Supporting Information for
Carbon-Related Quantum Emitter
in Hexagonal Boron Nitride with
Homogeneous Energy and Three-fold Polarization
Authors:
Ding Zhong
1,2,3
, Shiyuan Gao
4
, Max Saccone
5
, Julia R. Greer
6
, Marco Bernardi
4
,
Stevan Nadj-Perge
1,3
, Andrei Faraon
1,2,3*
Affiliations:
1
Thomas J. Watson, Sr., Laborator
y of Applied Physics, Califo
rnia Institute of Technology,
Pasadena, CA 91125, USA.
2
Kavli Nanoscience Institute, California Inst
itute of Technology, Pa
sadena, CA 91125, USA.
3
Institute for Quantum Informati
on and Matter, California Institu
te of Technology, Pasadena, CA
91125, USA.
4
Department of Applied Physics and Material
Science, California In
stitute of Technology,
Pasadena, CA 91125, USA.
5
Division of Chemistry and Chemic
al Engineering, California Inst
itute of Technology, Pasadena,
CA 91125, USA
6
Division of Engineering and Applied Science, Ca
lifornia Institute of Technology, Pasadena, CA
91125, USA
*
Correspondence to:
faraon@caltech.edu
Contents:
S1. The Fabrication Control: O Implantation.
S2. Absorption/emission dipole orie
ntation 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 implanta
tion 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 implan
tation. Thus, we conducted a control experiment in which
16
O
+
ions
are implanted, with the implantati
on parameters rema
ining the same.
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 incl
ude 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
intensity between [2.19, 2.25] eV, centered arou
nd only the type I emitter. The majority of the
hotspots are preserved in Figure S1c, indicating that
these are type I emitters, as circled out by the
white marker. This result is verified by individually examining the spectrum at such spots.
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) Th
e 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 ty
pe I emitter’s energy. (d) Raster scan of another flake prior t
o
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 th
e type I emitter’s energy. No
type I emitter is found.
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 emis
sion hotspots in Figure S1
e compared to Figure
S1d. These are due to activation
and migration of defects during im
plantation and annealing. There
are no strong hotspots in Figure S1f, which only cap
ture intensity around t
ype I emitters’ energy.
As we examine the spectrum pixel by pixels, we di
d 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 in
trinsic emitters, which is not
evidenced by our observation. The
slight difference in mass should no
t 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 intr
oduced 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 th
e 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 th
at intercepts more ions from the beam.
S2. Absorption/emission dipole orientatio
n for energy-preselected type II emitters.
S3. Schematics for PLE setup.
Figure S2. Absorption/emission dipo
le orientation for 10 type II
emitters between 580 and 590 nm.
(a)
The scatter plot
of 10 type II emitters with close emissi
on energy, with the error bar shown. Th
e gray line serves a guide for eye as
absorption dipole angle align with emission
dipole angle. This data reveals no di
scernible pattern in the absorption or
emission di
p
ole orientations.
S4. Additional PLE results of
type I and type II emitters.
S5. Excitation power-dependent autocorrelation.
Assuming a power dependent excitation rate
푟
ଵଶ
=
훽∗푃
, we could obtain these coefficients
quantitatively by conducting the expe
riment with differen
t power. First of a
ll, the decay rate
휆
ଵ
ൌ
푟
ଵଶ
푟
ଶଵ
approaches asymptotically to
푟
ଶଵ
in the zero-power limit,
allowing for obtaining
푟
ଶଵ
by
Figure S4. Additi
onal PLE results.
(a) Three more type II emitters results ar
e 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 emitt
ers PLE results are presented, exhibiting highly reproducible
PLE patterns.
Figure S3. Schematics of PLE setup.
(a) The laser from the supercontinuum is fi
rst 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 excita
tion 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 spectr
ometer (Spec) records the
spectrum. Polarization components are added de
pending on experiment needs (not shown).
extrapolation. As shown in Figure S5a, we obtained a relaxation rate of
푟
ଶଵ
ൌ
183.3 MHz, which
corresponds to a lifetime
푡
ଵ
ൌ
5.5
ns. In addition,
푟
ଶଷ
and
푟
ଷଵ
can be extracted from the power
dependence of
휆
ଶ
and
훼
, as shown in Figure S5b, c. We find that
푟
ଷଵ
increases rapidly and levels
off at high power, which can be explained by a fa
ster 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
.
푟
ଶଷ
is only several hundred Hertz,
more than 5 orders of magnitude smaller than
푟
ଶଵ
. In fact, as seen from the expression of
휆
ଶ
above,
low transition rates
푟
ଶଷ
and
푟
ଷଵ
can be inferred from a small
휆
ଶ
, which manifest as long bunching
characteristic decay time. In single photon genera
tion scenario, where the emitter is excited by a
laser pulse, the extremely low
푟
ଶଵ
/
푟
ଶଷ
ratio leads to a dominant relaxation through radiative
channel, making it a highly ef
ficient single photon source.
S6. Computed Properties of Carbon-Related Defects
A computational screening is done
for carbon-related defect candidate
s 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 car
ried out for most of the defects except those with a single-
particle 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 obser
ved emitter. However, they are not preferred
over the d=5.77 Å 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.
type
defect
symbol
ground
state spin
polarization
single-particle
transition
(PBE, eV)
ZPL
(constrained
DFT, eV)
singlet
exciton
(BSE, eV)
radiative
lifetime
(BSE, ns)
double-site
defects
C
N
V
B
1 1.15 1.05-0.11 1.02 8.0×10
4
C
N
V
B
-
1/2 0.44 0.72-0.42
C
N
N
B
1/2 2.20 2.53-0.18 2.36 4500
C
N
N
B
+
0 2.44 2.38-0.20 3.47 14
B
N
C
B
1/2 1.10 1.11-0.37
Figure S5. Excitation Powe
r dependent parameters. a
, Antibunching decay rate
휆
ଵ
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
훼
and decay rate
휆
ଶ
on the excitation
power.
c
, Transition coefficients
푟
ଶଷ
and
푟
ଷଵ
as function of power.
B
N
C
B
-
0 1.70 2.15-0.20 1.27 8500
V
N
C
B
0 1.93 1.82-0.78 2.61 121
V
N
C
B
+
1/2 1.70 1.69-0.90 1.58 640
V
N
C
B
-
1/2 0.42 0.62-0.39
triplet-site
defects
C
N
V
B
C
N
1/2
1.49 1.34-0.18 0.78* 9400
C
N
V
B
C
N
-
0 0.23 0.50-0.37
C
B
V
N
C
B
1/2
1.28 1.24-0.29
C
B
V
N
C
B
-
0 2.07 1.98-0.09 2.47* 1.4×10
4
C
N
C
B
C
N
1/2
1.12 1.27-0.12
C
B
C
N
C
B
1/2
1.23 1.29-0.19
donor-
acceptor
pairs
(DAPs)
C
B
-C
N
d=2.95 Å
0 2.37 2.76-0.33 3.46 4.4
C
B
-C
N
d=5.77 Å
0 1.39 2.27-0.47 2.51 16
C
B
-C
N
d=7.21 Å
0 1.10 2.16-0.50
Table 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 forci
ng the occupation of the highest occupied band (HOB) to be 0 and
lowest unoccupied band (LUB) to be 1. Ty
pically, the HOB-LUB transition is the main
component of the exciton wave function,
with a few exceptions indicated by an as
terisk (*) on the exciton energy column.
References:
1. Treussart, F., Clouqueur, A., Grossman, C. & Roch, J.-F. Photon antibunching in the fluorescence of a single dye
molecule embedded in a thin polymer film.
Opt. Lett.
26
, 1504–1506 (2001).
2. Wu, E.
et al.
Narrow-band single-photon emission in the near infrared for quantum key distribution.
Opt. Express
14
, 1296 (2006).