Optical Properties of MoSe2 Monolayer Implanted with Ultra-Low-Energy Cr Ions

This paper explores the optical properties of an exfoliated MoSe2 monolayer implanted with Cr+ ions, accelerated to 25 eV. Photoluminescence of the implanted MoSe2 reveals an emission line from Cr-related defects that is present only under weak electron doping. Unlike band-to-band transition, the Cr-introduced emission is characterized by nonzero activation energy, long lifetimes, and weak response to the magnetic field. To rationalize the experimental results and get insights into the atomic structure of the defects, we modeled the Cr-ion irradiation process using ab initio molecular dynamics simulations followed by the electronic structure calculations of the system with defects. The experimental and theoretical results suggest that the recombination of electrons on the acceptors, which could be introduced by the Cr implantation-induced defects, with the valence band holes is the most likely origin of the low-energy emission. Our results demonstrate the potential of low-energy ion implantation as a tool to tailor the properties of two-dimensional (2D) materials by doping.


Introduction
The properties of semiconductors, especially atomically thin monolayer (ML) semiconductors, depend strongly on the types and densities of defects in their crystal lattices.The most technologically relevant defects are dopants, i.e., foreign atoms in substitutional positions in the crystal lattice.Shallow dopants introduce free electrons or holes into the conduction or valence band and change thus semiconductor conductivity.As such they facilitate the fabrication of p-n junctions, which underpins most active optoelectronic devices.Doping with transition metal atoms has been shown to introduce ferromagnetic order in p-doped semiconductors. 1 Impurity atoms can also trap electrons or holes or bind excitons.
Radiative recombination involving such states can be detected as sub-bandgap photoluminescence (PL).4][5] The binding of excitons to the dopant atoms depends not only on electron and hole masses but also the dielectric constant of the semiconductors.Because of that, excitonic effects in bulk semiconductors are only observed at cryogenic temperatures.Foreign atoms can also act as colour centres in semiconductors and insulators.Spin qubits based on the colour centres have been realised in diamond [6][7][8][9] or SiC. 10,11 two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs), which feature weak electrostatic screening, substitutional atoms tend to introduce deep levels in the bandgaps. 12While excitons have considerable binding energies, they are predicted to be very weakly bound to individual doping atoms. 135][16][17] The transition responsible for the PL was found to occur between the hybridised defect states and 2D lattice electronic states.
Among several methods of doping bulk semiconductors, ion implantation offers the highest flexibility in choosing implanted elements.Ion energies of tens of keV are used for implantation since functional layers can be even a hundred nanometers below the surface.
High-energy ion implantation has been used [18][19][20][21][22] to modify 2D materials, but its efficiency is low in this case, as most atoms go through the 2D target. 23Moreover, the ions penetrating through the ML can cause undesirable effects, e.g., trapped charges in the substrate.
Implantation into 2D materials has the highest implantation efficiency with ion energies in the range of tens of eV.At these energies, the implantation efficiency and threshold energy depend on the ions' mass and also chemical properties. 24Ultra-low energy ion implantation 25,26 has recently been demonstrated to be efficient in doping graphene using 40 eV Mn ions, 27,28 or in Se ion implantation into MoS 2 with the ion energy of 20 eV. 29,30The ratio of the replaced S atoms with Se in the top sublattice was sufficient to form a Janus compound MoS 2-2x Se 2x as indicated by Raman spectroscopy and the transmission electron microscopy imaging.
Here, we study the optical properties of MoSe 2 ML implanted with 25 eV 52 Cr + ions.
Sub-bandgap defect-induced PL emission was observed only at the low n-doping level and with saturation behaviour, characteristic of defects with low density.Ab-initio molecular dynamics (MD) simulations of the implantation process were performed, and possible configurations of the Cr atoms in the MoSe 2 ML lattice were outlined to understand the atomic structure of the implanted MLs.The optical properties of the MoSe 2 ML with such defects were calculated using density functional theory (DFT).The most probable defect configurations were identified by combining experimental data and theoretical calculations.

Sample preparation and ion implantation
A sample for ion implantation was prepared by mechanical exfoliation of the MoSe 2 , graphene, and hBN flakes and their sequential transfer onto the Si/SiO 2 substrate with pre-patterned Ti/Au contacts.The use of the dry-viscoelastic transfer technique 31 ensured that the surface of the ML was sufficiently clean for the implantation.The MoSe 2 ML has to be grounded during the implantation.An electric contact to the ML was provided by placing the multilayer part of the exfoliated MoSe 2 flake on a Ti/Au metal contact.The ML was placed atop a graphite gate connected to another Ti/Au contact.The ML was separated from the gate with an hBN flake.Once completed, the device was implanted with 52 Cr + ions at 25

Optical spectroscopy data
Figure 2a shows PL spectra of weakly electron-doped pristine and Cr-implanted MoSe 2 MLs, measured at 10 K with the same laser power of 1 µW.Both spectra show similar features around the bandgap transitions, with an emission line from neutral excitons (X) and negative trions (X − ).The red shift of these transitions in the Cr-implanted sample (figure 2a) is most likely due to a difference in the dielectric environment or strain between the samples.The level of implantation is too low to expect changes in the bandgap. 33gnificant homogeneous broadening of the X line was determined by Voigt function fitting.
It resulted in the Lorentzian width of nearly 7 meV for the implanted sample, compared to about 2 meV for the pristine sample, suggesting a much shorter lifetime of the former.The most significant difference between the samples is a broad emission at around 1.51 eV, which we label D.  Excitation power ( W) The relative intensity of the D peak compared to X − and X depends on the excitation power P (figure 2b).It is the most intense line at low laser excitation powers (P < 1 µW) but saturates as the laser power increases, while X − and X continue to grow linearly.The saturating behaviour of D intensity, shown in figure 2c), can be expressed phenomenologically as: with saturation power P sat ≈ 10 µW.The saturating behaviour is expected when the exciton generation rate exceeds the recombination rate of the states responsible for D. The saturation threshold depends on the density of states and the lifetime of the recombining carriers. 14,16e low threshold for D is consistent with the low implantation level.The lifetime of carriers was measured from time resolved PL.The decay of the population of the excited states contributing to the D-peak after a pulsed excitation can be seen in figure 2d.As can be expected from measuring an ensemble of emitters, the decay is not a single exponential.The very fast initial decay of population by about 10%, which is faster than the time resolution of the experiment, is followed by a slower decay with the 1/e decay time of around 14 ns.
These decay times are 2-3 orders of magnitude longer than the lifetime of free excitons in MoSe 2 MLs 34-37 and one order of magnitude longer than that from the isolated, confined excitons, 38 pointing to a low oscillator strength of the emitters.
The doping-dependent PL from neutral and charged excitons shown in figure 3a is typical of MoSe 2 MLs.When increasing the gate voltage, the D emission only emerges after the signal from the positive trion, X + , entirely disappears.It reaches the maximum intensity around 1 V, the gate voltage of the transition between X and X − dominated spectra.The D line weakens strongly as the X − line intensifies with a further gate voltage increase.
This behaviour suggests a competition between the exciton capture at the defect state and the formation of an X − .This scenario is supported by PL excitation (PLE) spectroscopy measurement (figure 3b), which shows that the intensity of D emission is maximum when the excitation wavelength is resonant with the energy of X around 1.637 eV.D emission was not excited with laser resonant with X − (around 1.608 eV) even though the PL spectrum, measured at the same doping level, clearly shows that the ML is doped with electrons (X − emission is the strongest PL signal).Figure 4a compares gate-dependent PL at 22 K and 108 K.While X − emission is the most intense line in the spectra at the lower temperature, it is very weak at the higher temperature.X becomes the strongest line, but D diminished less than X − and remains up to room temperature (supplementary figure ??).We trace the change of PL signal counts from X − and D, both normalised to X signal counts, on the Arrhenius plot shown in figure 4b.X − dissociates into higher energy X and an electron at higher temperature.Its intensity can be fitted with the standard Arrhenius formula: [39][40][41] I(T ) = I(0) where I(0) is the PL intensity at temperature 0 K, A is a proportionality constant, E a is the activation energy for the dissociation of X − , and k B is the Boltzmann constant.Fitting the formula to the data gives E a ≈ 32 ± 5 meV, which is expected for a binding energy of the trion. 13,42D emission intensity first increased with temperature up to around 34 K before diminishing.To account for this initial increase in intensity, we assume that trapping of carriers that recombine requires overcoming activation energy.We use a modified multilevel model for the temperature dependence of D intensity: 41,43-46 where A 1 , A 2 are proportionality constants, and E a1 and E a2 are activation energies for trapping and detrapping of carriers.Fitting of the D peak yields E a1 ≈ 1 ± 6 meV, and E a2 ≈ 30 ± 9 meV.The intensities were then normalised to that of X (at the voltage where X is most intense).Lines: the best-fit line was according to equations ( 2) and ( 3).(c) The temperature-dependent bandgap of X and D (symbols).Line: the best-fit line was according to equation ( 4) Temperature affects not only the intensity but also the D emission energy.The temperaturedependent energy shift of X and D lines can be described by the modified Varshni relation 16,47,48 as where E g (0) is the emission energy at 0 K, S is the electron-phonon coupling, and hω is the average phonon energy.Fitting gives hω = 11.1 ± 1.3 meV and S = 1.82 ± 0.14 for X, similar to the reported values ( hω ≈ 12 -20 meV, S ≈ 2 [48][49][50][51][52] ).The fitted hω and S for D emission are smaller, at 10.7 ± 1.5 meV and 0.79 ± 0.09, respectively.Smaller S constant compared to excitonic lines has been reported for vacancy-induced PL emissions from TMD MLs 16,17,53 and explained as a result of the defect being decoupled from the conduction band, which varies with the temperature.Similar scenario is also likely to be the case in our sample.
To gain further insight, we measured the PL emission from the sample under out-of-plane magnetic field B varying from -8 to 8 T. Figures 5a show the splitting of X and X − spectra in two circular polarisation detection states under applied B-field.The valley splitting, caused by the Zeeman effect ( [54][55][56] ) and defined as (where E σ + and E σ − are the emission energy in the detected circular polarisation basis σ + and σ − respectively, g is the Landé g-factor, µ B is the Bohr magneton) changes linearly with the applied magnetic field (figures 5b).The g-factors derived from the data are -3.69 ± 0.04 and -4.80 ± 0.03, for X and X − , respectively.The g-factor value for X is close to the ones from previous experimental work [55][56][57][58][59][60][61] which are between -3.8 and -4.3 and well within the expected range from -3.22 to -3.82 predicted by recent ab initio calculations. 62,638][59] On the other hand, D emission shows little change with the magnetic field (figure 5c).Comparing the energy of photons from D peak in both circular polarisation gives g-factor of about -1.18 ± 0.06.The peak position was determined by fitting the data with three Voigt functions and then taking the maximum of the fitted line.The uncertainty here is high, partly owing to the D peak's large width.

First-principles molecular dynamics simulation of Cr ion implantation into MoSe 2 ML
To get insights into the defect formation process and types of defects which can appear upon impacts of energetic Cr ions, we carried out DFT MD simulations, as described below.The atomic structure of a free-standing MoSe 2 rectangular slab containing 90 atoms was fully optimised, then a Cr atom was placed 6 Å above its surface, figure 6(a) and kinetic energy of 25 eV was assigned to the atom.Normal incidence was simulated; that is, the initial velocity vector of the projectile was oriented perpendicular to the surface of the ML.The projectile was assumed to be a neutral atom, as at such low energies and low charge states, its neutralisation must occur well before it reaches the surface.We note that DFT MD on the Born-Oppenheimer surface cannot describe the evolution of charge transfer anyway, and the Ehrenfest dynamics 64,65 should be used.21 impact points were selected in the irreducible area of the primitive cell of MoSe 2 , figure 6(b), and the outcomes of the simulations were averaged with the corresponding weights.The MD runs continued until the kinetic energy brought up by the projectile was distributed over the whole supercell (normally after a few picoseconds), then the system's temperature was quenched to zero, and the atomic structure was analysed.Although the effects of substrate on defect generation in a 2D system can be significant for ions with much higher (keV range) energies, [66][67][68] the role of the substrate should be minimal for impacts of 25 eV Cr ions onto MoSe 2 , so that a free-standing slab was simulated.Spin-polarised calculations were carried out.Although computationally more efficient non-spin-polarised method with a correction for isolated atom polarisation energies can be used to simulate irradiation effects, 24 the account for spin effects is particularly important for Cr, as it is magnetic, which affects the energetics of defect configurations.
Figure 6(c) shows the most common atomic configurations which appear after Cr atom impacts.These are Cr adatoms, X-sub configuration (Cr at Se sites with a Se adatom 69 ), interstitials (the Cr atom between Mo atoms) and substitutional defects in Mo and Se sites, which are Cr@Mo and Cr@Se respectively.Table 1 lists the probabilities for the defects to appear.Ion irradiation also gives rise to the sputtering of Se atoms, that is the formation of Se vacancies (V Se ), but these events were not so common.Self-annealing of defects at finite temperatures at which irradiation was carried out in the experiment can affect their concentrations in the implanted samples.To get insight into the possible evolution of defects, we assessed the defect formation energies E f , as done previously. 69For adatoms, interstitials and X-sub defects, E f was calculated as the energy difference between the system with Cr atom and the pristine system plus isolated Cr atom.
For the Cr@Mo, Cr@Se and V Se configurations, the energies of isolated Mo and Se atoms were also taken as a reference.We note that the listed defect formation energies for the Cr@Mo, Cr@Se, and V Se cannot be used to assess the equilibrium concentrations of these defects, as the chemical potentials were chosen to match isolated, that is sputtered, atoms.
This can be done, though, if the chemical potentials of the displaced Se and Mo atoms are chosen in such a way that they reflect the actual experimental conditions that the potential can be anywhere between the values corresponding to the Se or Mo-rich limits.This would result in lower formation energies, as the sputtered atoms would be incorporated in the lattice.It can also be assumed that the displaced Se atoms form Se clusters at the surface, which would give rise the lowering of Cr@Se defect energies.
As evident from Table 1, E f for adatoms is lower than for the interstitials, so that at finite temperatures, the interstitials will most likely be 'pushed away' from the Mo plane and form adatoms.We note that this result was obtained for a relatively small 90-atom supercell, and in the larger system, the difference between these energies is smaller, as reported earlier. 69Nevertheless, even for equal formation energies at zero temperature, with account for the entropic term in the Gibbs energy, the probabilities for the adatoms should be higher due to a larger configurational space.Some X-sub defects may also be converted to Cr@Se configurations, especially in the Mo-rich limit, when Se vacancies are present, but the energetics of this process naturally depends on the experimental conditions, that is, the choice of Se chemical potential.The Cr@Se defects can also appear due to the adsorption of Cr atoms on Se vacancies, as this is energetically favourable due to the saturation of dangling bonds.Thus one can expect that the most prolific defects in the samples are Cr adatoms (or Cr clusters on top of MoSe 2 ), X-sub, as well as Cr@Mo and Cr@Se substitutional configurations.However, quantitative differences between theory and experiment should be expected due to the neglect of many-body effects and also due to the difference in the dielectric environment.

DFT calculations of optical properties
The theoretical spectra are shown in figure 7. Absorption below the bandgap (around 1.6 eV) is present for all defects and originates from transitions involving the defect states.
There is an optical transition for X-sub at 1.5 eV, which is in the same energy range of D emission from the PL spectra, between the valence band and an acceptor state of X-sub.
This state results from the coupling of the conduction band at the K point with the Cr defect state.[73][74] The weak transition involving a deep acceptor state at 0.9 eV is outside the spectral range of our experiments.We note that the coupling between the conduction band and the defect state shifts the conduction band minimum from K towards the Γ point (supplementary figure ??).However, the resulting suppression of PL would not be visible in the experiment due to the low density of defects and only the local opening of the bandgap.Well-defined spin-degenerate acceptor levels are also introduced by Cr substituting the Mo atom in the lattice (Cr@Mo).Optical transitions from this defect state into the valence band states can be seen in figure 7 in the range between 1.4 and 1.5 eV, which is also in a similar energy range to D peak PL emission.The band-to-band transition is shifted to higher energy compared to the pristine MoSe 2 ML because of the coupling between the conduction band and the defect state.However, similar to the X-sub configuration discussed above, it is unlikely to observe this blueshift in the PL spectra due to the low defect density.
The coupling of the defect and conduction band results in a gradual increase of the above-bandgap absorption for Cr substitution into the Se site (Cr@Se).This defect type also introduces a donor state at the Fermi level and two single-spin, deep defect levels.The signal from the donor state merges with the band-to-band absorption.Otherwise, the Cr defect at the Se site hardly affects the MoSe 2 band structure.Several weak optical transitions are present at a large range of energies (down to 500 meV below the bandgap).
Interstitial Cr introduces several deep defect levels in the bandgap, and again the highest state couples to the conduction band shifting the conduction band minimum to the Λ point.
The absorption spectrum does not contain discrete absorption lines but a gradually increasing absorption from 1.2 eV.

Discussion
Radiative recombination of an electron (e − ) bound to a defect state with the valence band hole (h + ) can explain the measured PL.Considering that our DFT calculations do not show donor states at high enough energy, the electron here is likely to occupy an acceptor.In this scenario, an exciton bound to a negatively charged acceptor (A − X) dissociates into A − h + and a free electron in the conduction band.Following radiative recombination, A − h + becomes neutral acceptor A 0 .Theoretical modelling of A − X indicated a binding energy of only a few meV compared with A 0 + e − state, 13 which is of the same order of magnitude as the activation energy of the D-line determined from the Arrhenius plot.Among the potential defects identified by MD calculations, Cr@Mo, X-sub, and Cr@Se have non-zero matrix elements for optical transitions between acceptor states and valence band.Other configurations, e.g.interstitial Cr or Se vacancies, are unlikely to be present.Besides, neither would explain the data (see figure 7 and supplementary information note 4).
The measured 1/e recombination time is longer than the lifetimes reported for band-toband and localised states recombination in MoSe 2 .Low oscillator strength of the transition can result from the spatial separation of electrons and holes, as for Cr@Se or X-sub.However, since this lifetime is longer than that of the spin dark states in WSe 2 , which is only a few ns, 75 this transition could also be from a spin forbidden state.Such a state would correspond to the charge configuration of A 0 for Cr@Se defect in the absence of exchange interactions between electrons in the conduction band.
The g-factor of D emission is negative but much smaller than the ones for X or X − .
With large g-factors for electrons in the valence band, it implies either a large g-factor for an electron on the acceptor level near the conduction band (e.g. in Cr@Mo or X-sub configuration) and valley-selective transitions or reduced g-factor of holes in the valence band.The latter could be caused by the hybridisation of the valence band with the defect level as in the Cr@Se configuration.Further insight would require higher magnetic field measurements and theoretical input.

Conclusion
In More generally, this study shows that while implantation of heavier elements into metal sub-lattice of TMD MLs is possible without a visible loss of the material quality, the implantation process is complex, and simulations of the possible outcomes are necessary to identify material systems of the desired properties.In the search for single photon emitting sites, it is also worth noting that upon implantation with a very low fluence, it should be possible to address individual Cr atoms at different lattice sites.

Atomistic simulation
We used DFT-MD as implemented in the VASP code. 76,77The Perdew-Burke-Ernzerhof (PBE) exchange and correlation functional was employed. 78The evolution of the system was modelled using the microcanonical ensemble.A cutoff value of 300 eV was chosen for DFT MD, and sampling over the Brillouin zone was done using a 3×3×1 k-point mesh.The time step was chosen to be 0.1 fs, which provided energy conservation better than 0.1 eV.

Band structure and absorption spectra calculation
Density functional theory (DFT) simulations were performed in supercells of 5×5 primitive unit cells.Each constructed with lattice constants of a = 3.28 A and c = 12.918A of the hexagonal lattice.An internal structure parameter of z = 0.125 was used.The defect systems were spatially relaxed using FLEUR 79 until the residual atomic forces had fallen below 5 × 10 −2 eV/ A. The subsequent calculation of the macroscopic dielectric function in SPEX 80,81 is based on the random-phase approximation 82,83 and includes local-field effects.
Calculations of 2D materials with 3D periodic boundary conditions are computationally expensive because the decoupling of neighbouring layers in the z direction requires large supercells in this direction.In the case of 2D systems with defects, the computational cost grows considerably, particularly in the case of low defect concentrations, because suppressing the unwanted defect-defect coupling requires large supercells in the x and y directions.To facilitate the calculations of the dielectric function, we had to reduce the reciprocal cutoff radius from 4.1 to 3.6 Bohr −1 in the case of the X-sub defect system.However, this should not affect the form of the respective spectrum shown in figure 7.
The band structures presented in the Supplementary Information are made up of 320 k points along the unfolded high-symmetry path Γ − M − K − Γ.Here, "unfolded" means that the high-symmetry points refer to the ones of the defect-free MoSe 2 ML.The necessary unfolding of the band structures of the defect systems has been carried out with a new implementation 71 in the FLEUR code adapting the technique described in Ref. 84 to the LAPW basis. 85In this technique, a spectral weight is assigned to each state plotted in the band structure.The weight w n (k) for the n-th state at k of the unfolded path is given by where k = k + G with a suitable reciprocal lattice vector G that folds k back into the (smaller) Brillouin zone of the defect system.The G sum runs over the set of all reciprocal lattice vectors (of the defect system) at k , and the G sum runs over the set of reciprocal lattice vectors (of the pristine system) at k.The latter is a subset of the former.The wave functions are represented in the LAPW basis {χ kG (r)} with coefficients C kn (G) and overlap matrix S GG (k) = χ kG |χ kG . 71

Sample preparation
Si with 90 nm thick dry-thermally grown SiO 2 chips with 60 nm thick Ti/Au contacts (pre-patterned by electron beam lithography) were used as the substrate.Before flake transfer, the chips were cleaned in acetone and isopropanol (IPA) under bath sonication, blown dry with N 2 and treated with oxygen plasma (300 W, 200 sccm for 10 minutes).Fewlayer graphite, MoSe 2 (from 2D Semiconductors) MLs, and hBN (from Takashi Taniguchi and Kenji Watanabe) multilayers were mechanically exfoliated from bulk crystal using polydimethylsiloxane (PDMS) stamps (Gel-pak DGL X4 films) and transferred onto the substrate using dry viscoelastic transfer process. 31The process was performed in a N 2 filled glovebox.
After transferring the graphite (5.5 nm thick) and bottom-hBN (20 nm thick) flakes, the sample was annealed in H 2 /Ar (1:10 ratio) atmosphere at 300 • C for 3 hours to improve the top surface for the subsequent MoSe 2 ML transfer.After transferring the top-hBN (15 nm thick), the sample was annealed in low vacuum (5 × 10 −3 mbar) at 200 • C for 2 hours to improve interfaces in the vdW stack.Electrical contacts, provided by the Ti/Au lines, were made to the MoSe 2 flake and the graphite back gate.After each transfer, the heterostructure surface was checked with atomic force microscopy to ensure a sufficiently flat area in the stack and to obtain the flakes' thickness.MoSe 2 ML's quality was confirmed with Raman and PL spectroscopy at room temperature. 86

Ion implantation
Bronze tips were used to fix the sample on a holder, making contact with the sample's Au pads and, thus, the ML.To remove volatile contamination from the sample, the sample chamber was then evacuated to 10 −9 mbar for several hours.The sample was heated to 150 • C for 10 minutes to remove residual volatile adsorbates, then to 220 • C during the implantation.A foil is used as the feedstock to provide 52 Cr + ions.After extraction, the ions are decelerated from 30 keV to 25 eV directly in front of the sample.Since the deceleration voltage is set relative to the potential of the source anode, this energy represents the upper limit, with a tail towards lower energies.The fluence of the ions was set to 3 × 10 12 cm −2 .
The fluence was verified by test implantations using Rutherford backscatter spectrometry (more information in Supplementary information ??).A detailed description of the source and the implantation system can be found in the references. 25,265 Optical measurements PL spectroscopy was performed at 10 K (unless otherwise specified) in a He-cooled cold-finger cryostat (Cryoindustries) with a heating element (allowing a sample temperature range from 10 to 300 K).For PL measurements, the laser beam -688 nm (1.80 eV) from a Ti:Sa laser -is passed through a 680 ± 5 nm band-pass filter before being focused by an aspheric lens (NA = 0.47) into a spot of 1.6 µm in diameter on the sample.Unless otherwise specified, the laser power on the sample was at 1 µW for PL experiments.PL signal is collected by the same lens and passed through a 700-nm low pass filter before being focused by an achromatic doublet (NA = 0.24) through the entrance slit of a Czerny-Turner spectrometer, dispersed by a 600 l/mm grating onto a CCD camera.For gate dependence and temperature dependence PL, the laser power was kept at 1 µW.For PLE, excitation power ranged from 2 to 5 µW, and PL intensity is normalised to the power density for final data.
For time-resolved PL, the excitation was done using a pulsed laser at 660 nm (1.

Supplementary note 2 -Spatial distribution of D peak
Figure S2 shows the 2D integrated micro-PL (µ-PL) maps for D, X and X − emissions.Compared to the excitonic emission map of X and X − , D emission is observed only in the implanted MoSe 2 ML area and does not come from the hBN or Gr layer underneath.The emission is also not from localised sites, e.g.wrinkles, scratches or bubbles in the ML, but rather the whole ML.The apparent difference between the bright and dark halves in the ML is likely from inhomogeneous doping provided by the bottom Gr gate.

Supplementary note 3 -Polarization resolved PL
A linear polariser, a λ/2-waveplate and a λ/4-waveplate were inserted in the excitation path (before the beamsplitter) to set the polarisation state of the laser beam from a diode laser (655 nm in wavelength and 4.59 µW in power on the sample).On the detection path, a λ/4-waveplate, a λ/2-waveplate and a linear polariser were placed to set the detected polarisation state.D line shares polarisation properties with the X and X − as shown in figure S3.Excitation with circularly polarised light resulted in a low degree of circular dichroism for X and X − emissions, typical for MoSe 2 [2-4].The degree of dichroism, defined as P C = (I + − I − )/(I + + I − ) where I ± are PL intensity detected in σ ± states, is similar for D compared with X and X − .Supplementary note 4 -Raman and PL spectroscopy studies of vacancies in MoSe 2 ML According to MD simulation (table ??), we should exclude the Se vacancy as the signal's origin.Vacancy introduces a donor state at the Fermi level hybridised with the valence band and an acceptor state deep in the bandgap [5-8].An optical transition between the defect levels is not allowed (figure ??).The lowest allowed energy optical transition is between the valence band state at the Γ point and the deep acceptor level.The existing literature reports that vacancies form non-radiative recombination sites that quench PL [9, 10] or that they contribute to sub-bandgap PL but only at low temperature [11-13], which is in contrast with our data, (see RT PL from our samples in figure S4b).In addition, the energy shift of the D line with the temperature [14] (figure ??) is weaker than that of X, unlike the fast change reported for vacancies in MoSe 2 [11].At sufficient density (around 8%), vacancies can blueshift the PL and downshift the Raman lines [7].In contrast, we did not see such changes in our Cr-implanted MoSe 2 ML (figure S4).Raman spectra are all normalised to Si signal at 520.5 cm −1 .
To ensure that one can exclude the role of vacancies in the D emission, room temperature Raman and PL spectra of MoSe 2 MLs with vacancies were compared to Cr-implanted MoSe 2 .To create vacancies, one sample of MoSe 2 was annealed at 300 • C in low vacuum (5 × 10 −2 mbar) for 2.5 hours [13].Another two samples were implanted with Kr + , which, together with other noble gases, is commonly used for creating vacancies and their complexes in 2D materials [12, 13, 15-22].Ion implantation was done at 25 eV energy for introducing vacancies [23, 24], with fluences of 3 × 10 11 and 3 × 10 12 cm −2 at elevated temperature of 220 • C, after being pre-annealed for 30 minutes at the same temperature in the implant chamber to remove volatile adsorbates.The higher fluence corresponds to the same Cr fluence in the main experiment.The lower fluence is about 10 times higher than the upper limit of potential vacancies density predicted for the Cr implanted sample by the atomistic MD simulation in the main text.
Figure S4 shows the room temperature Raman and PL spectra of MoSe 2 MLs before and after Cr implantation, annealing and Kr implantation (as already described above or in the main text).Since slight variations in PL and Raman spectra are possible from sample to sample, the spectra from the same ML before and after processing are shown.Cr-implantation introduces a small upshift in the out-of-plane Raman vibrational mode A (figure S4a).The upshift is expected for Cr atoms in the lattice because it stiffens the lattice bonds and increases the restoring force and the A frequency.Annealing and Kr implantation downshift this Raman line (figures S4c and S4e).Such a downshift has been reported before for MoSe 2 MLs with vacancies [7, 25-27].It was explained by the lattice bond loosening and lowering the restoring force.PL emission of the Cr-implanted ML is 15 meV redshifted compared with the pristine ML.It also shows an emission band around 120 meV below the free exciton line (figure S4b).This low-energy emission is also observed at low temperatures.On the other hand, the annealed ML has a very slight blueshift (figure S4d), consistent with several other reports [7, 25].Kr-implanted MLs' PL is heavily quenched (figure S4f).Some signal is visible only when the excitation laser power is raised 15000 times (from 17 nW to 261 µW).The disagreement from these experiments doesn't favour vacancies being the origin of the D emission from the Cr-implanted ML.
Raman and PL spectra presented in this section were acquired under ambient conditions (room temperature and pressure) using a confocal Raman microscope (Renishaw inVia) with 532 nm excitation laser (Coherent Compass 315M 150SL).The laser power was set between 0.017 and 261 µW for sufficient signal intensity while preventing the sample from heating during exposure.An objective lens (50×, NA = 0.75, Leica N-plan EPI) collected the Raman signal, which was then dispersed by a 2400 l/mm grating on the CCD camera, giving a spectral resolution of 1 cm −1 .PL signal was dispersed with a 600 l/mm grating, yielding a resolution of 0.147 nm.

Supplementary note 6 -Unfolded band structures including implanted defects
The main text shows the dielectric functions of MoSe 2 MLs containing several Cr-implantation introduced defects.In the following, their unfolded band structures are shown, which means that the band structures are shown in the first Brillouin zone of the pristine unit cell to visualise better the perturbation that the defect introduces.The methodology is briefly recapitulated in the method section of the main text.
Single atomic defects should show up as flat energy levels if the computational supercell is large enough for the periodic images of the defect atom not to interact.It is not always the case here due to the computational resources that such large supercell would require.Wherever a defect state crosses and interacts with a band of the host lattice, a hybridisation of the bands is visible.means that the symmetry of this state corresponds to the one of the primitive cell (pristine material).

eV and a fluence of 3 ×
10 12 cm −2 (equivalent to 0.003 Cr per ML MoSe 2 unit cell, using the MoSe 2 ML in-plane lattice constant 3.32 Å32 ).The implantation was performed with the device heated to 220 • C. Following the implantation and initial characterisation, another hBN flake was deposited on the ML MoSe 2 , and the device was annealed at 200 • C. The complete device is shown in figure 1.More details are available in the Methods section.

Figure 1 :
Figure 1: Cr-implanted MoSe 2 ML with hBN encapsulation and graphite backgate.(a) Micrograph of the finished device.The ML part of the exfoliated MoSe 2 flake is encapsulated between two thin hBN flakes.The few-layer graphite back gate and the thick part of MoSe 2 flake make contacts with the two Ti/Au lines to the right.(b) Schematic diagram of the device cross-section.Back gate voltage V g can be applied to the graphite back gate via the Au contact, while the MoSe 2 flake is grounded via the other Au contact.

Figure 2 :
Figure2: PL of Cr-implanted MoSe 2 ML at 10 K. (a) PL spectra of Cr-implanted MoSe 2 ML (red curve) at low n-doping (V g = 0.8 V), plotted with that of pristine MoSe 2 ML (black).In addition to the X − and X from MoSe 2 ML, the Cr-implanted sample also shows the broad D peak at around 1.51 eV.(b) PL spectra of Cr-implanted ML under laser power ranging from 36 nW to 123 µW.Spectra are normalised to X − .Here the sample is slightly n-doped at V g = 0.8 V. (c) Power dependence of PL.Best fit lines (dashed), with their standard deviations (shaded region around the lines), are plotted together with extracted intensity from PL spectra (dots).Unless explicitly shown, the error bars are smaller than the size of the data points.X − and X are fitted with power law I ∝ P α , and D is fitted with the saturation curve described by equation(1).(d) Time-resolved PL of Cr-implanted MoSe 2 .1/e time is around 14 ns.

Figure 3 :
Figure 3: Doping level and excitation energy dependencies of PL.(a) Gate dependent PL, where the back gate voltage V g was varied from -12 to 8 V to tune the doping level in the ML from p-via neutral to n-doping.The carrier concentration n is calculated using the simple parallel plate capacitor model (more details in supplementary note).(b) PLE of D peak, taken at V g = 0.7 V.The D peak intensity was integrated around its PL emission energy between 1.48 and 1.52 eV.Inset: PL spectrum under 688 nm (1.80 eV) excitation under the gate voltage as applied for the PLE measurements.

Figure 4 :
Figure 4: Temperature dependence of PL emission.(a) Gate voltage-dependent PL at 22 K and 108 K. (b) Arrhenius plot of X − and D (symbols).At each temperature, the two peaks' integrated intensities were acquired at the doping levels, where each emission is the brightest.The intensities were then normalised to that of X (at the voltage where X is most intense).Lines: the best-fit line was according to equations (2) and (3).(c) The temperature-dependent bandgap of X and D (symbols).Line: the best-fit line was according to equation(4)

Figure 5 :
Figure5: Magneto-PL measurement of Cr-implanted MoSe 2 ML at 1.8 K. PL spectra acquired with out-of-plane magnetic field B (varying between -8 and 8 T) applied to the sample and excited with an H-polarised laser.The detection is set to measure either σ + (black) or σ − (red) polarisation states.The figure shows the polarisation-resolved PL spectra of (a) X and X − , (c) D, with their Zeeman splitting ∆E Z shown in (b) and (d).The splitting was calculated from the peak positions (extracted from fitting Voigt functions to the PL spectra), with the error bars representing the propagated standard deviation of the fit procedure.The Zeeman splitting of the three emissions reveals expected g-factors around -4 for X and X − , only around -1.18 for D.

Figure 6 :
Figure 6: First-principles MD simulation of ion implantation process into ML MoSe 2 .(a) The setup for simulations of ion impacts.(b) Impact sites used in the simulation.(c) Atomic structures of the defects likely to appear upon impacts of energetic Cr ions.
To investigate if Cr defects introduce states in the bandgap of the MoSe 2 ML that are optically active we have simulated optical absorption spectra for MoSe 2 with Cr defects in various positions.The simulations are based on a 5x5 supercell.Each supercell hosts one Cr defect.The unfolded band structures are shown in the supplementary figure ??.All defects give rise to states in the bandgap.The absorption spectrum Im[ε(ω)] with the energy dependent macroscopic dielectric function ε(ω) has been calculated within the random-phase approximation in the limit k → 0. Optical matrix elements and local-field effects are taken into account.It should be pointed out that self-energy corrections (such as GW ) or electron-hole interactions (as described by the Bethe-Salpeter equation) are neglected.Self-energy corrections and electron-hole interactions are known to have a partially compensating effect on the bandgap:70 While the former tends to increase the bandgap, the electron-hole interactions make the optical bandgap smaller.Due to this compensating effect, the present theoretical results can be seen as approximate spectra specifically showing the impact of the defects.

Figure 7 :
Figure 7: Comparison of calculated absorption functions for pristine MoSe 2 ML (black line) and MoSe 2 ML with Cr in various positions of the crystal structure: Cr at interstitial position (red), Cr at Mo position (Cr@Mo -blue), Cr at Se position with additional Se adatom (X-sub -green) and Cr at Se position (Cr@Se -purple).Spectra are offset vertically for clarity.The vertical dotted line at about 1.6 eV marks the calculated bandgap of pristine MoSe 2 ML.
conclusion, we demonstrated the ultra-low energy ion implantation of Cr ions (at 25 eV) into a MoSe 2 ML.The implantation was performed with ions at 25 eV and the ion fluence of 3 × 10 12 cm −2 , the resultant material retains high optical quality as evidenced by clear excitonic PL.Implanted Cr ions introduce an additional low energy PL signal at around 1.51 eV visible at the onset of n-doping.Molecular dynamics calculations identified defects that can be generated by implantation.We found that Cr atoms can substitute for both Mo and Se atoms.In the latter case, the Cr atom is slightly more likely to bind an additional Se atom than not.The defects' stability, including interstitial Cr, depends on the post-implantation treatment and the final configuration of Se and Mo, which are not in the lattice.DFT calculations revealed that all the probable defects introduce one or more defect states in the MoSe 2 bandgap with non-zero matrix elements for optical transitions.It is impossible to identify with certainty which defect is the origin of D-line, Cr at Se site with Se adatom (X-sub), and perhaps Cr at Mo (Cr@Mo) seem to fit best with the measured data.Further experiments, for example, implantation of Cr only into the Se sub-lattice or implantation through the hBN protective layer to avoid environmental changes, could be considered to distinguish between the cases.
88 eV) with 200ps pulse length, 2.5 MHz repetition rate and 2.8 µW average power.The PL signal is directed through an 800 nm (1.55 eV) low-pass filter on the detection path before entering an avalanche photodiode with 30 ps time resolution.The histogram of the time difference between the laser pulses and PL emission was acquired with a time tagger.The sample was mounted on an x-y-z Attocube stage in a He flow cryostat (attoDRY2100) for magneto-optics measurement at temperature T = 1.8 K.A magnetic field up to ±8 T was applied perpendicularly to the sample (Faraday configuration).The excitation laser beam (688 nm, i.e. 1.80 eV at 4 µW) was passed through a 680 nm bandpass filter and a linear polariser in an H-configuration.The laser was focused by an aspheric lens (NA = 0.47) into a spot of ≈ 1.6 µm in diameter on the sample.The emitted PL was collected by the same objective.It was passed through a combination of λ/4, λ/2 waveplates, and a linear polariser set to pass σ ± polarised light.It was then propagated via a single mode optical fiber towards the entrance slit of a Czerny-Turner spectrometer, where it was dispersed by a 600 l/mm grating onto a CCD camera.A long pass filter (with 700 nm band edge) was inserted between the fiber output and the spectrometer entrance to remove any remaining laser light.
FIG. S2: µPL maps of Cr-implanted MoSe2 ML.The PL intensity was integrated around (a) D, (b) X, and (c) X − emission.The integrated PL signal is summed over the energy range indicated in the shaded region in respective single spectra in (d), (e), and (f).
FIG.S3: Polarization-dependent PL of Cr-implanted MoSe2 at 10 K.The sample is excited with left (σ + ) circularly polarised light, and PL is detected in left -red curve -and right (σ − ) -dotted black curve -states.D, X − and X exhibit low circular dichroism PC at below 0.05.

FIG
FIG. S4: Optical spectroscopy of defected MoSe2 ML.Room temperature Raman (a,c,e) and PL (b,d,f) spectra of Cr-implanted MoSe2 ML (a,b), annealed ML (c,d) and Kr-implanted MLs (e,f), with a pristine ML's spectrum for comparison.Raman spectra are all normalised to Si signal at 520.5 cm −1 .
FIG.S5: DFT calculation for unfolded band structure of Cr-implanted MoSe2 ML with different Cr defect configurations: (a) Cr@Mo, (b) Cr@Se, (c) interstitial Cr atom, (d) X-sub.Calculations were performed in 5×5 supercells (with a reciprocal cutoff radius of 4.1 Bohr −1 for (d), and 3.6 Bohr −1 for its respective absorption spectrum in the main text)[5].The calculations include two spins, shown here in red and blue, without spin-orbit coupling.Defects (and bands) in (a) and (d) are spin degenerate.Defect-induced states in (b) and (c) can be occupied by one electron.The influence of the implanted defect is visible via the defect-induced states inside the bandgap.A thick symbol size (high unfolding weight) means that the symmetry of this state corresponds to the one of the primitive cell (pristine material).

Table 1 :
Results of DFT MD simulations of 25 eV Cr ion irradiation on single layer MoSe 2 .The probabilities p of likely defect configurations to appear along with the formation energies E f of these configurations are listed.According to the DFT MD simulations, the most probable defects which appear upon 25 eV Cr ion irradiation are Cr adatoms, Cr@Mo, and X-sub defects.The Cr atoms which pass through the MoSe 2 sheet will likely form adatoms attached to the bottom of MoSe 2 .