Recently, two-dimensional van der Waals materials have emerged as promising platforms for optoelectronics , , , candidates for future UV-LEDs ,  and host materials for emitters of non-classical light , , , , , , , , , . Especially atomic defects in hexagonal boron nitride (hBN) have been shown to belong to the brightest emitters of non-classical light ever reported. hBN is a semiconductor with a large band gap of around 6 eV . Therefore, it is widely believed that at the origin of the emission are localized defects in the host material that give rise to electronic transitions between discrete energy levels within the band gap, as it is the case for color centers in diamond , . However, the exact nature of the defects still remains unclear and is the subject of ongoing experimental and theoretical investigations , , , . For application in quantum information one needs narrowband and background free emission lines. The emitters selected in this work fulfill these criteria and exhibit spectra consisting of an asymmetric zero phonon line (ZPL) and a phonon side band approximately 165 meV red shifted from the ZPL. This energy shift corresponds to a well-known phonon mode in hBN , , . The asymmetry of the ZPL is commonly attributed to phonon interaction, and the ZPL wavelengths have been shown to spread across a range from 500 to 800 nm , which is attributed to strain inside the host crystal , . Independent of the emission wavelength, the ZPL is assumed to consist of a single, linearly polarized dipole transition giving rise to single photon emission. In this publication, on the contrary, we provide strong evidence for the presence of two independent emitters in each defect and show that the second line causing the asymmetry of the ZPL indeed is a second electronic transition. By carefully evaluating photon correlation measurements, we see that we only are able to fully reproduce our data by using an extended g(2)-function that takes into account two independent transitions. We gain full access to the parameters of the g(2)-function via independently measuring the spectra and the excitation power-dependent photon emission rates of the corresponding emitters. We further confirm the existence of double defects via measuring polarization-dependent spectra and performing time-correlated single photon counting (TCSPC) measurements.
2 Investigation of single photon emission from point defects in hBN
We spectroscopically investigate micrometer sized multi-layer flakes of hBN in a home-built laser scanning confocal microscope under continuous wave excitation at λ=532 nm. Experiments are performed at room temperature if not indicated otherwise. The commercially available flakes (Graphene Supermarket, Graphene Laboratories Inc., Ronkonkoma, NY, USA) are diluted in a solution (50% water, 50% ethanol) with a concentration of 5.5 mg/ml and put in an ultrasonic bath to break up agglomerates. The solution is drop cast (5–10 μl) onto a silicon wafer with an iridium layer for enhanced photon collection efficiency. The substrate is heated on a hotplate to 70°C to evaporate the liquid. After drop casting, individual flakes can be examined in the confocal microscope.
Figure 1A, D and G show typical spectra of point emitters inside the flakes. Although they differ in their central wavelengths, their spectral shapes are very similar. The spectra are fit with four Lorentzian lines which we will discuss later in closer detail. Saturation measurements in Figure 1B, E and H show typical saturation count rates (≈1–2 Mcts/s) and saturation powers (≈1 mW) of these emitters, in good agreement to previous reports , , . The red lines are fits according to
Here, Isat and Psat are the saturation count rates and saturation powers of the emitters, whereas Cback describes a potential contribution due to linear background emission stemming from the host material. Note that this contribution is negligible in the presented data. This is in accordance with the very clean spectra presented in Figure 1A, D and G, where also no significant background contribution is visible. In approximately one out of 50 flakes background-free emission can be found. Contrary to these findings, Figure 2A) shows a spectrum, which clearly contains additional background emission. This background emission is also visible as a prominent linear increase in a corresponding saturation measurement in Figure 2B. Note that the saturation measurements are always taken by integrating the emission intensity over the ZPL and the two sidebands (cf. the four Lorentzian lines in Figure 1).
As a last step, we perform g(2)-photon correlation measurements (Figure 1C, F and I to get information about the photon statistics. In order to reduce the potential influence of background emission (although not present in the current experiments) on the photon statistics measurements, we restrict the spectral window from which we collect photons for the g(2)-measurements to the region of the ZPL (regions enclosed by dashed lines in the corresponding spectra) and take the measurements at excitation powers far lower than the emitters’ saturation powers. Despite vanishing background fluorescence, the g(2)-functions do not vanish at all at zero time delay as one would expect for an ideal single photon source. Figure 2D–F further shows an example, where background emission from the host material is present but becomes relevant only at about 20×Psat. Nevertheless, for almost vanishing excitation power (P=3.5 μW), the value of g(2)(0) is still much larger than zero. As we show below also the timing jitter of the photon detectors does not explain the deviation from ideal single photon statistics as the emitter fluorescence lifetime is larger than the jitter. Instead, we have to assume that the asymmetric shape of the ZPL is due to the presence of two independent emission lines.
In the following we develop a model for the photon correlation functions that, besides background emission and the timing jitter of the photon detector, accounts for the presence of a second emitter and prove that this model fully reproduces the measurements. We start with the well-known g(2)-function for a three-level system:
We now, step by step, include all experimental parameters that influence the shape of the g(2)-function: Although negligible in the presented data (but not in general), we start with uncorrelated background emission, that can be extracted from saturation measurements. Including this into the model, the g(2)-function reads 
Here, p is the fraction of measured photons stemming from the emitter compared to the measured total count rate. Note, that one should also consider dark counts of the detector in the description. In our case, these dark counts (≈100–200 cts/s) are negligible compared to the signal from the emitters. Second, we include the timing jitter σ of the counting electronics. This jitter is an uncertainty in the time between the arrival and the detection of a single photon and has been measured via ultra-fast laser pulses (σ≈490 ps). It is included via the convolution of Eq. (3) with the Gaussian shape of the instrument response function IRF(t).
Equation (4) is the final description for the case that we collect emission from exactly one single emitter. The blue solid lines in Figure 1C, F and I are fits to the data according to this model. It strikes the eye that this function is not able to reproduce the data. In particular, the model demands a much lower value for g(2)(0) than it is provided by the data. We want to stress that we also can reproduce the data by taking the signal to background ratio p as a fit parameter. This, however, strongly contradicts our findings of vanishing background in the spectrum and the saturation measurement.
Therefore, as a last step, we also take into account the influence of a second emitter in the detection focal volume. Let Itot=I1+I2 be the total detected emission with I1=z·Itot and I2=(1–z)·Itot being the relative fractions of the emission of emitter 1 and emitter 2, respectively. This leads to
In order to reduce the number of fit parameters, we assume Because of the independence of I1 and I2, the two mixing terms will be constant for all τ and by making the assumption that (corresponding to the observed vanishing background), we find We eventually arrive at
In contrast to reports in literature, where the asymmetry of the ZPL is attributed to phonon interaction , we here fully reproduce the lineshape by fitting two Lorentzian lines representing two independent electronic transitions. By calculating the areas under the individual Lorentzians, we get information about the relative oscillator strengths of both emitters, corresponding to the parameter z in Eq. (5) (numbers also given in the spectra in Figures 1 and 2). By taking into account the double emission spectrum within the model (Eq. (5)) for the g(2)-function, we are able to perfectly describe the measured photon correlation data (solid red lines in Figures 1C, F, I and 2C and F).
Interestingly, our photon correlation measurements correspond perfectly to reports in literature in terms of bunching dynamics and dips in the g(2)-function at zero time delay , , . Non-vanishing values of g(2)(0) in these reports were always attributed to residual background fluorescence which, however, is not further defined or shown. To our knowledge, the full set of information needed to accurately describe the situation has never been reported , , , . Furthermore, we want to point out that most of the emitters measured in this work show very strong bunching on a timescale of several hundreds of microseconds up to milliseconds as it has been shown in previous work (see, for example, Figure 2C) , . Therefore, a proper normalization of the g(2)-function to the constant number of events for long time delays τ or to the recorded photon count rates is imperative. The absence of satisfactorily explanations in literature and the excellent agreement of measured photon correlation functions with the double defect model suggest that most probably the majority of single emitters in literature are indeed double defects.
3 Spectroscopic evidence for double defects
We now turn in closer detail to the emitters optical spectra providing further evidence for our model. Figure 3 shows a typical photoluminescence spectrum of a defect in hBN at room temperature and at a temperature of 5 K. For the low-temperature experiments the sample was mounted in a helium-flow cryostat. In analogy to the defects discussed in Section 2 the room temperature ZPL can be fit by the sum of two Lorentzian lines. The different widths of the two Lorentzians (also apparent in the spectra of Figures 1 and 2) are potentially a result of different electron-phonon coupling, e.g. due to a different symmetry or orientation of defects in the lattice resulting in coupling to a different subset of lattice phonons. Upon cooling to 5 K, these two lines shift to shorter wavelengths, their width strongly narrows and the lines become clearly distinguishable in the emission spectrum. This is clear evidence that the photoluminescence spectrum of this emitter indeed consists of two spectral lines. The emission lines at 5 K show a Gaussian line shape with similar widths (full width at half maximum) of 202 GHz and 222 GHz, respectively. The Gaussian line shapes indicate an inhomogeneous broadening mechanism such as spectral diffusion. In the following we discuss further spectroscopic features that support the double defect model.
Figure 4 shows normalized emission spectra of a collection of emitters in the multi-layer flakes under investigation. The central wavelength λ1 of the highest energy line (line 1) ranges from 600 to 720 nm. This wavelength range is limited by the spectral filter window in which we collect fluorescence. On the ordinate axis the energy separations between all lines are shown, where the energy of line 1 (black) is always set to zero. It is apparent from Figure 4 that the energy distances between the lines remain approximately constant independent of the central wavelength of line 1 in the spectrum. In literature, the spectrum is described as an asymmetric ZPL with a red shifted (169.5 meV) phonon side band the energy of which belongs to a well-known transverse optical (TO)phonon mode in hBN , , . We here first state that there are actually two ZPLs (line 1, black, and line 2, red) with two phonon side bands (line 3, blue, and line 4, orange). Averaged over all observed emitters with this particular spectral fingerprint, the energy difference between line 1 (black) and line 3 (blue) amounts to ΔE13=158 (17) meV, whereas the distance between line 2 (red) and line 4 (orange) yields ΔE24=174 (15) meV. Within the error bars, both values match the phonon mode at 169.5 meV. Staying in our picture of line 1 and 2 being electronic transitions, we thus attribute the lines 3 and 4 to be their respective phonon side bands. Note that an alternative interpretation of the results is possible: peaks 3 and 4 could originate from a coupling of the dominant ZPL line (line 1) to both the TO phonon mode at 169.5 meV and the longitudinal optical (LO) phonon mode at 199.6 meV. For the LO phonon mode, however, the electron-phonon scattering should be strongly reduced due to the cutoff of the phonon density of states close to this energy .
Next, we perform TCSPC measurements to gain further information about the lifetimes of the excited states of the investigated emitters. Two electronic transitions with potentially differing lifetimes should be visible as a bi-exponential decay. For the TCSPC measurements we use a white light laser filtered to 532 nm, with a pulse duration of 200 ps and a pulse repetition rate of 10 MHz. Measurements on two typical hBN emitters (Figure 5A and C) are shown in Figure 5B and D (black dots). The solid lines are fits according to
with one (blue, n=1) and two (red, n=2) time constants. As for the g(2)-functions the instrument response function IRF(t) with a timing jitter of σ=490 ps is included into the fit function via convoluting the Gaussian IRF(t) with the exponential decay of the electronic transition. In both measurements, the data points clearly follow a bi-exponential decay. The observed time constants (t1=0.82 ns, t2=4.0 ns and t1=1.7 ns, t2=4.5 ns) are compatible to time constants extracted from photon correlation measurements as in Section 2 and correspond to the range of typical lifetimes observed for this type of emitters , , . In literature, however, usually just a single exponential decay is used to fit the data in a regime between 2 and 10 ns, and the full information about the timing resolution of the setup is not considered. The presence of two time constants of the same order of magnitude further indicates the existence of two excited states in the defect and corresponds perfectly with the assumption of two independent emitters in the same defect.
As a last step we now turn to the polarization of the defect emission. Linear excitation dipoles with visibilities between 20% and 80% have been reported, whereas the emission dipoles are supposed to show close to unity visibility and are linearly polarized , . There is, however, a difference in the relative orientations of the excitation and emission dipoles between 30° and 90° , . However, to our knowledge, polarization-dependent spectra have not been investigated in literature yet. Figure 5E and F show normalized emission spectra of two different hBN emitters with ZPL (line 1) at around 790 nm and 650 nm where different curves correspond to different settings of the polarization analyzer in the detection path. One can clearly see that dependent on the angle of a linear polarizer in the detection path, the line shape of the dominant line in the spectrum strongly varies. This indicates that here the two dipoles contributing to the ZPL have different relative polarizations. Note that we also can find spectra in which the line shape does not change significantly upon changing the detection angle of the polarization analyzer.
In summary, we presented new insights into the nature of non-classical light emission from defects in multi-layer flakes of hBN. Via careful evaluation of g(2)-photon correlation measurements, TCSPC measurements and polarization-dependent emission spectra, we gather strong evidence that, in contrast to previous reports, these atomic defects are no single emitter systems but comprise two independent emitting systems here coined as “double defect”. We draw this conclusion via collecting all necessary information to describe the photon statistics through independent measurements of the background contribution, the timing jitter of the counting electronic and the spectra of the emitters. Interestingly, our photon correlation measurements correspond perfectly to reports in literature in terms of bunching dynamics and dips in the g(2)-function at zero time delay.
Our assumptions are corroborated by the decomposition of the asymmetric ZPL into two Lorentzian lines, both describing one individual electronic transition. Based on the existence of a characteristic phonon mode of hBN at 169.5 meV, we were able to assign the two dominant lines in the phonon side band to each of the electronic transitions. Eventually, the presence of a bi-exponential decay in TCSPC measurements and polarization-dependent emission spectra further support our model. We want to point out that our measured photon correlation functions perfectly correspond to the ones previously reported in literature. Based on these results we have to assume that many of the reported single photon emitters consist of “double defects” as described in this publication.
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About the article
Published Online: 2019-07-11
Funding Source: FP7 Information and Communication Technologies
Award identifier / Grant number: 61807
The authors want to thank Johannes Görlitz, Benjamin Kambs, Dennis Herrmann, Igor Aharonovich, Dirk Englund, Lee Bassett, Mike Ford and Adam Gali for helpful discussions. This work was partially funded by the European Union 7th Framework Program, FP7 Information and Communication Technologies under Grant Agreement No. 61807 (WASPS), Funder Id: http://dx.doi.org/10.13039/100011273.
Citation Information: Nanophotonics, Volume 8, Issue 11, Pages 2041–2048, ISSN (Online) 2192-8614, DOI: https://doi.org/10.1515/nanoph-2019-0123.
©2019 Christoph Becher et al., published by De Gruyter, Berlin/Boston. This work is licensed under the Creative Commons Attribution 4.0 Public License. BY 4.0