the recombination of excitons via a discrete recombination center17,18,19,20. However, strain potentials are challenging to control, which limits the applicability of such quantum emitters for a prospective integration into quantum photonic circuits20,21,22,23,24,25. In particular, scalable quantum technologies require the development of controlled approaches for the direct planar integration of quantum emitters with atomic scale resolution.

In this work, we propose and investigate an alternative route to engineer defect emitters that are of atomic scale. Specifically, we demonstrate theoretically and experimentally that localized defects in two-dimensional layers create trapping potentials in which bound complexes are formed that emit in a range of about hundred meV below the free exciton line in MoS2. Our experimental approach to deterministically create such point defects involves site-selective helium ion exposure of small areas (100 × 100 nm) of atomically thin MoS2. The precision with which defects are localized is expected to be solely limited by the resolution of the helium ion beam. Compared to strain engineering, a controlled exposure with helium ions is superior due to the sub-nm beam size that is very well suited to structure 2D materials at the nanometer scale26. First attempts to generate optically active defects in TMDCs have been made by exposing the host crystal with α-particles27 and helium ions28. However, in these works a strong dynamical inhomogeneous linewidth broadening of ~40 meV was imposed on the emission due to the fluctuating environment. Here, we demonstrate that the encapsulation of helium irradiated MoS2 monolayers with hBN allows one to define defect emitters with very narrow linewidths. The combination of ion exposure and subsequent encapsulation results in a hitherto unobserved new class of spatially localized and spectrally narrow defect emission in MoS2 at very distinct energies on the order of ~100–220 meV below the neutral exciton, denoted by $$\,{}^0X_{1s}^A$$. Our spectroscopic observations are consistent with photon emission that stems from defect centers in MoS2, which serve as highly localized exciton emission centers. The interpretation is corroborrated by analyzing in detail the lineshape of the new emission peaks. This allows us to determine the interaction of the localized exciton with phonons, which indicates that the emitters are localized on a nanometer scale. Our study opens up new routes for inducing highly controllable defect emitters in two-dimensional materials to create arrays of coupled single-photon sources1, to study Anderson’s orthogonality catastrophe29,30, and to realize lattices of interacting excitons similarly to optical lattices for ultracold atomic gases31.

## Results

### Defect creation in a van der Waals heterostructure by helium ion irradiation

The van der Waals heterostrutures studied in this work are iteratively stacked onto Si substrates covered with 290 nm thermally grown SiO2. Onto this substrate we first transfer a multilayered hBN virtual substrate, and a single layer of MoS2. Typical hBN thicknesses vary between ~10–30 nm as confirmed by atomic force microscopy. The samples are transferred into a helium ion microscope, and are site-selectively exposed to helium ions at a constant dose of σ = 2.2 × 1012 cm−2, see Fig. 1a. Figure 1b shows a helium-ion microscope (HIM) image of the exposed van der Waals heterostructure. After the ion exposure, the entire MoS2 crystal is fully encapsulated by another multilayer hBN capping using a dry viscoelastic transfer method.

We perform low-temperature μ-photoluminescence (μ-PL) spectroscopy on the samples in a helium flow cryostat at a lattice temperature of 10 K. For excitation, we use a cw laser with a photon energy of 2.33 eV and a low excitation power (power density) of less than 10 μW (0.884 kW cm−2). Figure 1c shows the spatially resolved and spectrally integrated μ-PL response of a typical sample as a false color representation. Representative luminescence spectra from five randomly selected positions of the exposed sample that show defect emission are presented in the bottom of Fig. 1d and compared to a spectrum of a pristine (unexposed) sample. All spectra reveal spectrally narrow neutral exciton $$\,^0X_{1s}^A$$ (FWHM = (8.3 ± 2.5) meV) and charged exciton $$\,^ - X_{1s}^A$$ (FWHM = (9.4 ± 2.9) meV) emission whose inhomogeneous linewidth is reduced due to the encapsulation with hBN6,32,33,34. Remarkably, for the helium ion exposed samples in addition to the delocalized excitons, we observe spectrally sharper emission peaks XL (FWHM ~ 0.5–6 meV) in a window of ΔEL ~ 100–220 meV red-shifted from $$\,^0X_{1s}^A$$ (spectral range highlighted by a dotted box in Fig. 1d). These features are superimposed on the so-called L-peak that is observed in monolayer MoS24,5,35 and has recently been attributed to the presence of sulphur vacancies36,37. The sharp spectral features are spatially localized and require helium ion exposure of MoS2 and the subsequent encapsulation with hBN. Spectrally sharp peaks do not occur in unexposed hBN/MoS2/hBN heterostacks (cf. bottom spectrum in Fig. 1d), neither in exposed MoS2 without hBN encapsulation nor in exposed hBN (See Supplementary Fig. 1).

To obtain further information on the origin of the sharp spectral emission, we statistically evaluate the energetic detuning ΔEL = E($$\,^0X_{1s}^A$$) − E(XL) of each localized emission peak E(XL) with respect to E($$\,^0X_{1s}^A$$). Figure 1d, top, shows a histogram of the localized XL emission energies as a function of detuning ΔEL for ~3500 emitters for one representative sample (See Supplementary Fig. 5).

The histogram shows that the spectral emitters possess a continuum of energies in the range of ΔE~ 100–220 meV below the neutral exciton. Intriguingly, we consistently observe that most of the helium ion induced emission peaks emit in a spectrally narrow (15) distribution at ΔEL ~ 193 meV (also See Supplementary Figs 4 and 5).

We also show the spatial occurence of emitters in three energy bins (cf. arrows in Fig. 1d), overlayed in Fig. 1c. So far, single-photon emitters have been found at sample edges or folds, where the bandstructure is strongly influenced by the crystal boundary, coupling of atomic-orbitals by local symmetry breaking or strain1. By contrast, we find spectrally sharp emitters homogeneously distributed all over the 2D sample; this is a direct consequence of the helium ion exposure.

The sharp emission lines reveal a saturating behavior with a threshold power of Psat ~ 10 μW (cf. Figure 1e), which is consistent with saturating a finite density of a single defect state as fitted by

$$I \propto \frac{P}{{P + P_{{\mathrm{sat}}}}} .$$
(1)

By contrast, the 2D neutral exciton $$\,^0X_{1s}^A$$ shows the expected linear dependence with the excitation power. MoS2 exhibits several defects, most prominently single sulfur vacancies and single molybdenum vacancies38,39,40. So far, sulphur vacancies have not been demonstrated to be optically active, because they are very likely to be passivated with oxygen41, although they are ubiquitous in exfoliated, unexposed MoS237. Here, we concentrate on molybdenum vacancies VMo, although we are aware that the discussed defect emitters might be of character that is more complex. Figure 1f–i show the ab-initio calculated density of states (DOS) for a neutral $$V_{Mo}^0$$, as well as a single, double and triple negatively charged molybdenum vacancy ($$V_{Mo}^{1 - }$$, $$V_{Mo}^{2 - }$$, and $$V_{Mo}^{3 - }$$). The vacancy states have a trigonal and mirror symmetry between the two layers of the sulphur and the molybdenum layer40. In turn, two singlet (a1) and two doublet (e) states are expected for all cases. The lowest a1-p [e-p] level stems from the six adjacent sulphur p orbitals, and are found inside [above] the valence bands. The e-pd and a1-pd states originate from the hybridization of the six sulphur p and six (second nearest neighbour) molybdenum d orbitals and are situated in the gap40. We find that all presented states are stable and relaxed within our DFT framework. Since ΔEL is significantly smaller than the quasi particle band gap in MoS2, we assume that the Fermi energy is close to the conduction band minimum (CBM). We interpret the experimentally observed sharp emission lines as resulting from excitons that also involve particle-hole excitations from the defect state orbitals42.

Figure 1f–i demonstrates that for instance, for $$V_{Mo}^{2 - }$$ and $$V_{Mo}^{3 - }$$, the DFT computed Fermi energy $$E_F^{DFT}$$ is consistently close to the CBM. Taking the computed energy differences between each state and the CBM, our ab-initio calculation suggests that in this interpretation, the lowest unoccupied state in the $$V_{Mo}^{3 - }$$, the e-pd state, is likely to be involved in the photoluminescence signal XL as in Fig. 1d (cf. Supplementary Figs 5 and 9). In particular, the computed energy difference ΔEDFT = E(CBM)DFT − E(e-pd)DFT = 0.22 eV coincides with the highest experimental detuning ΔEL in the top panel of Fig. 1d. However, the DFT calculation does not consider the binding energy of the exciton that is comprised of the different electronic orbitals with a complex distribution of weights and varying momentum dependencies42.

### Site-selective creation of optically active defects by local helium ion irradiation

In order to demonstrate the site-selective nature of our approach, we write a matrix of 100 × 100 nm fields with a pitch of 2 μm onto monolayer MoS2 that is deposited on hBN. An optical micrograph of the flake prior to exposure is presented in Fig. 2a. Subsequent to exposure, the nano-structured MoS2 monolayer is fully encapsulated in hBN. We record a spatially resolved PL mapping of the treated areas with a small step size (250 nm). The corresponding spatially resolved and spectrally integrated PL mapping is presented in Fig. 2b (grayscale). Here, an integration range of ΔE = (193 ± 5) meV is chosen since, statistically (cf. Figure 1d), the localized emission is the strongest at these energies. Enhanced PL emission is clearly observed at the irradiated spots. Moreover, from the data, we extract and overlay the occurence of localized emission XL with the PL mapping (highlighted in orange). We find that localized emission is activated at all positions that are exposed by the HIM. Conversely, sharp line emission is not observed from the unexposed regions. Corresponding spectra of five exposed positions are presented in Fig. 2c. Each spectrum exhibits a small number (1–3) of emission lines that are completely absent in unexposed areas (cf. black spectra in Fig. 2c). Importantly, the site-selectively created defect emitters exhibit emission at ΔE ~ 193 meV in agreement with the distribution obtained from statistics in Fig. 1d (also See Supplementary Fig. 5). Since no annealing step is needed for emitter creation, the writing accuracy is expected to be predominantly limited by the helium ion beam, and is, therefore expected to be on the nanometer scale. Near-field optical techniques and scanning tunneling microscopy can further be used to ultimately reveal the writing accuracy of atomistic defect states in the monolayer MoS2.

### Photoluminescence excitation spectroscopy and time stability of an individual single defect emitter

To further corroborate the above interpretation of optically active defects, we perform photoluminescence excitation (PLE) spectroscopy to probe the energetic structure of the involved states. Figure 3a presents a false color plot for a typical PLE scan of an emission line XL as the excitation energy is tuned across the $$\,^0X_{1s}^A$$. The emission occurs at E(XL) = (1.76 ± 0.01) eV energetically well below the $$\,^0X_{1s}^A$$. When measuring differential reflectivity ΔR/R using a broadband supercontinuum source, we identify $$\,^0X_{1s}^A$$ at an energy of E ($$^0X_{1s}^A$$) = 1.95 eV (cf. Figure 3b). Upon resonant excitation of $$^0X_{1s}^A$$, the XL emission is significantly increased. This is a consequence of the efficient creation of excitons, when the laser energy is on resonance with an exciton transition (See Supplementary Fig. 7 for excitation on $$\,^0X_{2s}^A$$ and $$\,^0X_{1s}^B$$). Most significantly, we can excite XL states also below the free exciton transitions. This is consistent with recently predicted absorbance spectra of single vacancy defects in 2D materials42 and in contrast to strain induced quantum dot-like emitters10,11,12,13,14,15,17,18,19,20.

Another key property of photonic emitters is their spectral stability. A representative time trace of a defect emitter is presented in Fig. 3c (with a spectrum acquired every second). Examples of two spectra highlighted in Fig. 3c are plotted in Fig. 3d. They demonstrate that the emitter exhibits a blinking behavior. This is an observed feature of various types of few-level systems43. In our case, the blinking behavior is not surprising since the defects are embedded in a two-dimensional plane with large surface-to-volume ratio and charges in the environment that are very likely to randomly fluctuate in position and time.

### Defect-phonon interaction and the independent boson model

Measuring the temperature dependence of the μ-PL spectra allows us to determine the interactions between the involved electron orbitals and phonons. We gradually change the lattice temperature from 10 K to 300 K while recording μ-PL spectra (cf. Figure 4a). The spectra reveal emission from the defect emitters that are strongly red-shifted and simultaneously broadened at elevated temperatures (similar as for the $$\,^0X_{1s}^A$$). We analyze the evolution of the emitter XL in detail by utilizing the independent boson model that has been successfully applied to the lineshape analysis of quantum dot states44,45,46 and defect-bound excitons47. Figure 4b highlights the spectra of XL for selected temperatures with lineshapes fitted by this model (red lines). In particular, the lineshape of each emitter is found to exhibit a very pronounced acoustic phonon sideband (~10 meV) at the low energy side. Most likely, this low energy tail results from interaction with a specific bandwidth of acoustic phonons since the defects are highly localized in real space42. Our model particularly accounts for the coupling with LA/TA phonon branches, while coupling with the ZA branch is found to be negligible. For low temperatures, we find the best agreement of the calculated lineshape with our data for an effective Bohr radius of aB = 2 nm. Taking into account a theoretical phonon lifetime of $$\frac{1}{{\gamma _{ph}}}\sim 40\,{\mathrm{ps}}$$48, we obtain an excitonic radiative lifetime (linewidth) of ~1 ps (~0.5 meV). The lineshape in Fig. 4b is most asymmetric at low temperatures where phonon emission is more likely to happen than phonon absorption while for higher temperatures, the lineshape becomes more symmetric. Moreover, the PL emission reduces in intensity at elevated temperatures with the defect emitters typically exhibiting activation energies that are far below kBT (See Supplementary Fig. 10).

The temperature-dependent peak positions in Fig. 4a manifest in a polaron shift for all spectral features (cf. Figure 4c), as phenomenologically described by49

$$E_G(T) = E_G(0) - S\langle \hbar \omega \rangle \left[ {{\mathrm{coth}}\frac{{\langle \hbar \omega \rangle }}{{2k_BT}} - 1} \right],$$
(2)

with the emission energy EG(0) at 0 K, the Huang–Rhys factor S, the average phonon energy 〈ω〉, and the Boltzmann constant kB. Fitting XL in Fig. 4c reveals average phonon energies of 〈ω〉 = (12.69 ± 1.17) meV and an electron–phonon coupling of S = 0.791 ± 0.071 (for $$\,^0X_{1s}^A$$: 〈ω〉 = (25.11 ± 1.02) meV and S = 2.135 ± 0.061). The experimentally observed value of Sexp = 0.791 is in very good agreement with Stheory = 0.75 as obtained from the independent boson model (See Supplementary Fig. 12). From our model, we can also distinguish between the fraction of photons emitted by the zero phonon line (ZPL) and the phonon sideband (PSB). Taking the relative spectral weight of ZPL and PSB, we find a Debye–Waller factor of ~0.2 at 10 K, comparable to other few-level systems50.

## Discussion

To start the discussion, we point out that the emission peaks occur homogeneously across the whole basal plane of the exposed MoS2 encapsulated into hBN (cf. Figure 1c). The sharp peaks neither occur in exposed hBN without MoS2 nor in unexposed hBN/MoS2/hBN (See Supplementary Fig. 1). This phenomenology suggests that the optically active defects can probably not be explained by sulphur vacancies, because the latter are ubiquitous in exfoliated, unexposed MoS237, although they are very likely to be produced under helium ion exposure as well28,38,40. However, sulphur vacancies are easily passivated by oxygen41, which especially applies to the discussed nano-fabricated TMDCs under ambient conditions. Figure 2b, c support this interpretation, since the emission XL only appears at the exposed areas, while the unexposed areas show the broad L-peak attributed to the presence of sulphur vacancies36,37. Equally, quantum emitters in hBN can be excluded for our sample (See Supplementary Figs 1 and 8)51. Intriguingly, the beam energy of the HIM (30 keV) and also the excess energy of the secondary electrons (<10 eV) produced in the exposed materials are sufficient to form defects with a large formation energy, such as molybdenum vacancies40,52, that are rare in pristine samples37,39. This argument could explain why we observe optically active defect sites only after the helium ion exposure of the MoS2 monolayers.

In our understanding, the influence of hBN is two-fold. On the one hand, the emission peaks XL have the lowest emission energy of ΔEL of ~193 meV below $$\,^0X_{1s}^A$$. Encapsulated in hBN, the excitonic emission energy is renormalized due to the dielectric environment6. On the other hand, the emission linewidth is strongly reduced for both XL and $$\,^0X_{1s}^A$$6,32,33,34. The combination of the hBN-effects explain the sharp spectral features, which are spread across the broad energy window ΔEL ~ 100–220 meV in Fig. 1d. However, most of the defects emit at an energy detuning of ~193 meV, which resembles the spectrally broad PL emission of helium ion exposed MoS2 on SiO2/Si substrate28 and on hBN (See Supplementary Fig. 2). This observation is also in good agreement with the emission properties of site-selectively activated defects in Fig. 2. From our consistent observations, we draw the conclusion that most of the emission indeed originates from the same helium ion induced defect that is deterministically created at designated positions in the MoS2 monolayer. The defect emission at smaller detunings ΔEL < 180 meV is most likely caused by dielectric effects, adsorbates or simply by another type of defect.

For all possibly created defects, the emission at ΔEL of ~193 meV must resemble the lowest unoccupied, optically active state. This interpretation is consistent with the saturating behavior as in Fig. 1e, and it also explains the blinking behavior in Fig. 3c, d. Furthermore, the PLE measurements in Fig. 3a are also consistent with this interpretation, since the expected joint density of states of localized electron orbitals at the defect and its environment sum up to a finite, continuous absorbance from the lowest unoccupied state (i.e., at ΔEL of ~193 meV) up to $$\,^0X_{1s}^A$$42. The excitation laser creates electrons that can occupy the defect states followed by optical recombination with a valence band hole and possible further local defect orbitals42.

We would like to note that there are few possible defects in MoS2, from the already mentioned sulphur and molybdenum vacancies to interstitials and defect complexes involving more than one atom.38,39,40. For the sake of clarity, we concentrate on VMo. Our DFT calculation in Fig. 1 neglects the momentum dependence of the involved electron states and variable binding energies per orbital42. In our experiment, the influence of ambient gases might have further effects28. Taking the argument of refs. 40,42, the complex admixture of p- and d-orbitals in the molybdenum defect (cf. Figure 1f–i) give rise to a continuous absorbance below $$\,^0X_{1s}^A$$, as recently discussed for single chalcogen vacancies40,42.

Figure 4b demonstrates that the effective exciton–phonon interaction can be described by the independent boson model, which suggests that the effective interaction length is localized within only ~2 nm. The independent boson model further suggests an excitonic lifetime of only 1 ps (See Supplementary Fig. 12). This theoretical value is a lower bound for the actual lifetime because we omit other sources of broadening mechanisms. Experimentally, we determine the upper bound of the radiative lifetime to be <150 ps (limited by the instrument response function), which renders second order time-correlation measurements of g(2) challenging. This experimental observation is in stark contrast to strain induced quantum dot-like emitters in TMDCs with nanosecond lifetimes based on an effective type-II band alignment10,11,12,13,14. Different excitation conditions in gated devices that could suppress the L-peak emission may enable to access the photon statistics and unambiguously proof the quantum nature of the defect emission.

In conclusion, we have demonstrated a method to deterministically and site-selectively generate optically active defects in MoS2. The superior optical quality resulting from hBN encapsulation reveals spectrally narrow emission at very distinct detunings with respect to the neutral exciton. The emission lines show a saturating power dependence and a blinking behavior. On a broader perspective, a controlled production of optically active defects in a periodic pattern using helium ion beam exposure may allow the exploration of exotic many-body physics in lattice systems, including the demonstration of coupled photon sources1, the Anderson orthogonality catastrophe29,30, as well as the Mott transition between a superfluid and an insulator31 in the presence of dissipation. The site-selective approach for writing optically active defects with high accuracy and ease at designated positions is expected to be highly beneficial for integration into photonic circuits. Moreover, the inherent proximity of the engineered defect states to surfaces opens exciting ways for possibly harnessing them as local nanometer scale sensors, investigating nuclear spin physics with wave functions only sampling a fraction of atoms or studying screening physics in the ultimate limit of a localized electronic defect state.

## Methods

### Sample structure

We employed the viscoelastic transfer method to transfer MoS2 monolayer crystals and hBN multilayers onto 290 nm SiO2 substrates. The MoS2 crystals used for exfoliation were purchased from SPI Supplies while high-quality hBN bulk crystals were provided by Takashi Taniguchi and Kenji Watanabe from NIMS, Japan.

### Helium ion microscopy

We used MoS2 monolayers transfered onto hBN/SiO2/Si substrates for He+ irradiation. For the data shown in Fig. 1, a beam current I ~ 1 pA and a beam energy of 30 kV are used. Large areas are exposed with a beam spacing of 5 nm. The dwell time was adjusted such that a dose of ~1012 He+ cm−2 is obtained, which is optimized for a high density of defect emitters (See Supplementary Fig. 6).

For the data shown in Fig. 2, a low beam current of I ~ 20 fA is used in order to obtain a low helium ion dose of ~1012 He+ cm−2 by accordingly adjusting the dwell time. Small areas of 100 × 100 nm are exposed. A beam spacing of 0.5 nm is used.

### Optical spectroscopy

Confocal optical spectroscopy was performed in a helium flow cryostat with the sample kept at a lattice temperature of ~10 K. For cw μ-PL experiments in Fig. 1, we used a doubled Nd:YAG laser with an excitation energy of 2.33 eV and typical excitation powers of less than 10 μW, which results in an excitation power density of 0.884 kW cm−2 at a laser spot diameter of 1.2 μm.

The μ-PL data in Fig. 2a are recorded with an excitation energy of 2.54 eV and an excitation power (density) of 900 nW (0.058 kW cm−2) with a laser spot diameter of 0.7 μm.

For measuring differential reflectivity spectra a supercontinuum white light source was used that was focused with an optical microscope onto the sample kept at a lattice temperature of ~10 K with a spot size of ~1–2 μm.

For PLE experiments, we used an optical parametric oscillator (OPO) pumped with a Ti:Sa at 820 nm with a repetition rate of 80 MHz and a 150 fs pulse width. For our measurements, we used the signal output of the OPO, which was incrementally tuned in steps of ~25 meV from 1.8–2.45 eV. The excitation power was kept at 20 μW for all excitation energies. The excitation laser pulse was filtered with a sharp edge filter before being dispersed on a grating and detected with a charge-coupled device (CCD).

### DFT calculations

The calculations were performed using density functional theory (DFT) as implemented in the Vienna ab-initio simulation package (VASP)53,54. The projected augmented wave method has been used55,56. The atomic and electronic structures were determined using the PBE functional. A plane wave basis with an energy cutoff of Ecut = 500 eV and a (6 × 6 × 1) Monkhorst-Pack k-point sampling has been used. The TMD layer has been modeled using a (9 × 9) supercell containing 242 atoms.