A substitutional quantum defect in WS$_2$ discovered by high-throughput computational screening and fabricated by site-selective STM manipulation

Point defects in two-dimensional materials are of key interest for quantum information science. However, the space of possible defects is immense, making the identification of high-performance quantum defects extremely challenging. Here, we perform high-throughput (HT) first-principles computational screening to search for promising quantum defects within WS$_2$, which present localized levels in the band gap that can lead to bright optical transitions in the visible or telecom regime. Our computed database spans more than 700 charged defects formed through substitution on the tungsten or sulfur site. We found that sulfur substitutions enable the most promising quantum defects. We computationally identify the neutral cobalt substitution to sulfur (Co$_{\rm S}^{0}$) as very promising and fabricate it with scanning tunneling microscopy (STM). The Co$_{\rm S}^{0}$ electronic structure measured by STM agrees with first principles and showcases an attractive new quantum defect. Our work shows how HT computational screening and novel defect synthesis routes can be combined to design new quantum defects.


INTRODUCTION
Point defects in semiconductors are considered as building blocks for quantum information science (QIS) applications.Optically-active quantum defects (OQDs) can be used in quantum sensing, memory, and networks [1][2][3][4] .The performance of an OQD depends on its fundamental properties and limitations that can vary across defects 5,6 .Certain defects, such as the silicon-divacancy center in diamond, show robust optical coherence but low spin coherence, while the NV − center in diamond shows high spin coherence but lower optical coherence 7,8 .The identification of new OQDs in a specific host with optimal spin, optical, and electronic properties is essential to the development of QIS applications.Two-dimensional (2D) materials, particularly transition metal dichalcogenides (TMDs), provide an enormous phase space of functionality with tunable and exceptional spin, optical and electronic properties [9][10][11][12][13][14][15][16][17] .Additionally, as materials are reduced from bulk to lower dimensionality, the spincoherence lifetime of an OQD is expected to increase 18 .A decisive factor for an OQD is the appearance of in-gap localized states making it important to understand and measure the electronic levels induced by a defect in a given 2D host.While a number of techniques can routinely resolve the atomic lattice, the electronic levels introduced by the defect in the host are not easily accessible by most experimental techniques.However, scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) can probe atomic-scale defects at the required length scale 19,20 .This has been used to characterize many defects in 2D materials, e.g., carbon radical dopants, chalcogen vacancies, oxygen substitutions, and a variety of metal substitutions 15,16,19,[21][22][23] .Next to these experimental developments, first-principles approaches have been successfully used to compute and understand the properties of quantum defects in bulk semiconductors and 2D hosts [24][25][26][27] .First principles techniques have even been used to suggest OQDs in 2D materials, but these studies have remained targeted on a few defects and have not browsed the large elemental space of possible defects [28][29][30][31][32] .
Here, we use first principles high-throughput (HT) computing to build a database of point defects in WS 2 considering all possible substitutional defects from 57 elements.We use this database to identify a handful of promising defects and show that the substitution of cobalt on sulfur (Co S ) in WS 2 is especially appealing.First principles computations indicate that the neutral Co S shows several localized levels in the band gap, spin multiplicity, and a potential for bright telecom emission.This defect is then synthesized in situ, examined with STM/STS, and the measured energy levels confirm and benchmark the theoretical predictions, which highlights a unique two-level quantum system.

HIGH-THROUGHPUT SEARCH
A greatly sought-after electronic structure for an OQD involves two localized defect levels (one occupied, the other unoccupied) well within the band gap 33 .This requires a precise matching of defect and band edge levels.Additionally, the optical transition between these defect levels should be bright and exhibit large transition dipole moments (TDMs).While having localized defect levels within the band gap is not in itself necessary for developing OQDs, this electronic structure has advantages in terms of brightness and robustness versus temperature 34 .With the 2.4 eV electronic band gap for WS 2 , finding defect levels that are at the same time isolated within the band gap and with transitions in the telecom or visible range (from 750 meV up to 2 eV) should be achievable.However, identifying defects that could act as an OQD within WS 2 is challenging.
To search for such a defect, we have built a database with the computed electronic structure of 757 charged point defects in WS 2 considering either the tungsten (M W ) or sulfur (M S ) substitution site (see Fig. 1a).All the elements from the periodic table are used with the exception of rare-earths and transuranides.We start our screening by computing the relaxed structure and formation energies of the defect in multiple charge states within Density Functional Theory (DFT) in the generalized gradient approximation (GGA).Single-particle energies and band gaps are notoriously underestimated within DFT and one of the gold standards in defect computation is to use hybrid functionals such as PBE0 which adds a fraction of Fock exchange to the GGA functional 35,36 .
Figs. 1 and 2 for a full list with their single-particle levels).We identify a series of potential singlet OQDs that could act as single-photon emitters and are formed through the substitution of W with a main group element: Sb −1 W , P −1 W , Pb −2 W , N −1 W , and C −2 W .Only two transition metal defects appear as promising singlets: Os W and Ti S .Spin multiplets that are of greater technological interest only appear through sulfur substitution: Co 0 S , Fe 0 S , Zn 0 S , Si −1 S , and W +1 S except for Ru 0 W .The W S defect has been suggested as an OQD by Tsai et al. as well, but in the zero charge state 28 .Notably, common substitutional defects to tungsten in WS 2 : Re, V, Nb, Mo, and Cr, do not show an adequate electronic structure (see Supplementary Fig. 3) 19,[38][39][40][41] .They all have at most one level in the band gap of the substitutional d orbital character that is slightly above the valence band edge (V) or below the conduction band (Cr and Re).They are only excitable optically through a transition between a localized defect state and a delocalized band level forming a bound exciton 34 .Our findings agree with experimental results from photoluminescence or STS on M W defects 19,38,40,41 .

r 5 t X e A H z n
x N E = < / l a t e x i t > P W Fig. 1: Two-Level Quantum Defect Screening in WS 2 .a Two defect configurations that are considered in this work: substitution on W site (M W ) and on S site (M S ).b Transition dipole moment vs. singleparticle excitation energy at the single-shot PBE0.The marker and color scheme stand for the defect structure and whether the ground state is singlet or not.Each point stands for a charge defect that is thermodynamically stable within a certain E F range in the band gap, and with electronic structures that possess two localized defect levels within the band gap, as shown in the inset.
While substitutional transition metals on W sites are easy to synthesize, our screening results show that this is not the most promising approach for OQD discovery.All our candidate transition metal OQDs except Ru 0 W and Os 0 W show up instead as M S .Fig. 2a shows the different electronic structure for M W and M S in a molecular orbital diagram picture when M is a transition metal 42  and d z 2 with an energy ∆d according to crystal field splitting theory.For the sake of simplicity, we assume here a C 3v and D 3h point group respectively for the M S and M W defects, where lower symmetry through Jahn-Teller distortions are also possible.We performed bonding analysis, and determined density of states, for all 3d transition metal defects (Supplementary Fig. 4) and we observed a smaller splitting between bonding and anti-bonding states for M S versus M W (∆ AB ).This can be rationalized by the different atomic positions for sulfur and tungsten orbitals.Additionally, the splitting between d orbitals (∆d) is higher for M S versus M W . Fig. 2b shows the positions of bonding and anti-bonding molecular orbitals across the 3d

CANDIDATES
While our analysis shows that within gap d-d transitions are more likely in M S and rationalizes why there are still differences between M S defects.Fig. 1 shows that Co 0 S is by far the most attractive OQD considering its non-singlet spin multiplicity, its large excitation energy, and transition dipole moment.
We compute the electronic structure and formation energy for this Co 0 S defect within full-fledged PBE0 computations including structural relaxation and self-consistency.We plot the defect formation energy for different charge states of Co S versus E F in Fig. 3a.The defect is stable in its zero charge state spanning a large E F range.The two thermodynamic charge transition levels correspond to (+1/0) at 0.4 eV above the valence band maximum (VBM) and (0/1−) at 0.4 eV below the conduction band minimum (CBM).The electronic structure of the neutral Co 0 S is shown in Fig. 3b.A full description of the electronic structure for all three charge states is given in Supplementary Fig. 5.The neutral defect undergoes a Jahn-Teller distortion towards the C s symmetry.While there is significant mixing with the host, the projection on the Co-3d orbitals is provided in Fig. 3b with the wavefunctions illustrated in Fig. 3c  h The apparent height difference of Co S compared to adsorption atop as-grown WS 2 is measured to be 0.15 nm, taken from linescans across both f and g red highlighted regions.
In order to investigate the evolved electronic structure with SPM, we make use of STS and differential conductance mapping, which are representative of the local density of states (LDOS) over a given defect.Point STS over Co S is shown in Fig. 5a-b, where in-gap states near 0.36 eV and 0.47 eV are measured.We attribute peak broadening to electronic-phonon coupling, where effective electron-phonon coupling strength is estimated with a single-mode Franck-Condon model 16 .We include multiple phonon modes and additional quanta of each mode (available for co-excitation) in the description detailed in Supplementary Fig. 6 to explain dI/dV signal strength and broadening observed beyond the model approximation.Additionally, a resonance peak is identified at negative voltages (−0.84 ± 0.06 eV) that is attributed to electronic charging from the underlying substrate to Co S , which shifts the defect to an anion state, where an electron is, on average, donated to available Co S defect levels.Spatially resolved DOS below the charging onset is comparable to that of the occupied orbitals in the anionic state and to the charge neutral state above this onset.Fig. 5c-e shows high-resolution differential conductance image maps that detail electronic orbital densities measured at −0.9 eV, 0.36 eV, and 0.47 eV.The LDOS at these energies are further benchmarked against calculations at the PBE0 level of theory and shown in Fig. 5f-h for each energy range experimentally measured, where Co S unoccupied orbitals are hybridized with bonded W atoms and are ∼1.5 nm in diameter (see Supplementary Fig. 7 for simulated STS for charge states presented).We find strong agreement between experiment and theoretically obtained energy levels and orbital symmetries, where we can then assign the dI/dV peak at 0.36 eV to predominately d x 2 −y 2 orbital density, and the peak measured at 0.47 eV to a mixing of d yz and d xz orbitals at the Co S charge neutral state.The peak at −0.84 eV is attributed to the Co S charging (to Co −1 S ), and is discussed in further detail below.Quantitatively, the d x 2 −y 2 state is experimentally 0.64 eV below the CBM while theory predicts a level 0.5 eV below the CBM, indicating a good agreement.We attribute the sharp peak at −0.84 eV to a charging process of the neutral cobalt to the anionic Co −1 S state.This charging is due to the localized tip-induced band bending process has been described in the literature on similar systems 16,46 .The Co S lowest unoccupied state is occupied at adequate negative voltages and alters the Co S charge state making it anionic, detailed in Fig. 5i-j.The neutral/anionic charge transition level is computed to be around 2.1 eV above the VBM (see Fig. 3) which is close to the charge transition level for V S (see Supplementary Fig. 13) for which a charging peak at a similar Our HT data indicates that fundamental electronic structure reasons make transition metal substitution on sulfur sites more likely to lead to a OQD with in-gap defect states that could emit in the telecom or visible than for the tungsten substitution.This motivates more efforts in the community along that direction.The fabrication process and HT computational screening used to identify Co S highlight the capability of combining HT screening and advanced synthesis techniques to identify and realize new OQDs.This can be performed across a wide range of atomic species within 2D materials and other hosts with many yet to be experimentally realized, which can be executed for a number of different desired material properties, e.g., from catalysis to QIS.

Scanning probe microscopy (SPM) measurements
All measurements were performed with a Createc GmbH scanning probe microscope operating under ultrahigh vacuum (pressure < 2×10 −10 mbar) at liquid helium temperatures (T < 6 K).Either etched tungsten or platinum iridium tips were used during acquisition.Tip apexes were further shaped by indentations onto a gold substrate for subsequent measurements taken over a defective substrate.STM images are taken in constant-current mode with a bias applied to the sample.STS measurements were recorded using a lock-in amplifier with a resonance frequency of 683 Hz and a modulation amplitude of 5 mV.

Sample preparation
Monolayer islands of WS 2 were grown on graphene/SiC substrates with an ambient pressure CVD approach.A graphene/SiC substrate with 10 mg of WO 3 powder on top was placed at the center of a quartz tube, and 400 mg of sulfur powder was placed upstream.The furnace was heated to 900 • C and the sulfur powder was heated to 250 • C using a heating belt during synthesis.A carrier gas for process throughput was used (Ar gas at 100 sccm) and the growth time was 60 min.The CVD grown WS 2 /MLG/SiC was further annealed in vacuo at 400 • C for 2 hours.Cobalt was deposited at a pressure of 1 × 10 −9 mbar for 60 seconds with the sample held at 5 K.

Neural network and Gaussian process implementation
The acquisition software used for autonomous experimentation was gpSTS, which is a library for autonomous experimentation for scanning probe microscopy 20,47 .An Intel Xeon E5-2623 v3 CPU with 8 cores and 64 GB of memory combined with a Tesla K80 with 4992 CUDA cores was used for training the neural network.Training data for WS 2 and V S was combined with Co S spectra obtained from an extended autonomous run.

First-principles calculations
We considered 57 elements that could substitute for W and S in the construction of a WS 2 quantum defect database, as highlighted in the periodic table in Supplementary Fig. 1.This collection covers the majority of the elements except the rare-earth elements and noble gases.All defect computations were performed at DFT level using automatic defect workflows that are implemented in ATOMATE software package [48][49][50] .
The defect structure generations and the formation energy computations are performed using PYCDT.
The DFT calculations were performed using Vienna Ab-initio Simulation Package (VASP) 51,52 and the projector-augmented wave (PAW) method 53 with the Perdew-Burke-Ernzerhof (PBE) functional 54 .Each charged defect is simulated in a 144-atom orthorhombic supercell and with a vacuum of approximately 14 Å.A plane-wave basis energy cutoff of 520 eV was used and the Brillouin zone is sampled using Γ point only.The defect structures were optimized at a fixed volume until the forces on the ions are smaller than 0.01 eV/Å.The charge states of each defect are determined by considering all the oxidation states of the elements documented in the ICSD database 49 and taking into account the formal charges in WS 2 (W 4+ and S 2− ).The total energy of the charged defects were further corrected to overcome the finite-size effect using the method of Komsa et al. 55,56 as implemented in SLABCC 57 .
The above procedures generated overall 757 substitutional charged defects in monolayer WS 2 .Based on the defect formation energy, we first identified 260 charged defects that are thermodynamically stable, meaning their charge states are accessible in a certain E F range.Among these stable defects, we further search for the ones that possess two in-gap, localized levels that would enable the optical intra-defect transition.The localization is defined using inverse participation ratio (IPR) as detailed below.We considered levels with IPR larger than 0.05 as localized states (bulk-like states in general have IPR smaller than 0.01 in WS 2 ).This trimmed down the list to 143 candidates, among which 112 have non-singlet ground states.The classification of singlets and multiplets is based on the electronic structure of the defect.In this case, the singlets and multiplets refer to the total magnetic quantum number of the unpaired electrons.Thus, defects with all electrons paired are classified as singlet, while those with one or two paired electrons are classified as doublet, triplet, etc.We note that due to limitations of Kohn-Sham (KS) DFT and possibility of spin contamination for spin-polarized systems, more powerful methods such as spin-flip Bethe-Salpeter are required in general to rigorously determine the total spin S 58 .Finally, we screened out the ones that would emit at telecom wavelength with reasonable brightness.The emission wavelength is approximated using the single-particle KS energy difference using the single-shot PBE0 incorporating 7% of Fock exchange.We refrained from applying potential corrections at this stage as the optical transition is approximated by the transition dipole moment (TDM) as detailed below.To search for the most relevant transitions, we consider the transitions that give the smallest energy difference, while also allowing an energy window of up to 100 meV to take into account the errors and band degeneracy.We then identified the transition with the largest TDM as the most relevant transition.The above procedures recommend 17 non-singlet candidates that emit at least 750 meV with a TDM of 3 D, as shown in Supplementary Table 1.
The localization of an orbital is described using the IPR.For a given KS State, the IPR is evaluated based on the probabilities of finding an electron with an energy E i close to an atomic site α [59][60][61] : where the summation runs over all atomic sites α.The participation ratio χ −1 stands for the number of atomic sites that confine the wave function.Thus, a larger (smaller) IPR indicate a localized (delocalized) state.IPR is unitless ranging between 0 to 1.We computed IPR using VASP PROCAR.The optical transition dipole moment was evaluated by the PYVASPWFC code based on the single-particle wavefunction calculated at the PBE level 62 .The transition dipole moment is written as: where ℏ is the Planck constant, ε i,k and ε f,k are the eigenvalues of the initial and final states, m is the electron mass, ψ i and ψ f are the initial and final wavefunctions, and p is the momentum operator.
For selected substitutional defects, we carried out the fully self-consistent hybrid functional (PBE0) calculations including structural relaxations.In line with the single-shot PBE0 calculations and following previous work 36 , we described the defect levels using the mixing parameter α = 0.07 for the Fock exchange, which generally satisfies the Koopmans' condition for localized defects in monolayer WS 2 .On the other hand, we used α = 0.22 for the pristine WS 2 to determine the band-edge position.The alignment of defect levels with respect to the band edges was then achieved through the vacuum level which serves a common reference level.Spin-orbit coupling (SOC) is taken into account unless otherwise specified.We used a planewave cutoff energy of 400 eV and a 2 × 2 × 1 k-point mesh for ground-state calculations.The zero-phonon line was assessed using a single Γ point by imposing occupation constraints (constrained DFT 27 ).For charged defects, the total energies are subject to finite-size effects and were corrected by the method of Komsa et al. 55,56 as implemented in SLABCC 57 , whereas the single-particle KS levels were corrected by the potential correction scheme (SCPC) of Chagas da Silva et al. 63 .The simulated STM images were plotted at a constant height of 3.5 Å above the surface using the STM-2DScan package 64 based on the Tersoff-Hamann theory 65 . SUPPLEMENTARY r z y r m A p 7 J 2 I o U D b O H N / 0 I 1 f B m D 0 7 W 2 w 7 7 t v h P O 3 X w T t / W b 4 o 7 l / e V A / 2 q 7 + s k p 2 y F e y R 0 J y S I 7 I K b k g L c L J X 3 J P H s i / 2 p O 3 6 z W 8 5 k u o V 6 t y t s i M e Y f P e L 3 E z w = = < / l a t e x i t > N W < l a t e x i t s h a 1 _ b a s e 6 4 = " L i X 4 o w a Y m W 6 K p 5 9 P 7 w 8 4 J A J M 9 q Q

Fe 0 S
< l a t e x i t s h a 1 _ b a s e 6 4 = " O h W O 1 8 B Y 0 H L 7 3 1 L a C o h 6 y + 3 0 k e s = " > A A A C f n i c b V H b S i N B E K 2 M l 9 W 4 3 l 8 E X 5 o N L g o a Z 2 T Z 9 V F Q 0 A c f l N 2 o m M T Q 0 6 n E J t 0 9 Q 3 e N G I b 8 h 6 / 6 V / 6 N P T G I i V t Q c D i n 7 h W n S j o K w 9 d S M D U 9 M / t t b r 6 8 8 H 1 x a X l l d e 3 K J Z k V W B O J S u x N z B 0 q a b B G k h T e p B a 5 j h V e x 7 3 j Q r 9 + Q O t k Y v 5 R P 8 W m 5 l 0 j O 1 J w 8 t R d w 2 p 2 a 1 r 5 3 8 F d H g 5 a K 5 W w G g 6 N f Q X R C F R g Z B e t 1 d J t o 5 2 I T K M h o b h z 9 S h M q Z l z S 1 I o H J Q b m c O U i x 7 v Y t 1 D w z W 6 Z j 4 c e 8 C 2 P N N m n c R 6 N 8 S G 7 O e M n G v n + j r 2 k Z r T v Z v U C v J / W j 2 j z m E z l y b N C I 1 4 b 9 T J F K O E F T d g b W l R k O p 7 w I W V f l Y m 7 r n l g v y l x r o M a 6 c o x j b J H z Sb W < l a t e x i t s h a 1 _ b a s e 6 4 = " j R + Y D J L N N t o I O t i Q T T v n d A R i h K M = " > A A A C f n i c b V F N S y N B E K 2 M r r p x / d 6 b l 8 b g 4 o L G G R H 1 K O y C H j y 4 i z F i E k N P p x K b d P c M 3 T V i G P I / 9 q r / a v + N P T G I i R Y U P N 6 r 7 4 p T J R 2 F 4 f 9 S M D P 7 Z W 5 + 4 W t 5 8 d v S 8 s r q 2 v q 1 S z I r s C Y S l d i b m D t U 0 m C N J C m 8 S S 1 y H S u s x / 1 f h V 5 / Q O t k Y q 5 o k G J L 8 5 6 R X S k 4 e e q u a T X 7 m 7 X z + v A u D 4 f t 1 U p Y D U f G P o J o D C o w t s v 2 W u m 2 2 U l E p t G Q U N y 5 R h S m 1 M q 5 J S k U D s v N z G H K R Z / 3 s O G h 4 R p d K x + N P W T b n u m w b m K 9 G 2 I j 9 n 1 G z r V z A x 3 7 S M 3 p 3 k 1 r B f m Z 1 s i o e 9 L K p U k z Q i N e G 3 U z x S h h x Q 1 Y R 1 o U p A Y e c G G l n 5 W J e 2 6 5 I H + p i S 6 j 2 i m K i U 3 y x 8 x I k X R w i l X 0 S J Z 7 0 i F p L k 2 x V X 6 O 6 g F 9 h z f e F y y E n d + y J 8 n t X v h H m N 0 z i 9 j / + T 6 4 X P b f i K Z v / x F c H 1 S j o + r B n 8 P K 6 f f x X x Z g E 7 Z g B y I 4 h l M 4 h 0 u o g Q A L / + A J n g M I f g R 7 w f 5 r a F A a 5 2 z A h A U n L 3 s 9 x F Y = < / l a t e x i t > Ru 0 W < l a t e x i t s h a 1 _ b a s e 6 4 = " d J j P E J N i g 9 p 7 O n 5 h W w H I k H J e n x k = " > A A A C f n i c b V F N S y N B E K 2 M r r p x 1 + + b l 2 a D 4 o L G G R H 1 K K y w H j y 4 a F R M Y u j p V J I m 3 T 1 D d 4 0 Y h v y P v e q / 2 n + z P T G I i R Y U P N 6 r 7 4 p T J R 2 F 4 b 9 S M D P 7 Z W 5 + 4 W t 5 8 d v 3 p e W V 1 b U b l 2 R W Y E 0 k K r F 3 M X e o p M E a S V J 4 l 1 r k O l Z 4 G / d / F f r t I 1 o n E 3 N N g x S b m n e N 7 E j B y V M P D a v Z l W z l V 8 O H f G / Y W q m E 1 X B k 7 C O I x q A C Y 7 t s r Z b u G + 1 E Z B o N C c W d q 0 d h S s 2 c W 5 J C 4 b D c y B y m X P R 5 F + s e G q 7 R N f P R 2 E O 2 5 Z k 2 6 y T W u y E 2 Y t 9 n 5 F w 7 N 9 C x j 9 S c e m 5 a K 8

2 W
r 8 8 K 5 g J u x f i a 5 A e 3 j r f q E P r w 1 A / + B 3 c D 7 v v h F M 3 / 4 v e C i X g p N S + e 6 4 e L E 9 / s s i 2 S G 7 Z J 8 E 5 J R c k B t S I V X C S U L e y D v 5 8 G a 8 A 8 / 3 y t + h X m 6 c s 0 U m z D v / A m K 3 x K s = < / l a t e x i t > Pb < l a t e x i t s h a 1 _ b a s e 6 4 = " 2 r d b D s G A 8 x Q P q 0 y K g L F R g / 5 l D A A = " > A A A C f n i c b V H b S i N B E K 2 M u + p m v b t v v j Q G x Q W N M y L q o 7 A L + i D o w s a I S Q w 9 n U p s 0 t 0 z d N e I Y c h / 7 K v + 1 f 6 N P T G I i R Y U H M 6 p e 8 W p k o 7 C 8 H 8 p m P n y d X Z u / l v 5 + 8 L i 0 v L K 6 t q 1 S z I r s C Y S l d i b m D t U 0 m C N J C m 8 S S 1 y H S u s x / 1 f h V 5 / Q O t k Y v 7 S I M W W 5 j 0 j u 1 J w 8 t R d 0 2 p 2 6 d p 5 f X i X h 8 P 2 S i W s h i N j H 0 E 0 B h U Y 2 1 V 7 t X T b 7 C Q i 0 2 h I K O 5 c I w p T a u X c k h Q K h + V m 5 j D l o s 9 7 2 P D Q c I 2 u l Y / G H r I t z 3 R Y N 7 H e D b E R + z 4 j 5 9 q 5 g Y 5 9 p O Z 0 7 6 a 1 g v x M a 2 T U P W n l 0 q Q Z o R G v j b q Z Y p S w 4 g a s I y 0 K U g M P u L D S z 8 r E P b d c k L / U R J d R 7 R T F x C b 5 Y 2 a k S D o 4 x S p 6 J M s 9 6 Z A 0 l 6 b Y K j 9 H 9 Y C + w x v v C x b C z m / Z k + R 2 L / w j z O 6 Z R e z / f B 9 c L v t v R N O 3 / w i u D 6 r R U f X g z 2 H l 9 M f 4 L / O w A Z u w A x E c w y m c w x X U Q I C F f / A E z w E E 2 8 F e s P 8 a G p T G O e s w Y c H J C 3 D R x F E = < / l a t e x i t > Os 0 W MW MS < l a t e x i t s h a 1 _ b a s e 6 4 = " d F H 6 a H h m t 0 7 X w 8 9 o j t e K b L e o n 1 b o i N 2 f c Z O d f O D X X s I z W n B z e r F e R n W j O j 3 k k 7 l y b N C I 1 4 b d T . For both substitutions, the d orbitals of the defect mix with either sulfur (M W ) or tungsten (M S ) forming bonding and anti-bonding states separated by ∆ AB .Additionally the different d orbitals are split in three groups: (d xz ,d yz ), (d xy ,d y 2 −x 2 )

Fig. 2 :
Fig. 2: Molecular orbital trend within the 3d transition metal series for M S and M W defects. a The molecular orbital diagram shows the splitting between anti-bonding and bonding state (∆AB) as well as the splitting with d orbitals (∆d) for a typical M W and M S defect.b A schematic of the bonding and anti-bonding state for different 3d transition metals in M W (blue) and M S (yellow) positions.

Fig. 3 :
Fig. 3: Thermodynamic charge transition levels and electronic structure of Co S .a Formation energy of Co S as a function of Fermi level.The charge transition levels are referenced to the band-edge positions of pristine WS 2 as obtained with PBE0 incorporating 22% of Fock exchange PBE0(0.22).b Orbital diagram of the localized defect states for neutral Co S .Resonant states within the valence band and conduction band manifolds are not depicted.The occupied (unoccupied) states are shown by the filled (empty) rectangles, the height of which indicates the degree of dispersion.The band-edge positions refer to those of the pristine WS 2 obtained with PBE0(0.22).Energies are referenced to the vacuum level.SOC is not taken into account for the localized defect states.c Top view of the charge density (in blue) for the three Co 0 S defect states as indicated in b.The isovalue is 0.001 e/Å 3 .
. The defect shows occupied d xy and d z 2 states well within the band gap that can be excited to the unoccupied d x 2 −y 2 , d xz or d yz levels that are also below the conduction band.The lowest energy transition is between the d z 2 and d x 2 −y 2 states and sits at a 1.5 eV difference in single-particle energies and shows a TDM of 1.2 D. All these values are obtained from full PBE0 but confirm the prediction from our screening at the single-shot level.The zero-phonon lines (ZPL) associated with this transition can be computed in constrained DFT by imposing the occupation of the unoccupied d x 2 −y 2 state and relaxing the structure.We compute a ZPL of 0.96 eV, well within the telecom region.Transition from the d z 2 to the next orbital (d xy )is significantly higher with a ZPL of 1.18 eV (and a TDM of 3.0 D).All these results confirm the interest of the neutral Co substitutional defect as it combines emission in the telecom and spin multiplicity.

Fig. 4 :
Fig. 4: Co S Defect Formation and Characterization.a The process of forming a high density of V S , b low-temperature deposition of Co atoms in situ, and c subsequent placement into a V S with the assistance of the STM probe that is used to selectively manipulate atoms at voltage ranges below −1.3 V is shown schematically.Corresponding scanning tunneling micrographs that capture WS 2 /Gr/SiC(0001) d after defect introduction via Ar + bombardment and e post Co deposition are plotted (I tunnel = 30 pA, V sample = 1.2 V).Scale bars, 2 nm.STM images f before a voltage excitation and g after Co substitution within an identified V S are also shown (I tunnel = 30 pA, V sample = 1.2 V, V excitation = −2.1 V).Scale bars, 2 nm.

Fig. 5 :
Fig. 5: Experimental and Simulated Co S Scanning Tunneling Spectroscopy.a STS spectra recorded on a Co S defect and the as-grown WS 2 monolayer on graphene (V modulation = 5 mV).b In-gap states identified are located at peak maxima of 0.36 eV and 0.47 eV, each with a full-width half maximum near 0.045 eV.Differential conductance (dI/dV) imaging maps over the defect are depicted at c −0.9 eV, d 0.373 eV, and e 0.486 eV (V modulation = 5 mV), showing Co S orbital geometries.Scale bars, 0.25 nm.f-h Simulated STS maps using PBE0 over Co S orbitals identifying energy range densities near experimentally measured values.Scale bars, 0.25 nm.A charging peak is identified in a, where the i lowest unoccupied Co 0 S state becomes j resonant with the E F of the substrate and an electron is donated to produce the Co −1 S defect.Both c and f are representative of the Co −1 S orbital densities collected at the specified energy (the charging ring onset in c is removed for clarity).