—

$J/\psi$ production and polarization

Maddalena Frosini
on behalf of LHCb Collaboration

Department of Physics
University of Florence, INFN of Florence, ITALY

> The study of the production of heavy quarkonium is crucial for a thorough
> understanding of Quantum Chromodynamics (QCD). This note reports the
> measurements of the $J/\psi$, $\chi_{c}$ and double charm production cross
> section, and discusses the prospects for the $J/\psi$ polarization at LHCb.

> PRESENTED AT
>
>
>
>
> CHARM 2012
> Honolulu, Hawaii, May 14–17, 2012

##  1 Introduction

Understanding the charmonium hadroproduction mechanism has been a long-term
program both experimentally and theoretically. At the LHC two different
components contribute: the “prompt” component, which includes “direct”
production in the $pp$ collisions and the “feed down” from higher charmonium
states, and the “delayed” component, coming from the $b$-hadron decays. In the
direct production the $c\overline{c}$ pairs are expected to be created mainly
through gluon-gluon fusion at the leading order (LO) and the bound states are
formed in the final color-singlet states. The most recent models allow the
formation of the $c\overline{c}$ pairs also through color-octet states, which
evolve toward the final state via exchange of soft gluons. Such evolution is
described in terms of a non-perturbative QCD (NRQCD) factorization approach.
The LHCb collaboration has given many contributions in understanding the
quarkonium production mechanism, some of them reported here. The measurement
of the $J/\psi$ production cross section together with the status of the
polarization analysis will be presented. Both measurements provide a critical
test for the color-singlet [1, 2] and color-octet models [3]. The study of
$\chi_{c}$, double $J/\psi$ and $J/\psi$ production associated with an open
charm hadron will also be presented. In particular the last two are rare
processes and they can be useful to investigate the contributions from other
mechanisms, such as the Double Parton Scattering (DPS) [7, 8, 9].

##  2 The LHCb detector

The LHCb detector [10] is a single-arm forward spectrometer covering the
pseudo-rapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high precision tracking
system consisting of a silicon-strip vertex detector surrounding the proton-
proton interaction region, a large-area silicon-strip detector located
upstream of a dipole magnet with a bending power of about 4 Tm, and three
stations of silicon-strip detectors and straw drift-tubes placed downstream.
The combined tracking system has a momentum resolution $\delta p/p$ that
varies from 0.4% at 5 GeV/$c^{2}$ to 0.6% at 100 GeV/$c^{2}$, and an impact
parameter resolution of 20 $\mu$m for tracks with high transverse momentum.
Charged hadrons are identified using two ring-imaging Cherenkov detectors.
Photon, electron and hadron candidates are identified by a calorimeter system
consisting of scintillating-pad and pre-shower detectors, an electromagnetic
calorimeter and a hadron calorimeter. Muons are identified by a muon system
composed of alternating layers of iron and multiwire proportional chambers.
The trigger consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage which applies a
full event reconstruction.

##  3 $J/\psi$ cross section measurement

The cross section is measured selecting $J/\psi$ decaying to two muons: the
data sample corresponds to an integrated luminosity $\mathcal{L}=\left(5.2\pm
0.5\right)$ pb-1 of $pp$ collisions at $\sqrt{s}=7$ TeV recorded by the
experiment during September 2010. The double differential cross section in
$J/\psi$ $p_{T}$ and $y$ is defined as following:

$\frac{d^{2}\sigma}{dp_{T}dy}=\frac{N(J/\psi\rightarrow\mu^{+}\mu^{-})}{L\times\varepsilon_{tot}\times\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})\Delta
p_{T}\Delta y},$ (1)

where $N(J/\psi\rightarrow\mu^{+}\mu^{-})$ is the number of selected $J/\psi$
decaying in two muons, $\mathcal{L}$ is the integrated luminosity,
$\varepsilon_{tot}$ is the total efficiency (estimated from Monte Carlo
including the detector acceptance, the reconstruction and trigger efficiency),
$\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})$ is the branching ratio of the
$J/\psi\rightarrow\mu^{+}\mu^{-}$ decay, $\Delta p_{T}$ and $\Delta y$ are
respectively the $J/\psi$ transverse momentum and rapidity bin sizes. The
analysis selection requires at least one reconstructed primary vertex in each
event. The $J/\psi$ candidates are formed from pairs of opposite sign charged
tracks reconstructed in the tracking system and identified as muons. The two
muons must have a good quality of the track fit and originate from a common
vertex. To separate the prompt and the delayed component the $J/\psi$ pseudo
proper time is used, defined as
$t_{z}=\frac{(z_{J/\psi}-z_{PV})m_{J/\psi}}{p_{z}},$ where $z_{J/\psi}$ and
$z_{PV}$ are the $J/\psi$ decay vertex and the primary vertex positions along
the beam axis and $m_{J/\psi}$ and $p_{z}$ are respectively the mass and the
momentum component of the $J/\psi$ along the beam axis.

Figure 1: Double differential cross section of $J/\psi$ prompt component.

Figure 2: Prompt $J/\psi$ differential cross section compared with different
theoretical models. The top plots show the direct component only and the
bottom include the feed down.

Figure 3: Double differential cross section of the delayed $J/\psi$ component.

Figure 4: Differential cross section of delayed $J/\psi$ component compared
with FONLL computation.

Figures 2 and 2 show respectively the double differential prompt cross section
and the differential prompt cross section integrated over rapidity as a
function of $p_{T}$. Results are compared with the prediction of three
different theoretical models (Colour Singlet Model, Colour Octet Model and
Colour Evaporation Model). In Fig.4 the double differential cross section of
the delayed component is shown and in Fig.4 it is integrated over rapidity and
compared with the FONLL computation. The total integrated cross sections are

$\sigma_{prompt}=(10.52\pm 0.04(stat.)\pm
1.40(sys.)^{+1.64}_{-2.20}(pol.))\mu\mathrm{b},$ (2)
$\sigma_{from\>b}=\left[1.14\pm 0.01(stat.)\pm
0.16(sys.)\right]\mu\mathrm{b}.$ (3)

The first and the second uncertainties are the statistical and the systematic,
where the main sources of systematic uncertainty come from the luminosity
measurement, the tracking and trigger efficiency. The third uncertainty on the
prompt cross section is due to the unknown polarization of the $J/\psi$ and it
is estimated calculating the total efficiency in two possible extreme
scenarios of fully transverse and fully longitudinal polarization. The
deviation from the case of zero polarization is assigned as systematic
uncertainty to the measurement. From Eq.3 the $b\overline{b}$ cross section is
extrapolated to the full solid angle using the formula

$\sigma(pp\rightarrow
b\overline{b}X)=\alpha_{4\pi}\frac{\sigma_{fromb}}{2\mathcal{B}(b\rightarrow
J/\psi X)}=\left[288\pm 4(stat.)\pm 48(sys.)\right]\mu\mathrm{b}.$ (4)

All these results have been published in Ref.[11].

##  4 Outlook for polarization measurement

With the full 2011 data sample the prompt $J/\psi$ polarization will be
measured studying the full angular distribution of the two muons:

$\frac{dN}{d(\cos\theta)d\phi}\propto
1+\lambda_{\theta}\cos^{2}\theta+\lambda_{\phi}\sin^{2}\theta\cos
2\phi+\lambda_{\theta\phi}\sin 2\theta\cos\phi,$ (5)

where $\theta$ and $\phi$ are the polar and azimuthal angles in the helicity
frame (using the $J/\psi$ momentum as polarization axis). The measurement will
be performed in bins of $J/\psi$ transverse momentum and rapidity. The
statistical sensitivity should be under 0.15 for $\lambda_{\theta}$ and about
0.01 for $\lambda_{\phi}$ and $\lambda_{\theta\phi}$. The systematic
uncertainty is expected to be of the same order of magnitude.

##  5 $\chi_{c}$ production

The study of the $J/\psi$ production through the radiative decays of the
$\chi_{c}$ states provides a useful test of both the color-singlet and color-
octet model. Moreover it is fundamental for the $J/\psi$ polarization
measurement, as the directly produced $J/\psi$ and those coming from
$\chi_{c}$ decays can carry different polarization and this represents a
possible source of uncertainty for the polarization measurement of the prompt
component. The measurement of the fraction of $J/\psi$ coming from $\chi_{c}$
decays can quantify this uncertainty.

Figure 5: Invariant mass difference spectrum $\Delta
m=m(\chi_{c})-m(J/\psi)=m(e^{+}e^{-}\mu^{+}\mu^{-})-m(\mu^{+}\mu^{-})$ using
converted photons.

Figure 6: Relative cross section $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ in bins
of $J/\psi$ transverse momentum.

The relative cross section $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ is measured
using two different data sample acquired by the LHCb experiment during the
2010 and 2011, respectively of 37 pb-1 [12] and 370 pb-1 [13]. In both cases
the $\chi_{c}$ states are identified through their radiative decay
$\chi_{c}\rightarrow J/\psi\gamma$ with the $J/\psi$ decaying to two muons
$J/\psi\rightarrow\mu^{+}\mu^{-}$. For the first measurement, made with a
smaller data sample, the photons reconstructed in the calorimeter system have
been used. This allows to have a higher statistics but the poor resolution of
the calorimeter doesn’t permit to separate the two $\chi_{c1}$ and $\chi_{c2}$
states. In the second measurement the photons converted in the detector
material before the magnet have been used, $\gamma\rightarrow e^{+}e^{-}$. In
this way it is possible to take advantage of the good resolution of the
tracker, which allows to resolve the two states, as it is shown in Fig.6.
In both measurements the efficiency is determined from the Monte Carlo
simulation and the number of signal events is extracted with a fit to the
invariant mass difference spectra, in four bins of $J/\psi$ transverse
momentum.
The results for the relative cross section
$\sigma(\chi_{c2})/\sigma(\chi_{c1})$ are shown in Fig.6. In the plot the
inner error bars correspond to the statistical uncertainties and the outer
bars correspond to the sum of all the sources of systematic uncertainties. The
shaded area represents the maximum effect due to the unknown $\chi_{c}$
polarization. In green and black the results obtained reconstructing the
photons in the calorimeter (2010 statistics) and the converted photons (2011
statistics) are shown. The results from the CDF collaboration are shown in
magenta [14]. The blue and red shaded area correspond to the color-singlet and
NRQCD prediction respectively.

Figure 7: Relative cross section $\sigma(\chi_{c})/\sigma(J/\psi)$ in bins of
$J/\psi$ transverse momentum. The results (black points) are compared with the
CDF measurement [16] and with the color-singlet and color-octet prediction
(respectively the blue and red area.)

The $\chi_{c}$ to $J/\psi$ ratio has been measured with the 36 pb-1 data
sample acquired by the experiment in the 2010 [15]. The $\chi_{c}$ states are
reconstructed through their radiative decay $\chi_{c}\rightarrow J/\psi\gamma$
with the $J/\psi$ decaying into two muons $J/\psi\rightarrow\mu^{+}\mu^{-}$.
The results are shown in Fig.7, compared with the CDF measurement and with two
theoretical models, the color-singlet (blue) and NRQCD approach (red).

##  6 Double charm production

Recently, both the production of double quarkonium and also the associated
production of quarkonium together with open charm have been suggested as
probes of the production mechanism. In the $pp$ collisions also other
mechanisms, as the DPS [7, 8, 9], can be involved in the production and their
contribution can be estimated with respect to the Single Parton Scattering
(SPS) [4, 5, 6].
Such a study has been performed at LHCb through the measurement of the double
$J/\psi$, taken from Ref.[17], and $J/\psi$ production associated with an open
charm hadron (such as $D^{0}$, $D^{+}$, $D^{+}_{s}$ and $\Lambda_{c}^{+}$)
[18], with the 2010 and 2011 datasets (respectively 37 pb-1 and 355 pb-1).

Figure 8: Invariant mass distribution of the first muon pair in bins of the
second muon pair for the double $J/\psi$ production.

The double $J/\psi$ production cross section has been measured reconstructing
the two $J/\psi$ mesons in their decay to two muons. Both the $J/\psi$ mesons
have been required to have rapidity and transverse momentum lying respectively
in the ranges $2<y<4.5$ and $p_{T}<10$ GeV/$c$.
The signal yield is determined fitting the invariant mass distribution of the
first muon pair in bins of the second muon pair and correcting the number of
signal events by the total efficiency.
The total efficiency is factorized in three different terms

$\varepsilon_{J/\psi J/\psi}^{tot}=\varepsilon_{J/\psi
J/\psi}^{sel\&reco\&acc}\times\varepsilon_{J/\psi J/\psi}^{\mu
ID}\times\varepsilon_{J/\psi J/\psi}^{trg},$ (6)

where $\varepsilon_{J/\psi J/\psi}^{sel\&reco\&acc}$ is the acceptance,
selection and reconstruction efficiency, $\varepsilon_{J/\psi J/\psi}^{\mu
ID}$ is the efficiency of the muon identification and $\varepsilon_{J/\psi
J/\psi}^{trg}$ is the trigger efficiency. To take into account the distortion
due to the unknown $J/\psi$ polarization $\varepsilon_{J/\psi
J/\psi}^{sel\&reco\&acc}$ is a function of the $J/\psi$ $\cos\theta$ where
$\theta$ is the angle between the $\mu^{+}$ in the $J/\psi$ center of mass
frame and the Lorentz boost from the laboratory frame to the $J/\psi$ frame.
The corrected invariant mass distribution of the first muon pair in bins of
the second muon pair is shown in Fig.8, in three bins of $J/\psi$ transverse
momentum in a particular bin of rapidity.
The double $J/\psi$ cross section is estimated to be

$\sigma_{J/\psi J/\psi}=\frac{N^{corr}_{J/\psi
J/\psi}}{\mathcal{L}\,\mathcal{B}^{2}(J/\psi\rightarrow\mu^{+}\mu^{-})}=\left(5.1\pm
1.0(stat.)\pm 1.1(sys.)\right)\mathrm{nb},$ (7)

where $N^{corr}_{J/\psi J/\psi}$ is the efficiency corrected signal yield,
$\mathcal{L}=37$ pb-1 is the integrated luminosity and
$\mathcal{B}(J/\psi\rightarrow\mu^{+}\mu^{-})$ is the branching ratio of the
$J/\psi$ decay into a muon pair.
The uncertainty are respectively statistical and systematic. The main
contributions to the systematic uncertainty come from the tracking and trigger
efficiency and from the unknown $J/\psi$ polarization.
The experimental result obtained by LHCb has been compared with the
theoretical contribution calculated in color-singlet model, from the SPS and
the DPS. The two contributions, estimated in the LHCb acceptance, are listed
together with the related uncertainties, in Tab.1 [17]. The sum of the two
contributions is in agreement with the experimental value reported in Eq.7,
although the uncertainties on the theoretical expectations are too large to
draw a definite conclusion on the production mechanism.

Model | Cross section (nb) | Uncertainty
---|---|---
Single Parton S. | 4.15 | 30%
Double Parton S. contribution | 2 | 50%
Table 1: SPS and DPS contribution to the double $J/\psi$ production cross
section estimated in the LHCb acceptance. The theoretical uncertainties are
also listed.

Figure 9: $J/\psi$ production cross section with associated open charm. The
experimental results (black points) are compared with the gluon-gluon fusion
expectation (yellow and green areas [4, 5, 6]).

Figure 10: Results for the prompt open charm cross sections and double open
charm cross section ratio compared with the theoretical expectation computed
with the DPS approach [7, 8, 9].

The production cross sections of a $J/\psi$ meson associated with an open
charm hadron, $D^{0}$, $D^{+}$, $D^{+}_{s}$ or $\Lambda_{c}^{+}$ have been
measured using 355 pb-1 out of the 2011 datasets. As control channels, the
$c\overline{c}$ events with two open charm hadrons reconstructed in the LHCb
acceptance have been also studied. The $J/\psi$, $D^{0}$, $D^{+}$, $D^{+}_{s}$
and $\Lambda_{c}^{+}$ hadrons have been reconstructed through the following
decays: $J/\psi\rightarrow\mu^{+}\mu^{-}$, $D^{0}\rightarrow\pi^{+}K^{-}$,
$D^{+}\rightarrow\pi^{+}\pi^{+}K^{-}$,
$D^{+}_{s}\rightarrow\pi^{+}K^{+}K^{-}$, $\Lambda^{+}_{c}\rightarrow
p\pi^{+}K^{-}$.
In Fig.10 (taken from Ref.[18]) the results for the production cross section
of the $J/\psi D$ processes are shown, compared with the theoretical
expectation estimated with gluon-gluon fusion model. In Fig.10 (from Ref.[18])
the ratios of the product of the prompt open charm cross sections and the
double open charm cross section show a good agreement with the theoretical
expectation from the DPS, assuming the effective cross section measured in
multi-jet events at Tevatron [19]. In the plots the inner error bars represent
the statistical uncertainties while the outer error bars are the sum in
quadrature of the statistical and systematic uncertainties. The main
contributions to the systematics are coming from the trigger efficiency, the
unknown $J/\psi$ polarization and the luminosity.

##  7 Conclusion

LHCb has provided many contributions in understanding the quarkonium
production mechanism in particular with the measurement of the $J/\psi$ and
$\chi_{c}$ production. Also the double $J/\psi$ and $J/\psi$ associated with
an open charm hadron production has been investigated, which provide a useful
test for the SPS and DPS approach. The measurement of the polarization of the
prompt $J/\psi$ component is ongoing and it will provide a critical test for
the validity of the color-singlet and color-octet models.

## References

  * [1] Berger E.L. and Jones D. Phys. Rev. D 23 1521, 1981
  * [2] Baier R. and Rückl Phys. Lett. B 102 364, 1981
  * [3] Bodwin G.T., Braaten E. and Lepage G.P. Phys. Rev. D 51 1125, 1995
  * [4] Phys. Rev. D57 (1998) 4385
  * [5] Phys. Rev. D73 (2006) 074021
  * [6] Eur. Phys. J. C61 (2009) 693
  * [7] Phys. Rev. Lett. 107 (2011) 082002
  * [8] Phys. Lett. B705 (2011) 116
  * [9] arXiv:1106.2184
  * [10] The LHCb Collaboration,
JINST 3 (2008) S08005

  * [11] The LHCb Collaboration,
Eur. Phys. J. C71 1645, 2011

  * [12] arXiv:1202.1080
  * [13] LHCb-CONF-2011-062
  * [14] Phys. Rev. Lett. 98 (2007) 232001
  * [15] arXiv:1204.1462
  * [16] Phys. Rev. Lett. 79 (1997), 578-583
  * [17] The LHCb Collaboration,
Phys. Lett. B 707 (2012), pp. 52-59

  * [18] arXiv:1205.0975
  * [19] Phys. Rev. D 56 (1997), 3811-3832


# Defect-engineering hexagonal boron nitride using low-energy Ar+ irradiation

Manuel Längle<EMAIL_ADDRESS>University of Vienna, Faculty of
Physics, Boltzmanngasse 5, 1090 Vienna, Austria  Barbara Maria Mayer
University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna,
Austria  Jacob Madsen  University of Vienna, Faculty of Physics,
Boltzmanngasse 5, 1090 Vienna, Austria  Diana Propst  University of Vienna,
Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria  Arixin Bo
University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna,
Austria  Clara Kofler  University of Vienna, Faculty of Physics,
Boltzmanngasse 5, 1090 Vienna, Austria  Vinzent Hana  University of Vienna,
Faculty of Physics, Boltzmanngasse 5, 1090 Vienna, Austria  Clemens Mangler
University of Vienna, Faculty of Physics, Boltzmanngasse 5, 1090 Vienna,
Austria  Toma Susi  University of Vienna, Faculty of Physics, Boltzmanngasse
5, 1090 Vienna, Austria  Jani Kotakoski  University of Vienna, Faculty of
Physics, Boltzmanngasse 5, 1090 Vienna, Austria<EMAIL_ADDRESS>
###### Abstract

Monolayer hexagonal boron nitride (hBN) has recently become the focus of
intense research as a material to host quantum emitters. Although it is well
known that such emission is associated with point defects, so far no
conclusive correlation between the spectra and specific defects has been
demonstrated. Here, we prepare atomically clean suspended hBN samples and
subject them to low-energy ion irradiation. The samples are characterized
before and after irradiation via automated scanning transmission electron
microscopy imaging to assess the defect concentrations and distributions. We
find an intrinsic defect concentration of ca. 0.03 nm-2 (with ca. 55% boron
and 8% nitrogen single vacancies, 20% double vacancies and 16% more complex
vacancy structures). To be able to differentiate between these and
irradiation-induced defects, we create a significantly higher (but still
moderate) concentration of defects with the ions (0.30 nm-2), and now find ca.
55% boron and 12% nitrogen single vacancies, 14% double vacancies, and 18%
more complex vacancy structures. The results demonstrate that already the
simplest irradiation provides selectivity for the defect types, and open the
way for future experiments to explore changing the selectivity by modifying
the irradiation parameters.

## Introduction

Although mostly known as an electrically insulating structural counterpart of
graphene, monolayer hexagonal boron nitride (hBN) has recently itself received
increasing attention as a solid state host for quantum emitters [1]. What
makes it particularly interesting is the good stability of hBN quantum
emitters over a wide temperature range [2], their bright emission into the
zero-phonon line [3], wide spectral range [4, 5, 6], and the possibility for
lifetime-limited emission at room temperature [7, 8]. This makes hBN
attractive for a number of different advanced applications [9]. However,
although it is well known that quantum emitters are associated with point
defects in the material [4, 5, 10, 11, 12], no direct correlation between the
defect structures and quantum emission properties has been established.
Therefore, being able to selectively create specific types of point defects
into hBN would be desirable.

It has been already shown that different kinds of irradiation can be used to
create quantum emitters in hBN, including lasers [13], ions [14], neutrons
[15] and electrons [16, 10]. So far only in the case of electrons [17] the
direct correlation between irradiation and the exact atomic structure has been
established. In the case of ion irradiation, analytical potential molecular
dynamics simulations [18, 19] have suggested that low-energy noble gas ions
should lead to formation of point defects with a high likelihood (40–80% per
ion) and similar probabilities for single boron and nitrogen vacancies.
Especially according to simulations [19] with the improved potential
benchmarked against density functional theory, the best selectivity should be
achievable at the lowest energies ($<$200 eV), where nitrogen single vacancies
become clearly more favorable for projectiles heavier than Ne. However, this
prediction has not been confirmed experimentally. Moreover, electron
irradiation experiments [17] have shown that it is more likely to displace
boron than nitrogen, also at intermediate energies (60–100 kV) where inelastic
interactions are significant. Whether these need to be taken into account also
for low-energy single-charged ion irradiation of hBN remains unclear.

Here, we prepare atomically-clean suspended samples from commercial monolayer
hBN grown via chemical vapor deposition and irradiate them with low-energy Ar+
ions. The intrinsic defect density and distribution are measured using
automated scanning transmission electron microscopy (STEM) annular dark field
(ADF) imaging at 60 kV in ultra-high vacuum. We find a fairly high intrinsic
defect density, which is approximately constant within each sample. There is a
high prevalence of single boron vacancies $V_{\mathrm{B}}$ (55%) followed by
single nitrogen vacancies $V_{\mathrm{N}}$ (8%). The defect concentration
after irradiation is selected to be ca. ten times higher than the intrinsic
one on the one hand to be high enough to clearly see the difference between
intrinsic and irradiation-induced defects, but on the other hand low enough so
that the vast majority of impinging ions encounter pristine non-defective hBN.
Also the post-irradiation defect distribution is dominated by boron single
vacancies (55%), followed by nitrogen single vacancies (12%), double vacancies
(14%) and more complex vacancy defects (18%). These results show that some
defect-selectivity indeed can be achieved with low-energy noble gas
irradiation. However, experimentally the most common defect is the boron
single vacancy in contrast to the prediction from molecular dynamics. Future
work should explore whether modifying irradiation parameters (ion species,
kinetic energy, charge state, irradiation angle) changes the distribution
either from boron to nitrogen single vacancies or more complicated defect
structures.

## Results and discussion

Commercial hBN grown via chemical vapor deposition was transferred onto a Au
Quantifoil TEM grid as described [20, 17]. The Quantifoil membrane with hBN
was subsequently further transferred onto a Si grid with a perforated SiN
membrane by mechanically delaminating it from the Au grid to create a hybrid
Quantifoil SiN grid (see Methods). A light microscopy image of a transferred
sample is shown in Fig. 1a. This hybrid grid allows a polymer-free transfer of
hBN onto the final grid, which is mechanically robust and allows sample
cleaning with a laser in vacuum [21]. After preparation, the samples were
inserted into an extensive vacuum system [22] that connects all instruments
used in this study through high-vacuum transfer lines (base pressure typically
below 10-8 mbar). Upon insertion, the samples are baked for ca. 10 h at 150∘C
in vacuum to remove water and the most severe contamination. The sample is
surveyed via scanning transmission electron microscopy (STEM) medium angle
annular dark field (MAADF) imaging using the Nion UltraSTEM 100 in Vienna at
60 kV under ultra-high vacuum conditions to find a location with good coverage
and reasonable surface cleanliness. After this, a $2$ ms laser pulse is used
to remove most of the remaining contamination (see Methods). An example large-
scale STEM-MAADF image of a cleaned sample is shown in Fig. 1b.

Figure 1: Overview of the sample. (a) Light microscopy image of the sample
after transfer. The purple/blue area corresponds to the Si grid, the light
blue squares to Quantifoil. The yellow square is the perforated SiN window
where the suspended sample can be found when holes in SiN and the Quantifoil
overlap. (b) STEM-MAADF image of a suspended sample area. The dark contrast is
clean suspended hBN and the gray areas correspond to fewlayer hBN (continuous
areas on the left-hand side and to contamination smaller areas throughout the
sample). The white area on the left corresponds to Quantifoil and the white
area on the right to SiN.

After cleaning, we carry out automated atomic-resolution STEM-MAADF imaging
[23] to estimate the intrinsic defect concentration and distribution. This
method allows collecting a large amount of data, and in combination with
automated machine-learning based analysis enables minimizing the electron dose
that the sample is exposed to. A total of five samples were prepared and pre-
characterized in this manner, and one sample was selected for ion irradiation.
In total, 16500 nm2 of the selected sample was imaged, out of which ca. 68%
was contamination-free and imaged with a resolution that allows atomic
structural analysis. The images are analyzed automatically with a
convolutional neural network using a pipeline similar to those described in
Refs. [24, 25] (see Methods for details). In short, the neural network first
separates image areas to either contamination or lattice. Next, each lattice
site is assigned an intensity value at different values of Gaussian blurring.
These values are provided to a classifier that determines whether the site
contains an atom or a vacancy. The process is illustrated in a previous
publication [26]. In total, 335 defects were identified in the data set
recorded with the sample selected for irradiation, corresponding to a defect
concentration of ca. 0.03 nm-2 with 55% boron and 8% nitrogen single
vacancies.

It is worth pointing out, that electron irradiation during imaging is known to
introduce defects into hBN [27, 28, 29] even under ultra-high vacuum [17].
While recording the images we should have created only ca. 29.7$\pm$2.8
defects (of which 59% should be boron and 41% nitrogen vacancies), taking the
typical beam current close to 20pA of our instrument [30] and the imaging
parameters [17] (see Methods). Therefore, ca. 90% of the defects must be
intrinsic to the sample and arise from growth or sample fabrication, leading
to an intrinsic defect concentration of ca. 0.027 nm-2.

Next, the selected sample was transported in vacuum to a chamber containing a
plasma generator, where low-energy Ar+ ion irradiation is used to create
defects (Fig. 1a) following Ref. [25]. With the parameters used for the plasma
source (see Methods), the beam profile (Fig. 2b), measured with a biased
Faraday cup, reveals two peaks: one at a low energy of 228 $\pm$ 11 eV close
to the manufacturer specification, and another one at 89 $\pm$ 10 eV. Peak
intensities measured over several experiments show that the lower-energy peak
contains ca. 2/3 of all ions. The estimated total irradiation dose, based on
current measurement with the Faraday cup and taking pressure variations and
the geometry of the setup, is ca. 0.10 $\pm$ 0.04 ions/nm2.

Figure 2: Plasma setup, beam profile measurement and defect concentration. (b)
Schematic presentation of the plasma irradiation setup and the Faraday up. (d)
Measured ion current $I$ and the calculated beam profile
($\mathrm{d}I/\mathrm{d}V$) as a function of the bias voltage ($V$). The
purple points are measured data, and the black line correspond to a fit (top)
and its derivative (bottom). (c) Defect concentration for pre-characterized
samples (1199 in blue, 1213 in green, 1100 in yellow and 1270 in purple)
compared to the irradiated one (1270 in purple). All samples were cleaned by a
laser pulse before imaging.

After ion irradiation, the sample was further automatically imaged to estimate
the post-irradiation defect density and distribution at another sample
position. A comparison between the defect concentration in non-irradiated and
irradiated samples is shown in Fig. 2c, As is obvious from the data, the non-
irradiated samples have a non-negligible defect concentration, which varies
from sample to sample, but remains fairly similar within each of the
characterized samples, shown in Fig. 2c. These values are significantly lower
than those reported in Ref. [31], which may be explained by the neglect of
electron-beam induced damage in the earlier study and the additional damage-
inducing effect of a non-ultra-high vacuum atmosphere in their microscope
column [32].

Defect distributions for the irradiated sample before and after irradiation
are shown in Fig. 3a,b. After irradiation, a total area of ca. 14,500 nm2 was
imaged with ca. 50% that could be used for the analysis (clean and sufficient
resolution). In total, 2169 defects were identified, leading to a defect
concentration of ca. 0.30 nm-2, i.e., close to ten times higher than before
the irradiation. The amount of irradiation-induced defects is thus ca. 0.27
nm-2. We point out that the defect density is also higher than the estimated
total irradiation dose (by a factor of nearly three). This most likely reveals
the inherent uncertainty in estimating accurately the current of the plasma
source by measurements carried out separately from the irradiation experiment.
The defect density is low enough so that the vast majority of the ions have
impinged on pristine defect-free hBN. After the irradiation, ca. 55.6% of
defects are boron and 11.5% nitrogen single vacancies. Further 14.4% are
double vacancies and the rest (18.4%) more complex vacancy defects. The
spatial distributions for $V_{\mathrm{B}}$ and $V_{\mathrm{N}}$ as well as all
other defects are shown in Fig. 3c. The grid-like pattern of the defect
locations arises from the images recorded in discrete non-overlapping parts of
the sample and the larger defect-free areas have been obscured by surface
contamination. Overall, the spatial distribution shows that the defects have
been created uniformly on the sample. Example STEM-MAADF images of the most
typical defects are shown in Fig. 4.

Figure 3: Defect concentration and distribution. (a) Intrinsic defect
concentration as a function of the defect size (number of missing atoms).
11,242 nm2 of valid area were analysed before and 7,246 nm2 of valid area were
analysed after the irradiation. (b) Post-irradation defect concentration as a
function of the defect size. The inset shows a magnified view of the defect
concentration for defects with at least two missing atoms. (c) Spatial
distribution of boron and nitrogen single vacancies ($V_{\mathrm{B}}$ and
$V_{\mathrm{N}}$, respectively) and all other defects.  Figure 4: Example
STEM-MAADF images of the most typical defects. Pink circles mark the positions
of missing B and blue circles missing N atoms. From left to right:
$V_{\mathrm{B}}$, $V_{\mathrm{N}}$, double vacancy, triple vacancy with one
missing N and two missing N, and triple vacancy with one missing B and two
missing N. All images have a field of view of 2$\times$2 nm2.

Interestingly, the results are in a clear contradiction with theoretical
studies based on analytical-potential molecular dynamics simulations, where it
was found depending on the potential used that either low-energy Ar
irradiation should lead to about 17% single vacancies of B and 12–17% single
vacancies of N [18] per impinging ion or that the probability would be between
35–55 % for B and 40–65 % for N [19] for energies similar to the ones we
determined experimentally. On the experimental side, since we do not have an
accurate measurement of the ion current during the irradiation, we can not
precisely know what the probability for creating each type of single vacancy
is.

However, since we observe about three times as many defects as we estimate
ions to have irradiated the sample, it seems a safe assumption that the
probability must be closer to one than the simulations suggest. Additionally,
carbon atoms from the ubiquitous contamination are known to migrate on the
surface of 2D materials and fill vacancies [33], especially at elevated
temperatures [34]. Due to the similar atomic number (and therefore contrast
[35]) of C as that of B and N, it is possible that our characterization has
missed some vacancies that have been subsequently filled with carbon. However,
here the same argument applies as above: since the defect concentration is
higher than expected based on the estimated ion current, it seems unlikely
that such a large number of N vacancies would have been filled with carbon
atoms that the experimental results would agree with the simulation
prediction. It is typically assumed [36] that the singly-charged ion impact
can be modelled without taking charges into account. This is because upon an
impact the ion receives an electron from the sample neutralizing. While for
conductive samples the missing charge distributes quickly through the
material, this is likely not true for an insulating 2D material such as hBN
where the charge may remain localized in the vicinity of the impact point.
This leads to a decrease in the displacement threshold energy. Therefore, the
most likely explanation seems to be that analytical molecular dynamics is not
a sufficiently accurate method to describe the ion irradiation process at the
lowest energies.

In accordance with the higher likelihood for obtaining boron vacancies, also
the displacement threshold as calculated with density functional theory-based
molecular dynamics for a neutral hBN lattice is lower for boron than for
nitrogen (19.36 eV vs. 23.06 eV, respectively) [29]. However, since energy
transfer from Ar to N is more efficient than to B due to the higher mass of N,
this fact by itself is not sufficient to explain our experimental results, and
the complete description may require including effects due to charging or
inelastic scattering as alluded to above. Nevertheless, assuming that the
lower energy ions of our beam (ca. 90 eV) would nearly exclusively produce
boron vacancies, whereas the higher energy ions (ca. 230 eV) would produce
both vacancies with a similar probability that would lead to a defect
distribution similar to the observed one. Overall, this discrepancy highlights
that more experimental and computational work is required to obtain a
comprehensive understanding of the capabilities of this method for defect-
specific engineering of hBN.

## Conclusions

We demonstrated that low-energy Ar+ irradiation is a suitable method for
defect-engineering hBN with a high selectivity for boron single vacancies. The
intrinsic defect concentration in the as-prepared and cleaned samples was
found to be below 0.27 nm-2 (with 55% boron and 8% nitrogen vacancies).
Additional ca. 0.003 defects per nm2 was estimated to have been created during
the automated imaging of the sample pre-irradiation. The irradiation dose was
chosen high enough to separate the irradiation-induced defects from the
intrinsic ones, but sufficiently low to avoid ions impinging on already
defective sites. Most (ca. 55.6%) of the irradiation-induced defects were
boron single vacancies, followed by nitrogen single vacancies (11.5%), double
vacancies (14.4%) and more complicated vacancy structures. These results are
in contrast to earlier computational work predicting either similar
probabilities for B and N single vacancies or a prevalence of N vacancies as a
result of Ar+ irradiation at similar energies. This shows clear promise for
selectively creating specific defects with low-energy ions, but also that more
research is needed both experimentally and computationally to fully exploit
the possibilities for defect-engineering hBN with low-energy ions.

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## Methods

### Sample preparation and cleaning

Suspended monolayer hBN samples were fabricated from commercial hBN grown via
chemical vapor deposition (Graphene Supermarket). First, hBN was transferred
from the Cu growth substrate onto a Au Quantifoil TEM grid (a periodicity of 2
$\mathrm{\mu m}$ and a hole size of 2 $\mathrm{\mu m}$) following the
procedure described in Refs. [20, 17] (Cu was etched in a bath of $1.5$ g of
iron chloride mixed with $240$ g deionized water for 47 h, after which the
sample was washed in three cycles of water and isopropyl alcohol, for ca. 1
min each). Then, hBN on Quantifoil was placed onto a Si grid with a perforated
SiN window (hole size of 1 $\mu$m) where it was being adhered by putting a
small drop of isopropyl alcohol on it and baking at 150∘C for 15 min and after
that it was mechanically delaminated from the Au grid with a tweezer. The
suspended sample used for the experiments can be found where the holes of the
Quantifoil and the SiN overlap.

Upon being inserted into the vacuum system used for all experiment, the
samples are baked for ca. 10 h at 150∘C in vacuum. After precharacterization
to find a suitable sample area, it is cleaned by applying a laser pulse in the
column of the scanning transmission electron microscope used for imaging. Due
to an incidence angle of 25∘, the laser spot has the shape of an ellipse with
a main axis of 28 $\pm$ 3 $\mu$m and a minor axis of 35 $\pm$ 3 $\mu$m. The
loss in the optical system is about 66%, which means that the 2 ms and 10 mW
pulse of a continuous wave laser used for cleaning corresponds to ca. 6.8
$\mathrm{{\mu}}$J with an energy density of 2150$\pm$70 Jm-2 or 13400 $\pm$
400 eVnm-2.

### Ion irradiation

The samples were irradiated with an low-energy Ar+ beam using a SPECS ECR-HO
microwave plasma source operated in hybrid mode with an anode voltage of 0 V
and extractor voltage of -60 V. The pressure of the chamber was kept
approximately constant at ca. $3.5\times 10^{-6}$ mbar, though variations from
this could not be entirely avoided, and the irradiation time was ca. $150$ s.
The irradiation is carried out at room temperature, similar to all other the
experiments except for sample cleaning. The current was measured with a
Faraday cup placed in the same place as the sample with a slightly larger
distance, which due to the beam divergence leads to a difference in the
measured current and the current at the sample of approximately a factor of
$1.4$ (current at the sample being higher). To get an accurate estimate of the
ion energies, the current was measured as a function of the bias voltage,
where the ions appear as drops in the measured current that deviates from the
quadratically decaying background current. This reveals that the ion beam
consists of two distinct Gaussian distributions, one centered at 89 $\pm$ 10
eV and the other one at 228 $\pm$ 11 eV, the lower-energy peak contributing
ca. 2/3 of the ions. The total current was calculated by summing up the ions
contributing to each of these distributions. From the ion current and the
irradiation time, we estimate a total dose at the sample to be 0.10 $\pm$ 0.04
ions per nm2.

### Microscopy

All electron microscopy images were recorded with the Nion UltraSTEM 100
microscope in Vienna at 60 kV in ultrahigh vacuum (10-10 mbar) using the
medium angle annular dark field (MAADF) detector with annular ranges of 60–200
mrad. The convergence semi-angle was 30 mrad, and the beam current in this
mode is typically about 20 pA.

For obtaining defect concentrations and distributions, we used automatic image
acquisition [23]. With this method, the algorithm records images in a
predefined area of the sample along a serpentine path. Here, we defined the
grid of recorded images to avoid overlap between the images by leaving an
empty area of a similar size as the images between each pair of subsequent
images. During the automatic image acquisition minor adjustments of the
electron energy and the correction of astigmatism and coma were done manually.
The images were recorded with a (calibrated [37]) field of view of
4.2$\times$4.2 $\mathrm{nm}^{2}$, a pixel dwell time of 16 $\mathrm{\mu s}$
and 512$\times$ 512 pixels.

Taking the imaging parameters, the flyback time at the end of each scan line
(120 $\mu$s) and half of the time to move the stage from one position to the
next (0.5$\times$2 s), the electron dose per frame is (3.6 $\pm$ 0.14)
$\times$ 105 electrons Å-2 using a current of $19.4\pm 0.6$ pA [30]. Since
there are ca. 36.8 atoms nm-2, with the correct displacement cross section
[17], we estimate that ca. 0.046 $\pm$ 0.005 defects are created per image (or
0.0026 $\pm$ 0.0003 per nm2, of which 0.0016 $\pm$ 0.0003 are boron and 0.0011
$\pm$ 0.0005 per nm2 nitrogen). Therefore, ca. 29.7 $\pm$ 2.8 (out of 335)
defects pre-irradiation and 19.1 $\pm$ 1.9 (out of 2169) defects post-
irradiation can be estimated to have been created during imaging.

### Automated image analysis

The convolutional neural network implemented in Pytorch [38] has a UNET
structure with rotational equivariance [39, 40], and its architecture is
identical to that described in Ref. [26]. The neural network has two output
branches producing a segmentation map of contaminated areas and a density map
of lattice sites. The density map has a high value at every lattice site,
whether an atom is present or there is a vacancy. This was found to be more
robust than training the network to detect the defects directly. The neural
network is trained from simulated data (as in Ref. [26]). For the simulated
data, randomized atomic models of hBN are generated, and the models are used
as input for the multislice algorithm to simulate annular dark field images
[41]. Finally, random distortions and noise are applied to the simulated
images.

The neural network is strictly trained for images with a pixel size of 0.1 Å,
and therefore images with different pixel sizes are resized. The scaling
factor is determined by finding diffraction spots in the Fourier-transformed
images.

Given the density map of lattice sites, a discrete set of points representing
the detected lattice is extracted. Whether a lattice site represents a vacancy
is determined by looking at the local intensity at varying levels of Gaussian
blurring. Given these intensity features, a small random forest classifier is
trained from twenty hand-labeled experimental images. The trained classifier
is then applied to the whole set of images to label every lattice site as a
vacancy or a non-vacancy.

In order to arrive at the final classified defects, a geometric analysis of
the lattice sites is also performed. First, a geometric graph is created by
connecting neighboring lattice sites. A graph coloring algorithm separates the
two sublattices; each sublattice may then be assigned to boron or nitrogen
based on local intensity. A local lattice segment comprised of each point and
its three neighbors in the graph are matched to a template representing the
expected local geometry using the quaternion characteristic polynomial method
[42]. The root-mean-squared distance between the expected and measured local
lattice is used to measure how well each local segment of the lattice matches
an ideal hexagonal lattice. Lattice segments that deviate too much are thrown
away from the analysis, as they indicate severe scan distortions, noise, or
highly distorted lattice areas. Given each labeled lattice site and the
geometric graph, the defects are classified based on how many boron and
nitrogen atoms they contain by finding the connected vacancy sites.