SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NNANO Quantum emission from hexagonal boron nitride monolayers Toan Trong Tran, Kerem Bray, Michael J. Ford, Milos Toth, and Igor Aharonovich 1. Materials Monolayer and multilayer hbn samples were obtained from Graphene Supermarket. The monolayer hbn sample was grown on a copper foil, and transferred onto a silicon substrate using the following method. The sample was first spin-coated with 100 µl of 2% PMMA in chlorobenzene at 2000 rpm for 2 min. It was then dipped in 68% HNO 3 solution for 2 min to completely dissolve the copper foil substrate. The resultant membranes were placed on a silicon substrate and heated to 80 C under low acetone flow. The acetone flow was stopped once the PMMA was removed (~ 15 min). The sample was then rinsed thoroughly with copious amounts of acetone to remove any remaining contamination on the surface. Finally, the sample was dried under flowing N 2. The multilayer hbn sample was annealed in argon to activate the color centers and to desorb surface contaminants. We tried a range of different annealing temperatures, and find that 850 C yields maximum fluorescence intensity. In a typical thermal treatment, a solution comprised of 20 µl of multilayer hbn in ethanol was drop-cast onto the silicon substrate and dried under ambient conditions. The sample was then placed in a high-temperature tube furnace (Linberg/Blue M ), and annealed at 850 C for 30 min, under 1 Torr of argon (to prevent oxidation). The sample was then cooled to room-temperature overnight under 1 Torr of argon. NATURE NANOTECHNOLOGY 1

2 2. Structural and elemental characterization Scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) measurements were performed using a field emission gun SEM (Zeiss Supra 55VP FEG ) and a 20 mm 2 EDX (Oxford X-Max ) silicon drift detector. Transmission electron microscopy (TEM) and selected area electron diffraction (SAED) analysis were conducted by using a Tecnai G2 TEM ) operating at 200 kv accelerating voltage. Raman spectroscopy was carried out using a Renishaw invia Raman microscope. Figure S1. EDX maps of multilayer hbn annealed in argon at 850 C. a, A representative SEM image of multilayer hbn. Corresponding EDX maps of boron (b), nitrogen (c), carbon (d), oxygen (e), and silicon (f). 2

3 3. Photoluminescence analysis A continuous wave (CW) 532 nm laser (Gem 532, Laser Quantum Ltd.) was used for excitation and scanning. The laser was directed through a Glan-Taylor polarizer (Thorlabs Inc.) and a half waveplate, and focused onto the sample using a high numerical aperture (NA = 0.9, Nikon) objective lens. Scanning was performed either using an X-Y piezo scanning mirror (FSM-300 ) or an X-Y-Z nanocube system (PI instruments). The collected light was filtered using a 532 nm dichroic mirror (532 nm laser BrightLine, Semrock Inc.) and an additional long pass filter (Semrock ). The signal was then coupled into a graded index fiber, where the fiber aperture serves as a confocal pinhole. A fiber splitter was used to direct the light into a spectrometer (Acton SpectraPro, Princeton Instrument Inc.) or into two avalanche photodiodes (Excelitas Technologies ) used for single photon counting. Correlation measurements were done using a time-correlated single photon counting module (PicoHarp300, PicoQuant ). Lifetime measurements were performed using a 510 nm pulsed laser excitation source (PiL051X, Advanced Laser Diode Systems GmbH) with a 100 ps pulse width and an 80 MHz repetition rate. Cryogenic PL was done using a Janis ST500 cryostat. The cryostat is cooled with liquid N 2 and thermally regulated with a gold-plated heating stage. The setup is shown schematically in the main text (Fig. 2c). 3

4 Figure S2. a, The confocal map presented in Fig. 2a. b, A close-up showing a typical single color center. c, Line profile (indicated by the dashed line in b) of the defect center shown in b. The circles and the solid trace are the experimental data and a Gaussian fit, respectively. d, Antibunching curve obtained from the defect show in b. The Gaussian fit in b has a full width at half maximum of 429 nm. This value is expected from a single emitter given that the ZPL wavelength is ~623 nm, the PSB extends out to ~700 nm, and a background emission is present, as indicated by the g2(τ) curve shown in d. 4

5 Figure S3. Representative PL spectrum taken from an ensemble of emitters in hbn monolayers at 77 K. Figure S4. Line profile of the 532 nm CW laser used as the excitation source in this study. 5

6 Figure S5. Second order autocorrelation functions of 15 SPEs found at random in multilayer hbn. The g2(0) value is shown for each emitter. Each curve was acquired for 10 min using a 300 µw, 532 nm CW laser as the excitation source. 6

7 Figure S6. Histogram of the g 2 (0) values shown in Fig. S5. 4. Photophysics and quantum efficiency The hbn quantum emitter was analyzed in the frame of an extended three level system 1 (see Fig. S7). To gain information about the level transition rates, the second order correlation function g 2 (τ) was recorded as a function of excitation power. The results are shown in Fig. S8a. The g 2 (τ) is given by equation (1), where τ 1 and τ 2 represent the radiative transition lifetime and the metastable state lifetime, respectively, and a is a bunching factor. 1 g τ 1 1 a e ae (1) 7

8 Figure S7. Schematic illustration of the proposed extended three-level model used to interpret the temporal population dynamics of the defect center in hbn. Figure S8. a, Second order autocorrelation function obtained versus laser power from an SPE in multilayer hbn. The g 2 (τ) traces are normalized and shifted vertically for clarity. b, The 8

9 parameter a, (c) radiative lifetime τ 1 and (d) metastable state lifetime τ 2 of the defect center as a function of laser power. We obtain the values of a, τ 1 and τ 2 by fitting the power-dependent g 2 (τ) (Fig. S8a) using equation (1). From these power-dependent values, we plot a (Fig. S8b), τ 1 (Fig. S8c) and τ 2 (Fig. S8d) as a function of excitation power. By fitting these curves (double exponential and single exponential fits for a and τ 1, and τ 2, respectively) and extrapolating them to extremely high and vanishing excitation powers, we arrive at a 0 = , a = 0.349, τ 0 1 = ns, τ 1 = ns, τ 0 2 = ns, and τ 2 = ns, where the superscripts and 0 denote extremely high and vanishing excitation powers. The transition rates between the three levels, namely, pumping rate from the ground state (level 1) to the excited state (level 2), radiative decay rate from the excited state (level 2) to the ground state (level 1), shelving rate from the excited state (level 2) to the metastable state (level 3), and de-shelving rate from the metastable state (level 3) to the ground state (level 1) are denoted by k 12, k 21, k 23, and k 31, respectively (Fig. S7). By measuring g 2 (τ) as a function of excitation power, we can essentially deduce all of the above transition rates. Specifically, the parameters τ 1, τ 2 and a are deduced using equations (2) (5). 1 τ, (2) A k k k k (3) B k k k k k k k k (4) a (5) 9

10 Based on the moderate bunching behavior, we assume that k 21, and k 31 are power-dependent transition rates, while k 23 is assumed to be a power-independent rate. All the transition rates are given by equations (6) (10). 1 k. k (6) k (7) d (8) k k d (9) k k (10) Here, P represents the excitation power, and the coefficients d and c the saturation behavior of transition k Using a combination of equations (2) (10), we obtain k 0 31 = MHz, d = MHz, k 23 = MHz, and k 21 = MHz. Next, we estimate the quantum efficiency using equation 11: 1 (11) where I, η det, and η qe are the maximum fluorescence detected by the APDs, collection efficiency and fluorescence quantum efficiency, respectively. We measured the setup collection efficiency by accounting for the contribution of each component in the collection path: Dichroic mirrors (~ 95%), objective lens (~ 35%), lenses and coupling to optic fibers (~ 10%), and the APD efficiency at 630 nm (60%). The estimated collection efficiency for our setup is therefore η det ~ This estimate is an upper limit (i.e. the actual quantum efficiency of the emitter can 10

11 potentially be higher). To ensure that there is no loss due to dipole orientation misalignment of the emitter with respect to the laser, we only performed this calculation on emitters that are perfectly aligned with respect to the laser beam (based on polarization measurements). By inserting the above values into equation (11), the quantum efficiency of the color center is ~ 65%. 5. Theoretical calculations VASP 2,3,4 calculations were performed using the Generalised Gradiant Approximation to the exchange correlation functional proposed by Perdew, Burke and Ernzerhof. 5 All calculations are spin-polarized and use the projector augmented wave (PAW) pseudopotentials supplied with the VASP code. A plane-wave cutoff of 450 ev was used for all calculations, this is considerably higher than default values for the pseudopotentials used and represents a well-converged calculation. Pristine single-layer hbn was first geometry optimized using the conventional cell and a 21 x 21 x 1 Monkhurst-Pack reciprocal space grid to an energy tolerance of 0.01 ev. A vacuum spacing of 20 Å was used to separate periodic images of the single layer and to ensure that interaction between these layers is negligible. Relaxation of the lattice vectors using a conjugate gradient approach or by hand plotting the energy as a function of lattice parameter give the same optimized unit cell. The computational conditions are clearly good enough that basis size effects are not important. The optimized lattice parameter is 2.5 Å, with a bond length of Å. 11

12 Figure S9. Chemical bond lengths (in Angstroms) in the N B V N defect center of hbn. 12

13 Figure S10. Spin-resolved calculation of the imaginary dielectric tensor for X and Y components of the N B V N defect center. Red, blue, green, and purple solid lines represent spin-up of the X and Y components, and spin-down of the X and Y components, respectively. The two uncharged defect structures were then generated from this optimized structure using a 7 x 7 supercell and the atomic positions were re-optimized. For the nitrogen vacancy defect (V N ) the BN bond length expands for the nearest-neighbors surrounding the defect by approximately 1.8%. The optimized structure for the boron substituted, nitrogen vacancy defect (N B V N ) is shown in Fig. S9. 13

14 Fig. S10 shows the X and Y components of the imaginary dielectric tensor for the N B V N defect resolved into its two spin components. There is no transition in the vicinity of 2 ev in the spindown component. The feature at approximately 2 ev in Fig. 4f is therefore due to the transition in the spin-up channel between levels at 1.95 ev and 3.90 ev as shown in Fig. 4e. Fig. S11 shows the electronic structure of the V N and N B V N defects in 3 layer hbn. In both cases the middle layer contains the defect and the outer layers are pristine. The stacking sequence is the eclipsed AA' which is believed to be the preferred stacking order. 6,7. The interlayer spacing has been optimized from a 3 layer, conventional cell calculation and is 3.64 Å. As expected this is larger than the experimental value, by about 10%, due to there being no inclusion of the longrange van der Waals forces in our calculations. This is not expected to change the conclusion we find in this calculation that the electronic structure of the defect is relatively unaffected by the additional layers other than a small shift in the energies and a slight narrowing of the band gap. Figure S11. Electronic band diagram of (a) V N, and (b) N B V N defect centers hosted in the middle layer of three-layer hbn. Black and grey arrows represent occupied and unoccupied states, respectively. 14

15 References 1. Neu, E., Agio, M. & Becher, C. Photophysics of single silicon vacancy centers in diamond: implications for single photon emission. Opt. Express 20, (2012). 2. Kresse, G. & Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal amorphous-semiconductor transition in germanium. Phys. Rev. B 49, (1994). 3. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Computational Materials Science 6, (1996). 4. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, (1996). 5. Perdew, J.P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, (1996). 6. Pease, R.S. Crystal Structure of Boron Nitride. Nature 165, (1950). 7. Constantinescu, G., Kuc, A. & Heine, T. Stacking in Bulk and Bilayer Hexagonal Boron Nitride. Phys. Rev. Lett. 111 (2013). 15