Abstract

Quantum emitters in hexagonal boron nitride (hBN) have attracted significant interest due to their bright and narrowband photon emission even at room temperature. The wide-bandgap two-dimensional material incorporates crystal defects of yet-unknown configuration, introducing discrete energy levels with radiative transition frequencies in the visible spectral range. The commonly observed high brightness together with the moderate fluorescence lifetime indicates a high quantum efficiency, but the exact dynamics and the underlying energy level structure remain elusive. In this study we present a systematic and detailed analysis of the photon statistics recorded for several individual emitters. We extract the individual decay rates by modeling the second-order correlation functions using a set of rate equations based on an energy level scheme involving long-lived states. Our analysis clearly indicates excitation-power-dependent non-radiative couplings to at least two metastable levels and confirms a near unity quantum efficiency.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

M. A. Feldman, A. Puretzky, L. Lindsay, E. Tucker, D. P. Briggs, P. G. Evans, R. F. Haglund, and B. J. Lawrie, “Phonon-induced multicolor correlations in hBN single-photon emitters,” Phys. Rev. B 99(2), 020101 (2019).
[Crossref]

2018 (5)

T. T. Tran, M. Kianinia, M. Nguyen, S. Kim, Z. Q. Xu, A. Kubanek, M. Toth, and I. Aharonovich, “Resonant Excitation of Quantum Emitters in Hexagonal Boron Nitride,” ACS Photonics 5(2), 295–300 (2018).
[Crossref]

A. Dietrich, M. Bürk, E. S. Steiger, L. Antoniuk, T. T. Tran, M. Nguyen, I. Aharonovich, F. Jelezko, and A. Kubanek, “Observation of Fourier transform limited lines in hexagonal boron nitride,” Phys. Rev. B 98(8), 081414 (2018).
[Crossref]

A. W. Schell, M. Svedendahl, and R. Quidant, “Quantum Emitters in Hexagonal Boron Nitride Have Spectrally Tunable Quantum Efficiency,” Adv. Mater. 30(14), 1704237 (2018).
[Crossref]

M. Kianinia, C. Bradac, B. Sontheimer, F. Wang, T. T. Tran, M. Nguyen, S. Kim, Z.-Q. Xu, D. Jin, A. W. Schell, C. J. Lobo, I. Aharonovich, and M. Toth, “All-optical control and super-resolution imaging of quantum emitters in layered materials,” Nat. Commun. 9(1), 874 (2018).
[Crossref]

M. Koperski, K. Nogajewski, and M. Potemski, “Single photon emitters in boron nitride: More than a supplementary material,” Opt. Commun. 411, 158–165 (2018).
[Crossref]

2017 (4)

J. Wang, F. Ma, W. Liang, R. Wang, and M. Sun, “Optical, photonic and optoelectronic properties of graphene, h-NB and their hybrid materials,” Nanophotonics 6(5), 943–976 (2017).
[Crossref]

N. R. Jungwirth and G. D. Fuchs, “Optical Absorption and Emission Mechanisms of Single Defects in Hexagonal Boron Nitride,” Phys. Rev. Lett. 119(5), 057401 (2017).
[Crossref]

X. Li, G. D. Shepard, A. Cupo, N. Camporeale, K. Shayan, Y. Luo, V. Meunier, and S. Strauf, “Nonmagnetic Quantum Emitters in Boron Nitride with Ultranarrow and Sideband-Free Emission Spectra,” ACS Nano 11(7), 6652–6660 (2017).
[Crossref]

B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96(12), 121202 (2017).
[Crossref]

2016 (9)

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
[Crossref]

T. T. Tran, C. Elbadawi, D. Totonjian, C. J. Lobo, G. Grosso, H. Moon, D. R. Englund, M. J. Ford, I. Aharonovich, and M. Toth, “Robust Multicolor Single Photon Emission from Point Defects in Hexagonal Boron Nitride,” ACS Nano 10(8), 7331–7338 (2016).
[Crossref]

T. T. Tran, C. Zachreson, A. M. Berhane, K. Bray, R. G. Sandstrom, L. H. Li, T. Taniguchi, K. Watanabe, I. Aharonovich, and M. Toth, “Quantum Emission from Defects in Single-Crystalline Hexagonal Boron Nitride,” Phys. Rev. Appl. 5(3), 034005 (2016).
[Crossref]

N. Chejanovsky, M. Rezai, F. Paolucci, Y. Kim, T. Rendler, W. Rouabeh, F. Fávaro de Oliveira, P. Herlinger, A. Denisenko, S. Yang, I. Gerhardt, A. Finkler, J. H. Smet, and J. Wrachtrup, “Structural Attributes and Photodynamics of Visible Spectrum Quantum Emitters in Hexagonal Boron Nitride,” Nano Lett. 16(11), 7037–7045 (2016).
[Crossref]

S. Choi, T. T. Tran, C. Elbadawi, C. Lobo, X. Wang, S. Juodkazis, G. Seniutinas, M. Toth, and I. Aharonovich, “Engineering and Localization of Quantum Emitters in Large Hexagonal Boron Nitride Layers,” ACS Appl. Mater. Interfaces 8(43), 29642–29648 (2016).
[Crossref]

L. J. Martínez, T. Pelini, V. Waselowski, J. R. Maze, B. Gil, G. Cassabois, and V. Jacques, “Efficient single photon emission from a high-purity hexagonal boron nitride crystal,” Phys. Rev. B 94(12), 121405 (2016).
[Crossref]

K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. Castro Neto, “2D materials and van der Waals heterostructures,” Science 353(6298), aac9439 (2016).
[Crossref]

N. R. Jungwirth, B. Calderon, Y. Ji, M. G. Spencer, M. E. Flatté, and G. D. Fuchs, “Temperature Dependence of Wavelength Selectable Zero-Phonon Emission from Single Defects in Hexagonal Boron Nitride,” Nano Lett. 16(10), 6052–6057 (2016).
[Crossref]

Z. Shotan, H. Jayakumar, C. R. Considine, M. Mackoit, H. Fedder, J. Wrachtrup, A. Alkauskas, M. W. Doherty, V. M. Menon, and C. A. Meriles, “Photoinduced Modification of Single-Photon Emitters in Hexagonal Boron Nitride,” ACS Photonics 3(12), 2490–2496 (2016).
[Crossref]

2015 (1)

M. Berthel, O. Mollet, G. Dantelle, T. Gacoin, S. Huant, and A. Drezet, “Photophysics of single nitrogen-vacancy centers in diamond nanocrystals,” Phys. Rev. B 91(3), 035308 (2015).
[Crossref]

2014 (2)

P. Miró, M. Audiffred, and T. Heine, “An atlas of two-dimensional materials,” Chem. Soc. Rev. 43(18), 6537–6554 (2014).
[Crossref]

M. Davanço, C. S. Hellberg, S. Ates, A. Badolato, and K. Srinivasan, “Multiple time scale blinking in InAs quantum dot single-photon sources,” Phys. Rev. B 89(16), 161303 (2014).
[Crossref]

2012 (2)

E. Neu, M. Agio, and C. Becher, “Photophysics of single silicon vacancy centers in diamond: implications for single photon emission,” Opt. Express 20(18), 19956–19971 (2012).
[Crossref]

D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Measurement and Control of Single Nitrogen-Vacancy Center Spins above 600 K,” Phys. Rev. X 2(3), 031001 (2012).
[Crossref]

2011 (1)

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys. 13(2), 025012 (2011).
[Crossref]

2010 (1)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref]

2006 (1)

2000 (2)

R. Brouri, A. Beveratos, J.-P. Poizat, and P. Grangier, “Photon antibunching in the fluorescence of individual color centers in diamond,” Opt. Lett. 25(17), 1294–1296 (2000).
[Crossref]

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett. 84(6), 1148–1151 (2000).
[Crossref]

1998 (2)

S. C. Kitson, P. Jonsson, J. G. Rarity, and P. R. Tapster, “Intensity fluctuation spectroscopy of small numbers of dye molecules in a microcavity,” Phys. Rev. A 58(1), 620–627 (1998).
[Crossref]

C. Eggeling, J. Widengren, R. Rigler, and C. A. Seidel, “Photobleaching of Fluorescent Dyes under Conditions Used for Single-Molecule Detection: Evidence of Two-Step Photolysis,” Anal. Chem. 70(13), 2651–2659 (1998).
[Crossref]

1993 (1)

J. Bernard, L. Fleury, H. Talon, and M. Orrit, “Photon bunching in the fluorescence from single molecules: A probe for intersystem crossing,” J. Chem. Phys. 98(2), 850–859 (1993).
[Crossref]

1962 (1)

R. H. Silsbee, “Thermal broadening of the Mössbauer line and of narrow-line electronic spectra in solids,” Phys. Rev. 128(4), 1726–1733 (1962).
[Crossref]

Agio, M.

Aharonovich, I.

T. T. Tran, M. Kianinia, M. Nguyen, S. Kim, Z. Q. Xu, A. Kubanek, M. Toth, and I. Aharonovich, “Resonant Excitation of Quantum Emitters in Hexagonal Boron Nitride,” ACS Photonics 5(2), 295–300 (2018).
[Crossref]

A. Dietrich, M. Bürk, E. S. Steiger, L. Antoniuk, T. T. Tran, M. Nguyen, I. Aharonovich, F. Jelezko, and A. Kubanek, “Observation of Fourier transform limited lines in hexagonal boron nitride,” Phys. Rev. B 98(8), 081414 (2018).
[Crossref]

M. Kianinia, C. Bradac, B. Sontheimer, F. Wang, T. T. Tran, M. Nguyen, S. Kim, Z.-Q. Xu, D. Jin, A. W. Schell, C. J. Lobo, I. Aharonovich, and M. Toth, “All-optical control and super-resolution imaging of quantum emitters in layered materials,” Nat. Commun. 9(1), 874 (2018).
[Crossref]

B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96(12), 121202 (2017).
[Crossref]

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11(1), 37–41 (2016).
[Crossref]

T. T. Tran, C. Elbadawi, D. Totonjian, C. J. Lobo, G. Grosso, H. Moon, D. R. Englund, M. J. Ford, I. Aharonovich, and M. Toth, “Robust Multicolor Single Photon Emission from Point Defects in Hexagonal Boron Nitride,” ACS Nano 10(8), 7331–7338 (2016).
[Crossref]

T. T. Tran, C. Zachreson, A. M. Berhane, K. Bray, R. G. Sandstrom, L. H. Li, T. Taniguchi, K. Watanabe, I. Aharonovich, and M. Toth, “Quantum Emission from Defects in Single-Crystalline Hexagonal Boron Nitride,” Phys. Rev. Appl. 5(3), 034005 (2016).
[Crossref]

S. Choi, T. T. Tran, C. Elbadawi, C. Lobo, X. Wang, S. Juodkazis, G. Seniutinas, M. Toth, and I. Aharonovich, “Engineering and Localization of Quantum Emitters in Large Hexagonal Boron Nitride Layers,” ACS Appl. Mater. Interfaces 8(43), 29642–29648 (2016).
[Crossref]

Alkauskas, A.

Z. Shotan, H. Jayakumar, C. R. Considine, M. Mackoit, H. Fedder, J. Wrachtrup, A. Alkauskas, M. W. Doherty, V. M. Menon, and C. A. Meriles, “Photoinduced Modification of Single-Photon Emitters in Hexagonal Boron Nitride,” ACS Photonics 3(12), 2490–2496 (2016).
[Crossref]

D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Measurement and Control of Single Nitrogen-Vacancy Center Spins above 600 K,” Phys. Rev. X 2(3), 031001 (2012).
[Crossref]

Antoniuk, L.

A. Dietrich, M. Bürk, E. S. Steiger, L. Antoniuk, T. T. Tran, M. Nguyen, I. Aharonovich, F. Jelezko, and A. Kubanek, “Observation of Fourier transform limited lines in hexagonal boron nitride,” Phys. Rev. B 98(8), 081414 (2018).
[Crossref]

Ari, O.

O. Ari, N. Polat, V. Firat, O. Çakir, and S. Ates, “The effect of electron-phonon interactions on the spectral properties of single defects in hexagonal boron nitride,” arXiv:1808.10611 (2018).

Ates, S.

M. Davanço, C. S. Hellberg, S. Ates, A. Badolato, and K. Srinivasan, “Multiple time scale blinking in InAs quantum dot single-photon sources,” Phys. Rev. B 89(16), 161303 (2014).
[Crossref]

O. Ari, N. Polat, V. Firat, O. Çakir, and S. Ates, “The effect of electron-phonon interactions on the spectral properties of single defects in hexagonal boron nitride,” arXiv:1808.10611 (2018).

Audiffred, M.

P. Miró, M. Audiffred, and T. Heine, “An atlas of two-dimensional materials,” Chem. Soc. Rev. 43(18), 6537–6554 (2014).
[Crossref]

Awschalom, D. D.

D. M. Toyli, D. J. Christle, A. Alkauskas, B. B. Buckley, C. G. Van de Walle, and D. D. Awschalom, “Measurement and Control of Single Nitrogen-Vacancy Center Spins above 600 K,” Phys. Rev. X 2(3), 031001 (2012).
[Crossref]

Badolato, A.

M. Davanço, C. S. Hellberg, S. Ates, A. Badolato, and K. Srinivasan, “Multiple time scale blinking in InAs quantum dot single-photon sources,” Phys. Rev. B 89(16), 161303 (2014).
[Crossref]

Becher, C.

E. Neu, M. Agio, and C. Becher, “Photophysics of single silicon vacancy centers in diamond: implications for single photon emission,” Opt. Express 20(18), 19956–19971 (2012).
[Crossref]

E. Neu, D. Steinmetz, J. Riedrich-Möller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys. 13(2), 025012 (2011).
[Crossref]

Benson, O.

B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96(12), 121202 (2017).
[Crossref]

Berhane, A. M.

T. T. Tran, C. Zachreson, A. M. Berhane, K. Bray, R. G. Sandstrom, L. H. Li, T. Taniguchi, K. Watanabe, I. Aharonovich, and M. Toth, “Quantum Emission from Defects in Single-Crystalline Hexagonal Boron Nitride,” Phys. Rev. Appl. 5(3), 034005 (2016).
[Crossref]

Bernard, J.

J. Bernard, L. Fleury, H. Talon, and M. Orrit, “Photon bunching in the fluorescence from single molecules: A probe for intersystem crossing,” J. Chem. Phys. 98(2), 850–859 (1993).
[Crossref]

Berthel, M.

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Figures (7)

Fig. 1.
Fig. 1. (a) Representative fluorescence image of the sample containing hBN nano-flakes, obtained with a cw excitation power of 2.5 mW. The indicated bright spot in the center is emitter A and the scalebar is $2~\mu$m. (b) Photoluminescence spectra of emitters A–D (recorded with cw laser) shifted along the energy-axis to match the ZPL energy. The respective ZPL wavelength is shown in the legend. (c) Mean photocurrent $\bar {I}$ for the emitters A–C and half photocurrent for emitter D as a function of cw excitation power P. The solid line is a fit to the data with a saturation law as explained in the text. The data for emitter D is multiplied by a factor of 0.5 (denoted as D/2) to avoid overlap with the data of emitter C.
Fig. 2.
Fig. 2. Energy level diagram used here to model the emitter dynamics. With an optical excitation, the population is non-resonantly transferred from the ground state (level 1) to the optically excited state (level 2). The excited state may decay via a radiative transition back to level 1 and emit a photon or non-radiatively to one of the shelving states (levels 3…N). The shelving states subsequently relax to level 1. The diagram shows the possible transition pathways together with the corresponding transition rates. The manifold of vibrational sublevels of the ground and excited states (see details in text) are shown as gradients.
Fig. 3.
Fig. 3. Characterization of emitter A: (a) Measured ${g^{(2)}(\tau )}$ functions at different cw optical excitation powers expressed in units of saturation power $P_{\mathrm {sat}}$ together with corresponding fits using Eq. (2). Plots in the left column show full time scale, and plots on the right show zoom-in of the antibunching region. (b–c) Power dependence of transition rates (cf. Figure 2) obtained from the fits of the measured correlation functions with Eq. (2). Solid lines are the linear fits to the power dependencies. The obtained linear trends are described by $k_{23} = 1.2(2)\,\mathrm {MHz}\,\frac {P}{P_{\mathrm {sat}}}+2.0(2)\,\mathrm {MHz}$, $k_{31} = 1.07(3)\,\mathrm {MHz}\,\frac {P}{P_{\mathrm {sat}}}$, $k_{24} = 5.4(1)\,\mathrm {MHz}\,\frac {P}{P_{\mathrm {sat}}}$, $k_{41} = 6.0(2)\,\mathrm {MHz}\,\frac {P}{P_{\mathrm {sat}}}$, and $k_{\mathrm {exc}} = 211(7)\,\mathrm {MHz}\,\frac {P}{P_{\mathrm {sat}}}$. The error bars show one standard deviation for the fitting parameters.
Fig. 4.
Fig. 4. (a) Photon count of emitter A at a cw excitation power of 0.44 $P_{\mathrm {sat}}$. The blinking is clearly visible and a threshold value (dashed line) was set to discriminate between a high and low fluorescence level. (b) ${g^{(2)}(\tau )}$ functions evaluated separately for experimental data points corresponding to the bright (blue) and dark (red) fluorescence levels. The solid lines are fits obtained with Eq. (2). The inset shows a zoom at the anti-bunching region. (c)–(d) Transition rates for the bright and the dark fluorescence levels for excitation powers 0.44, 0.69, and $1.52\,P_{\mathrm {sat}}$. The solid lines are plotted as a reference and obtained from the continuous acquisition [see Figs. 3(b) and (c)]. The triangles are the rates obtained from the gated acquisition presented in (b), where solid (open) triangles belong to photon counts above (below) the threshold. (e) Photoluminescence spectrum zoomed in to the ZPL as a function of time at cw excitation power $1.52\,P_{\mathrm {sat}}$. (f) Fluorescence count rate recorded simultaneously with the spectrum. (g) Integrated spectra for the dark (red) and bright (blue) levels fitted with double Lorentzian functions. (h) Count-rate histogram clearly showing two distinct brightness levels.
Fig. 5.
Fig. 5. (a) Photon count trace of emitter A obtained with pulsed laser excitation with a power of 0.4 mW and pulse repetition rate 5 MHz. Three distinct count-rate levels are clearly identified and highlighted by coloring. (b) Time-resolved fluorescence histograms (solid lines) extracted for each distinct count-rate level shown in panel (a) and together with exponential fits (dotted lines). All decays are well described by a decay time constants of $2.5 \pm 0.1$ ns except level 3, which requires a second exponential function with time constant of $1.2 \pm 0.1$ ns.
Fig. 6.
Fig. 6. Internal quantum efficiency of emitters A–D as a function of excitation power. Error bars indicate one standard deviation and are propagated errors from the transition-rate analysis.
Fig. 7.
Fig. 7. Characterization of emitters B, C, and D, similar to analysis of emitter A presented in Fig. 3: Plots of transition rates obtained by fitting ${g^{(2)}(\tau )}$ functions measured at different cw optical excitation powers with Eq. (2). Scaling of transition rates with excitation power is linearly approximated as follows: Emitter B: $k_{23} = 1.07(5)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{31} = 0.20(1)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{24} = 7.3(3)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{41} = 7.8(2)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$; Emitter C: $k_{23} = 7(2)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}} + 2.5(5)\,\mathrm {MHz}$, $k_{31} = 2.1(5)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{24} = 8.3(5)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{41} = 11.8(3)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$; Emitter D: $k_{23} = 0.4(1)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{31} = 0.5(1)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{24} = 3.0(3)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$, $k_{41} = 5.2(5)\,\mathrm {MHz}\frac {P}{P_{\mathrm {sat}}}$;

Tables (1)

Tables Icon

Table 1. Summary of parameters for emitters A–D. The total decay rate k tot = 1 / t L T is determined by low-power lifetime measurements, where t L T is the excited-state lifetime obtained by fitting measurement data with a single-exponential function. The maximum photon count rate I , the saturation power P sat , and the power-dependent background b are determined from fluorescence saturation measurements. The constant pump-independent background c was set to 1 kHz during fitting.

Equations (2)

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ρ 1 ˙ = k exc ρ 1 + k rad ρ 2 + k 31 ρ 3 + k 41 ρ 4 , ρ 2 ˙ = k exc ρ 1 ( k rad + k 23 + k 24 ) ρ 2 , ρ 3 ˙ = k 23 ρ 2 k 31 ρ 3 , ρ 4 ˙ = k 24 ρ 2 k 41 ρ 4 ,
g fit ( 2 ) ( τ ) = 1 σ 2 + σ 2 g mod ( 2 ) ( τ ) .

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