Carbon-Related Quantum Emitter in Hexagonal Boron Nitride with Homogeneous Energy and 3-Fold Polarization

Most hexagonal boron nitride (hBN) single-photon emitters (SPEs) studied to date suffer from variable emission energy and unpredictable polarization, two crucial obstacles to their application in quantum technologies. Here, we report an SPE in hBN with an energy of 2.2444 ± 0.0013 eV created via carbon implantation that exhibits a small inhomogeneity of the emission energy. Polarization-resolved measurements reveal aligned absorption and emission dipole orientations with a 3-fold distribution, which follows the crystal symmetry. Photoluminescence excitation (PLE) spectroscopy results show the predictability of polarization is associated with a reproducible PLE band, in contrast with the non-reproducible bands found in previous hBN SPE species. Photon correlation measurements are consistent with a three-level model with weak coupling to a shelving state. Our ab initio excited-state calculations shed light on the atomic origin of this SPE defect, which consists of a pair of substitutional carbon atoms located at boron and nitrogen sites separated by a hexagonal unit cell.

Contents: S1.The Fabrication Control: O Implantation.S2.Absorption/emission dipole orientation for type II emitters.S3.Schematics for PLE setup S4.Additional PLE results of type I and type II emitters.S5.Excitation power-dependent autocorrelation.S6.Computed Properties of Carbon Related Defects.

S1. The Fabrication Control: O Implantation.
The creation of type I emitters using carbon implantation suggests carbon related defect origin.However, this evidence on its own is not enough to rule out possibilities such as creation of intrinsic defects during implantation.Thus, we conducted a control experiment in which 16 O + ions are implanted, with the implantation parameters remaining the same.The same types of figures are plotted for the 16 O + implanted sample in Figure 1 d-f.There are minor changes in the number and locations of emission hotspots in Figure S1e compared to Figure S1d.These are due to activation and migration of defects during implantation and annealing.There are no strong hotspots in Figure S1f, which only capture intensity around type I emitters' energy.As we examine the spectrum pixel by pixels, we did not find any type I emitter, and some of the relatively high signal spots are from broad background signal.
The control experiment negates the possibility that the type I emitter is an intrinsic defect.If it were intrinsic, the 16 O + implantation would be able to displace intrinsic atoms to new sites, potentially forming the same intrinsic emitters, which is not evidenced by our observation.The slight difference in mass should not entirely prevent the formation of the same intrinsic defects.Additionally, the experimental data negates the possibility of emitter association with oxygen atoms, which may have been inadvertently introduced during hBN growth or through hydrocarbon contamination on the surface.
As a side note, we would like to note the density of type I emitters on each flake has variations.There is no reliable indicator found to predict the density of emitters on each flake, although in general we locate more type I emitters on thicker flakes.This is likely attributed to thicker flakes having larger effective collision cross section that intercepts more ions from the beam.

S5. Excitation power-dependent autocorrelation.
Assuming a power dependent excitation rate  = *  , we could obtain these coefficients quantitatively by conducting the experiment with different power.First of all, the decay rate    approaches asymptotically to  in the zero-power limit, allowing for obtaining  by  extrapolation.As shown in Figure S5a, we obtained a relaxation rate of  183.3 MHz, which corresponds to a lifetime  5.5 ns.In addition,  and  can be extracted from the power dependence of  and , as shown in Figure S5b, c.We find that  increases rapidly and levels off at high power, which can be explained by a faster excitation rate depopulating the ground state, leading to a faster deshelving rate from the metastable state.The same power dependence is also observed for single molecules 1 and color centers in diamond 2 . is only several hundred Hertz, more than 5 orders of magnitude smaller than  .In fact, as seen from the expression of  above, low transition rates  and  can be inferred from a small  , which manifest as long bunching characteristic decay time.In single photon generation scenario, where the emitter is excited by a laser pulse, the extremely low  / ratio leads to a dominant relaxation through radiative channel, making it a highly efficient single photon source.

S6. Computed Properties of Carbon-Related Defects
A computational screening is done for carbon-related defect candidates that satisfy the structural symmetry constrain, as discussed in the main text.Table S1 shows the results of the calculations.In this table, results of DFT and constrained DFT calculations are shown for all the defect candidates, while GW+BSE calculations are carried out for most of the defects except those with a singleparticle transition energy far away from 2 eV.Notably, the defects C N N B and C B V N C B -(negatively charged C B V N C B ) also have exciton energy close to the observed emitter.However, they are not preferred over the d=5.77Å C B -C N DAP because (1) they have very low brightness with much higher radiative lifetimes than the experimental value; (2) for C N N B , higher absorption peaks near the first peak is also present, which is inconsistent with the PLE spectrum for type I emitter.S1.Calculated properties of carbon-related defects.The superscripts "+" and "-" in the defect symbol column indicates +1 and -1 charge state of the defect, respectively.The single-particle transition energy is the energy difference between the lowest unoccupied and highest occupied band of the same spin species within PBE.The ZPL energy is written as the vertical excitation energy minus the Stokes shift, calculated within PBE by forcing the occupation of the highest occupied band (HOB) to be 0 and lowest unoccupied band (LUB) to be 1.Typically, the HOB-LUB transition is the main component of the exciton wave function, with a few exceptions indicated by an asterisk (*) on the exciton energy column.

Figure
Figure S1.a and b shows the raster scan results before and after the 12 C + (10 keV, 0 o angle, room temperature) and annealing (900 o C, 1 Torr Ar, 30 min), with each pixel's color denoting the average intensity between [1.8, 2.25] eV, which include both the type I and type II energy.There is an increased number of the emission hotspots in the region, owning to emerging of new emitters after the implantation.We further plot the same plot with the color representing the average

Figure S1 .
Figure S1.Controlling dopant for creating type I emitters.(a) PL raster scan of a portion of the flake after mechanical exfoliation, prior to any treatment.Color represents average intensity between [1.8, 2.25] eV.(b) The scan over the same area after 12 C + implantation and annealing.Circles mark locations of confirmed type I emitters.(c) The same image as in (b) but plotting the average intensity between [2.19 2.25] eV, at the type I emitter's energy.(d) Raster scan of another flake prior to implantation with 16 O + .(e) The scan over the same area after 16 O + implantation and annealing.(f) The same image of (e) but showing the average intensity between [2.19 2.25] eV, at the type I emitter's energy.No type I emitter is found.

Figure S2 .
Figure S2.Absorption/emission dipole orientation for 10 type II emitters between 580 and 590 nm.(a) The scatter plot of 10 type II emitters with close emission energy, with the error bar shown.The gray line serves a guide for eye as absorption dipole angle align with emission dipole angle.This data reveals no discernible pattern in the absorption or emission dipole orientations.

Figure S4 .
Figure S4.Additional PLE results.(a) Three more type II emitters results are presented.They are plotted versus energy offset from their respective emission energies: 2.15 eV for SPE 1, 2.08 eV for SPE 2 and 2.04 eV for SPE 3. No consistent patterns are observed among these results.(b) Four type I emitters PLE results are presented, exhibiting highly reproducible PLE patterns.

Figure S3 .
Figure S3.Schematics of PLE setup.(a) The laser from the supercontinuum is first being cut off by a short pass filter (SPF).Then a grating disperses the light, which passes through a slit on a translational stage, leaving a semi-monochromic beam.The secondary grating in conjugate position disperses the beam back to a position regardless of selected wavelength.A dichroic mirror reflects the excitation light towards to cryostat (Cryo).The single photon emission together with the remnant of excitation light goes through a long pass filter (LPF) where the latter is filtered.The spectrometer (Spec) records the spectrum.Polarization components are added depending on experiment needs (not shown).

Figure S5 .
Figure S5.Excitation Power dependent parameters.a, Antibunching decay rate  as function of power.The red line is a linear fit with y-axis intercept at 183.3 MHz.b, Dependence of the bunching amplitude  and decay rate  on the excitation power.c, Transition coefficients  and  as function of power.