Carbon-Related
Quantum
Emitter
in
Hexagonal
Boron
Nitride
with
Homogeneous
Energy
and
3
‑
Fold
Polarization
Ding
Zhong,
Shiyuan
Gao,
Max Saccone,
Julia R. Greer,
Marco
Bernardi,
Stevan
Nadj-Perge,
and Andrei
Faraon
*
Cite
This:
Nano
Lett.
2024,
24, 1106−1113
Read
Online
ACCESS
Metrics
& More
Article
Recommendations
*
sı
Supporting
Information
ABSTRACT:
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.
KEYWORDS:
Single-photon
emitters,
Hexagonal
boron
nitride,
Carbon
defect,
Three-level
systems
S
ince
their
discovery,
1
−
4
single-photon
emitters
(SPEs)
in
van
der
Waals
materials
such
as hexagonal
boron
nitride
(hBN)
have
seen
a rapid
development.
5
−
19
This
platform
exhibits
a high
photon
extraction
rate
and
enables
on-chip
engineering
based
on
electric
fields,
20
magnetic
fields,
21
doping,
22
and
strain,
23
−
25
with
versatile
control
of the
SPE
properties.
These
SPEs
are
stable
when
the
material
is
transferred,
enabling
integration
with
photonic
devices
26
−
28
or van
der
Waals
heterostructures
29
for
complex
systems.
Progress
has
also
been
made
to suppress
their
spectral
diffusion
30
and
blinking.
31
However,
a primary
challenge
limiting
the application
of these
SPEs
is large
inhomogeneity,
which
is believed
to originate
from
possibly
two
main
sources:
environmental
fluctuations,
such
as strain
and
electrostatic
noise,
or the presence
of multiple
species
within
the emitters.
32
In terms
of energy,
their
emission
energy
ranges
seemingly
randomly
from
1.66
to 2.20
eV.
1,33
Additionally,
their
optical
dipole
orientations
show
significant
randomness,
34
further
adding
to their
unpredictability.
In fact,
no clear
correlation
has
been
identified
between
their
dipole
orientations
and
the
crystallographic
axes
of hBN.
35,36
These
disadvantages
not only
add
complexities
to device
fabrication,
often
necessitating
preselection
based
on desired
wavelength
and
polarization,
but
also
pose
challenges
to achieving
coherence
between
emitters.
Such
coherence
is essential
for applications
such
as quantum
computing,
37
quantum
networking
38
and
quantum
metrol-
ogy.
39
Here,
we report
the identification
of a new
type
of quantum
emitters
in carbon-implanted,
layered
hBN.
Using
photo-
luminescence,
we first
identify
a cluster
of emitters
centered
around
2.24
eV.
These
emitters
also
exhibit
a strong
correlation
between
optical
dipole
orientation
and
crystal
directions
with
3-fold
symmetry
in hBN.
Photoluminescence
excitation
(PLE)
spectra
for these
emitters
exhibit
consistent
resonances,
in contrast
to emitters
reported
in previous
studies,
where
variations
were
observed.
1,6
As for quantum
character-
istics,
autocorrelation
measurements
show
single-photon
statistics
that
are
consistent
with
a three-level
system
with
very
weak
coupling
to a shelving
state,
indicating
a high
single-
photon
generation
efficiency.
Low-temperature
measurements
show
a very
narrow
energy
distribution
(2.444
±
0.0013
eV),
a
substantial
reduction
in inhomogeneity
compared
to previous
reported
types.
Ab initio
calculations
indicate
that
a pair
of
substitutional
carbon
atoms
separated
by a hexagonal
unit
cell
are the most
probable
microscopic
origin
of the emitter.
Received:
September
20, 2023
Revised:
January
11, 2024
Accepted:
January
12, 2024
Published:
January
19,
2024
Letter
pubs.acs.org/NanoLett
© 2024
The Authors.
Published
by
American
Chemical
Society
1106
https://doi.org/10.1021/acs.nanolett.3c03628
Nano
Lett.
2024,
24, 1106
−
1113
This article is licensed under CC-BY 4.0
Downloaded via CALIFORNIA INST OF TECHNOLOGY on February 1, 2024 at 17:46:58 (UTC).
See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
■
RESULTS
AND
DISCUSSION
The
emitters
we studied
were
identified
in multilayer
hBN
implanted
with
carbon
12+
and
annealed
(see
Methods
for
details).
Using
532
nm
continuous-wave
laser
excitation,
we
performed
raster
scans
over
the
hBN
flakes
at room
temperature
to identify
the
locations
of the
emitters.
Figure
1a shows
an optical
image
of a representative
hBN
flake.
Figure
1b shows
a portion
of the raster
scan
map
on the flake
with
its
Figure
1.
Photoluminescence
characterization
of the emitters.
(a) Optical
image
of the measured
hBN
flake.
The
image
has a size
of 100
μ
m by 118
μ
m.
(b)
Photoluminescence
map
of the flake
in the region
marked
with
a rectangle.
The
red circles
mark
the locations
of the emitters.
(c) Energy
distribution
of multiple
emitters
from
the flake.
(d)
Energy
distribution
of multiple
emitters
from
a
16
O
+
-implanted
flake.
(e) Representative
spectra
of four
type
I emitters
(blue
shaded)
and
four
type
II emitters
(gray
shaded).
(f) Count
rate
as a function
of laser
power.
The
black
curve
is a fit to
the data.
Figure
2.
Polarization
and
photoluminescence
excitation
characterization.
(a) The
absorption
polarization
of 27 emitters
with
their
types
color-
coded,
excited
by a 2.33
eV laser.
(b) Typical
ZPL
intensity
as a function
of excitation/detection
polarization
angle
for a type
I emitter.
The
axis
for
the
maximum
intensity
for excitation/detection
polarization
indicates
the
intrinsic
absorption/emission
dipole
orientation
of the
emitter.
(c)
Photoluminescence
excitation
of a type
I and
type
II emitter
plotted
against
the energy
offset
from
their
respective
emission
energy
(2.00
eV for
type
II and
2.24
eV for type
I). (d)
The
absorption
polarization
and
emission
polarization
when
the type
II emitter
is excited
at 2.19
eV (0.19
eV
offset),
as indicated
by the black
arrow
in (c).
(e) The
absorption
and
emission
dipole
orientations
for the type
II emitter
at a 2.69
eV excitation
energy
(0.69
eV offset),
as indicated
by the purple
arrow
in (c).
Nano
Letters
pubs.acs.org/NanoLett
Letter
https://doi.org/10.1021/acs.nanolett.3c03628
Nano
Lett.
2024,
24, 1106
−
1113
1107
color
representing
the average
intensity
between
[1.8,
2.25]
eV
for
each
pixel,
where
several
representative
local
intensity
hotspots
corresponding
to the
emitter
locations
are
circled.
The
peak
energy
distribution
of 24 emitters
from
the
flake
is
plotted
in Figure
1c.
While
many
of them
are
distributed
between
2.18
eV (568
nm)
and
2.00
eV (620
nm),
a large
fraction
is centered
around
2.24
eV
(553
nm).
This
concentration
of emitters
with
energy
around
2.24
eV
is
absent
in a control
sample
where
16
O
+
was
implanted
with
the
same
parameters,
as shown
in Figure
1d. (for
more
details,
see
the
Supporting
Information).
We
attribute
this
class
of
homogeneous
emitters
at 2.24
eV to a new
type
of defect
color
center
and
refer
to them
as “type
I”. We
attribute
the
other
class
of emitters
with
large
inhomogeneity
in emission
energy
to previously
reported
quantum
emitter
type(s)
in
hBN
1,5,40
and
refer
to them
as “type
II” in this
work.
Figure
1e displays
the
normalized
spectra
from
representa-
tive
emitters
of both
types.
The
type
I emitters
display
a more
homogeneous
peak
shape
than
the type
II emitters
in terms
of
both
peak
energy
and
peak
width.
Both
types
of emitters
exhibit
an energy
gap
of
∼
165
meV
between
the zero-phonon
line
(ZPL)
and
the phonon
sideband
(PSB).
This
is expected,
as both
emitters
couple
to the same
optical
phonons
in hBN,
and
based
on calculations,
41
the
density
of states
(DOS)
of
hBN
phonons
has a maximum
at 165
meV.
Figure
1f shows
the
saturation
curve
of a type
I emitter.
We
fit the
experimental
data
to the function
I
(
P
)
=
I
∞
×
P
/(
P
+
P
S
), where
I
∞
is the
count
rate
at infinite
excitation
power
and
P
S
is the excitation
power
at saturation.
The
fitting
gives
values
of
P
S
= 37
μ
W
and
I
∞
= 200
kHz.
Measurements
under
linear
polarization
excitation
on these
two
types
of emitters
revealed
distinct
properties.
By tracking
the detected
ZPL
intensity
while
controlling
the polarization
of
the
excitation
laser
or measuring
the
polarization
of the
detected
PL
signal,
we
characterized
both
the
absorption
dipole
orientation
and
the
emission
dipole
orientation
(experimental
details
are
given
in the
Methods
section).
In
Figure
2a, for an ensemble
of emitters
on a single
flake,
we
show
the
absorption
dipole
orientations
of multiple
emitters
with
the
emitter
type
color-coded.
For
type
I emitters,
the
absorption
dipole
orientation
only
takes
three
discrete
values,
11
°
,
71
°
,
and
131
°
(
±
1
°
),
which
are 60
°
apart
(the
angular
offset
is arbitrary).
In contrast,
for type
II emitters,
we found
that
the
dipole
orientations
were
distributed
across
the
entire
range
without
an obvious
pattern,
which
is in agreement
with
previously
reported
SPEs
in hBN.
35
The
3-fold
distribution
for
the type
I SPEs
is consistent
with
the crystal
symmetry
of the
hBN
host
lattice,
suggesting
a symmetric
atomic
structure
for
the
type
I SPEs.
We
also
found
that
the
absorption
dipole
orientation
was
always
aligned
to the
emission
dipole
orientation
in type
I emitters
(Figure
2b),
while
for type
II
emitters,
this
behavior
was
observed
only
occasionally.
34,35
In
order
to show
that
this
polarization
feature
does
not
originate
from
energy
preselection
of emitters,
in the
Supporting
Information,
we present
the
results
of 10 energy-preselected
type
II emitters.
This
data
reveals
no discernible
pattern
in the
absorption
or emission
dipole
orientations.
Defining
the
polarization
degree
as
p
= (
I
max
−
I
min
)/(
I
max
+
I
min
), we
obtained
absorption
and
emission
polarization
values
of
p
=
96%
for type
I emitters,
which
is strong
evidence
for a linearly
polarized
dipole-like
emitter.
PLE
spectroscopy
was
performed,
and
it was
found
that
these
consistently
aligned
absorption
−
emission
dipole
ori-
entations
for the
type
I emitters
were
associated
with
their
repeatable
excitation
resonances.
In PLE
spectroscopy,
the PL
can
be detected
if the system
is excited
by light
with
the proper
wavelength
and
relaxes
onto
the excited
state
corresponding
to
the
ZPL
emission.
We
repeatedly
obtained
identical
PLE
spectra
for each
individual
type
I emitter,
with
one
example
shown
in Figure
2c in cyan
(more
examples
are shown
in the
Supporting
Information).
In the spectrum
from
2.33
(0.09
eV
offset)
to 2.77
eV (0.53
eV offset),
we observed
only
one
resonant
peak
close
to the
emission
energy,
and
the
PL
intensity
dropped
as the
excitation
energy
increased.
In
addition,
the
absorption
dipole
orientation
over
the
entire
excitation
resonance
peak
was
found
to always
align
with
the
emission
dipole
orientation
of the PL.
In contrast,
the
PLE
spectra
for the
type
II emitters
varied
between
individual
emitters.
In Figure
2c, we also
show
the
PLE
spectrum
(orange
plot)
from
a randomly
selected
type
II
emitter
(emission
energy:
2.00
eV;
more
examples
are shown
in the
Supporting
Information).
The
spectrum
consists
of a
continuum
extending
from
(close
to)
the
emission
energy
to
around
a 0.48
eV offset
energy
plus
a separate
peak
at 0.69
eV.
We
found
that
the
absorption
dipole
orientation
within
the
continuum
was
identical
to the
emission
dipole
orientation
(Figure
2d).
We measured
a different
dipole
orientation
for the
peak
at 0.69
eV,
although
the
emission
polarization
did
not
change
with
the excitation
energy,
as shown
in Figure
2e.
These
results
can
be explained
in the
framework
of the
Franck
−
Condon
principle.
42
Within
the
Born
−
Oppenheimer
approximation,
where
the nuclei
and
electronic
wave
functions
are treated
as independent,
the
probability
amplitude
for the
decay
process
can
be written
as
Figure
3.
Photon
autocorrelation
on type
I emitters.
(a) Autocorrelation
on a short
time
scale
featuring
antibunching.
The
red dots
represent
the
experimental
data,
which
are the
number
of coincidences
normalized
by coincidence
rate
at time
infinity.
The
blue
curve
is the
fit to the
data,
suggesting
g
2
(0)
= 0.07.
(b)
Autocorrelation
on a long
time
scale
featuring
bunching.
The
left side
of the curve
is noisier
due
to a smaller
bin size
compared
to the right
side.
(c) Schematic
of a three-level
model.
The
transition
rate
between
states
i
and
j
is denoted
by
r
ij
.
Nano
Letters
pubs.acs.org/NanoLett
Letter
https://doi.org/10.1021/acs.nanolett.3c03628
Nano
Lett.
2024,
24, 1106
−
1113
1108
r
A
R
R
R
d
(
)
(
)
n
n
n
n
,
,
2
,
,
2
=
|
| |
*
|
*
*
*
*
*
(1)
where
R
is the
nuclear
coordinate
and
φ
μ
,
n
is the
combined
wave
function
for an electronic
state
μ
and
vibronic
state
with
n
phonons
occupied.
For
a type
I emitter,
the
excitation
is
between
(
μ
0
, 0) and
(
μ
1
,
n
1
), which
means
the emitter
is first
excited
to a higher
vibronic
sublevel
of the
excited
state,
followed
by fast
vibrational
relaxation,
and
then
the
ZPL
is
radiated.
The
identical
absorption
and
emission
dipole
moments
are
a consequence
of
|⟨
μ
0
|
r
|
μ
1
⟩|
2
possessing
time-
reversal
symmetry.
For
a type
II emitter,
the continuum
below
0.48
eV offset
energy
is similarly
a transition
between
(
μ
0
′
, 0)
and
(
μ
1
′
,
n
1
′
). However,
for the
resonance
peak
at 0.69
eV
offset
energy,
the distinct
absorption
dipole
orientation
and
the
clear
isolation
of this
peak
suggest
that
it corresponds
to a
higher
electronic
state
(
μ
2
′
,
n
2
′
) with
a different
transition
dipole.
Following
Kasha’s
rule,
43
the system
still
relaxes
to the
lower
excited
state
(
μ
1
′
, 0) first
before
it emits
a photon
with
energy
and
polarization
related
only
to the
ZPL
transition,
such
that
the
emission
dipole
is independent
of excitation
energy.
Previous
studies
35
on type
II emitters
have
found
that
the excitation
energy
offset
with
respect
to emission
energy
is
positively
correlated
with
misaligned
absorption
and
emission
dipole
orientations.
From
our
measurements,
we tentatively
argue
that
this
is because
higher
electronic
states
are
more
likely
to be accessed
with
a higher
excitation
energy,
which
have
a different
excitation
dipole
orientation.
Next,
we
investigated
the
type
I emitters
using
intensity
autocorrelation
on a Hanbury
Brown
−
Twiss
setup.
Figure
3a
shows
a representative
background-corrected
g
2
(
τ
)
with
g
2
(0)
= 0.07
(
g
2
(0)
= 0.23
before
the
correction),
which
is
characteristic
of a single-photon
emitter.
The
background
correction
formula
is included
in the Methods
section.
A bunching
feature
is seen
on a longer
time
scale
of 1
×
10
8
ns, as shown
in Figure
3b. The
emergence
of such
bunching
indicates
the presence
of a third
state.
In a three-level
model,
which
includes
a ground
state,
an excited
state,
and
a shelving
state,
when
excited,
the emitter
predominantly
relaxes
back
to
the
ground
state
but
less
frequently
relaxes
through
the
shelving
state.
The
process
is illustrated
in Figure
3c, with
the
transition
rate
between
states
i
and
j
denoted
as
r
ij
. By solving
the photon
dynamics
assuming
a 1 to 2 excitation
at time
zero,
the autocorrelation
function
can
be expressed
as
44
g
(
)
1
(1
) ex
p(
)
exp(
)
2
1
2
=
+
+
(2)
where
λ
1
=
r
12
+
r
21
is the
decay
rate
of the
antibunching
feature,
λ
2
=
r
31
+
r
23
r
12
/(
r
12
+
r
21
) is the
decay
rate
of the
bunching
feature,
and
α
=
r
12
r
23
/[
r
31
(
r
12
+
r
21
)] determines
the
bunching
amplitude.
Assuming
a power-dependent
excitation
rate
r
12
=
β
P
,
we could
obtain
these
coefficients
quantitatively
by
conducting
the
experiment
with
different
amounts
of power
(calculations
are
shown
in the
Supporting
Information).
We
obtained
a relaxation
rate
of
r
21
= 183.3
MHz,
and
r
23
was
the
order
of hundreds
of Hz,
which
is more
than
5 orders
of
magnitude
smaller
than
r
21
. The
high
r
21
/
r
23
ratio
signifies
a
dominant
radiative
relaxation
process,
making
it a highly
efficient
single-photon
source.
We
further
investigated
the properties
of this
defect
at a low
temperature.
In Figure
4a, we show
a spectrum
of the
type
I
emitter
at 4 K. Besides
the
slightly
blue-shifted
emission
energy,
the
peak
width
was
significantly
reduced
due
to the
weaker
effect
of acoustic
phonons
at low
temperatures.
45
(Note
that
the line
width
in Figure
4a is limited
by the
∼
150
μ
eV
resolution
of our
spectrometer,
and
thus,
the
actual
line
width
may
be even
narrower.)
By measuring
the spectrum
as a
function
of time,
we observed
the
spectral
diffusion
of the
emitter.
In Figure
4b,
we take
1 frame
per
second
for 300
consecutive
seconds.
Minor
shifts
in the
energy
between
frames
indicate
moderate
spectral
diffusion.
Over
the course
of
300
s, we found
a spectral
diffusion
range
of
∼
270
μ
eV,
possibly
originating
from
electrical
transitions
in nearby
defects
and
impurities
causing
electrostatic
fluctuations
in the
environment.
In Figure
4c, we fitted
the
peak
positions
of 36
type
I emitters,
which
gave
a distribution
of 2.2444
±
0.0013
eV. This
inhomogeneity
of 0.0013
eV is 2 orders
of magnitude
smaller
than
in previously
identified
type
II emitters.
1,33
On
the
basis
of these
experimental
results,
we
use
first-
principles
calculations
to look
for
an atomic
defect
with
properties
consistent
with
those
of the
type
I emitter.
This
search
used
the following
criteria:
(1)
The
defect
contains
carbon
but
no
other
external
elements.
(2)
To
account
for the
distinctive
absorption
polarization
with
60
°
spacing,
the
defect
should
possess
C
2
v
or
C
s
symmetry
with
a mirror
plane
along
the
zigzag
or
armchair
directions.
(3)
The
first
excited
state
has
a large
in-plane
transition
dipole
with
a ZPL
energy
of
∼
2.24
eV.
(4)
No optically
active
higher
excited
state
is present
within
0.5 eV of the first
excited
state,
to account
for the lack
of
resonant
peaks
in the PLE
spectrum.
Figure
4.
Properties
of type
I emitters
at low
temperature.
(a)
Low-temperature
spectra
of a type
I emitter.
(b)
Time
series
spectra
of a type
I
emitter
for 300
s with
1 frame
per
second.
(c)
Peak
energy
distribution
of 36 type
I emitters.
Nano
Letters
pubs.acs.org/NanoLett
Letter
https://doi.org/10.1021/acs.nanolett.3c03628
Nano
Lett.
2024,
24, 1106
−
1113
1109