# The Chlorine Vacancy in 4H-SiC: An NV-like Defect With Telecom Emission

Oscar Bulancea-Lindvall  Department of Physics, Chemistry and Biology,
Linköping University, SE-581 83 Linköping, Sweden  Joel Davidsson  Department
of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping,
Sweden  Rickard Armiento  Department of Physics, Chemistry and Biology,
Linköping University, SE-581 83 Linköping, Sweden  Igor A. Abrikosov
Department of Physics, Chemistry and Biology, Linköping University, SE-581 83
Linköping, Sweden

###### Abstract

The diamond nitrogen vacancy (NV) center remains an ever increasing topic of
interest. At present, it is considered an ideal example of a solid-state qubit
applicable in quantum communication, computing, and sensing alike. With its
success, the search for defects that share or improve upon its advantageous
features is an ongoing endeavor. By performing large-scale high-throughput
screening of 52 600 defects in 4H silicon carbide (SiC), we identify a
collection of NV-like color-centers of particular interest. From this list,
the single most promising candidate consists of a silicon vacancy and chlorine
substituted on the carbon site, and is given the name of the chlorine vacancy
(ClV) center. Through high-accuracy first-principle calculations, we confirm
that the ClV center is similar to the NV center in diamond in its local
structure and shares many qualitative and quantitative features in the
electronic structure and spin properties. In contrast to the NV center,
however, the ClV center in SiC exhibits emission in the telecom range near the
C-band.

##  I Introduction

Point defects in semiconductors have been studied for more than a decade for
applications within quantum technology. They exhibit extraordinarily stable
spin states that are optically addressable even at room temperature[1, 2, 3,
4], feature spin-photon entanglement for quantum communication purposes[5, 6,
7, 8], and enable delicate sensing of external fields on the nanoscale[9, 10,
11, 12, 13, 14, 15, 16]. The centerpiece of this development has been the
nitrogen-vacancy (NV) center in diamond, covering applications in all
mentioned categories. Its photoluminescence in the visible range[17] and spin-
dependent electron transition processes have been utilized to achieve spin-
photon entanglement for long-distance quantum communication[7]. Spin-dependent
biases within the radiative and nonradiative deexcitation processes of the NV
center have yielded effective and fully optical spin initialization and
readout methods[17]. NV spin-qubit registers utilizing nearby hyperfine-
coupled lattice spins have been demonstrated and are of interest in the design
of solid-state quantum processors and memories[18, 19, 20], in particular, due
to the long spin coherence time of the neighboring nuclear spins, such as the
14N spin. Various sensing methods have been achieved with the NV center, based
on altering its spin properties under a wide collection of external fields. In
particular, scalar and vector-field magnetometry[9, 10, 11], temperature[15],
and strain[16] sensing via the alteration of spin levels under the
corresponding fields are enabled by optically detected and electron spin
resonance (ODMR and ESR). Sensing techniques based on relaxometry near spin-
level anti-crossings have also been demonstrated[12], with the benefit of
being microwave-free. On the other hand, the visible range emission is a
disadvantage within modern fiber-optical networks. The propagation loss of
visible light in optical fibers is considerable, limiting both the viable
signal distance and spin-photon entanglement rate[21, 7]. Down-conversion of
the photons has been applied to alleviate this issue[21], yielding C-band
telecom wavelengths (ca 1550 nm) where propagation loss is minimal. However,
down-conversion inevitably decreases the signal-to-noise ratio[21], at times
by several orders of magnitude, which leaves an inherent telecom emission a
particularly desired feature.

The success and ongoing developments of the diamond NV center continue to
inspire exploration of other defects for further improved qualities in hosts
offering additional advantages compared to diamond. Silicon carbide (SiC) is
one such host with a long history within high-power electronics and electronic
device integration, featuring multiple polytypes for numerous defect
variations. It offers increased thermal conductivity and mature
nanofabrication processes, while its color centers show long coherence times
and strong optical emissions[22]. Following the properties of the diamond NV
center, the SiC divacancy and corresponding NV center have garnered attention
for their similarity to the diamond NV center in electronic structure, but
with emission in the infrared reducing the need for down-conversion[23, 24].
Combining dynamical decoupling schemes with recent techniques for increased
readout fidelity and integration-time, e.g. spin-to-charge conversion, the
divacancy has displayed coherence times of more than five seconds in isotope-
purified samples[2]. Meanwhile, the SiC NV center retains the advantage of a
hyperfine-coupled long-lived nuclear spin in the vicinity that can act as a
quantum memory. However, none of these defects have demonstrated emission
within the telecom range, and the search for further improved defects in this
regard remains an ongoing endeavor.

To accelerate the search for advantageous point defects, high-throughput
techniques have recently been applied to search the intrinsic defect space in
SiC[25] and extrinsic defect space in calcium oxide[26]. It has been
demonstrated that these can provide a detailed picture of possible defects and
further explain observed properties, such as optical spectra. We have applied
such high-throughput techniques for a large-scale study of extrinsic defects
in SiC, consisting of $s$\- and $p$-elements within single and double-defect
clusters. In this paper, we present the results from our high-throughput
defect screening focusing on NV-like defects emitting in the near-telecom
range, and provide a detailed characterization of the magneto-optical
properties of the most interesting defect, the chlorine vacancy (ClV) center,
which is noted in the screening as the most probable C-band emitter among the
candidates.

The article is structured as follows. First, section II describes the high-
throughput investigation performed in this work and summarizes the search
result for diamond NV-like candidates in SiC. Section III provides
computational details of the ab-initio methods applied to the ClV defect,
singled out as the most interesting candidate. In section IV.1, we introduce
the defect, covering its properties related to geometric and electronic
structure and its thermodynamical stability within 4H-SiC. In section IV.2 and
IV.3, we summarize the most interesting optical properties of the defect,
including both estimated brightness and electron-phonon coupling. In section
IV.4, we summarize the ground state electron spin properties of the most
stable spin-charge state. Finally, in sections V and VI, we discuss the
prospects of the defect, given the predicted magneto-optical properties and
similarity in electronic structure to other promising defects, and draw our
conclusions.

##  II High-throughput investigations

To efficiently search among feasible and interesting defects in SiC, we employ
the high-throughput workflow package ADAQ[27], a collection of workflows
designed for exhaustive defect generation and efficient point-defect
characterization, which is implemented with the high-throughput toolkit
_httk_[28]. It is capable of high-throughput defect screening, in which
possible charge and spin states are identified and analyzed for estimates of
their optical properties. For a detailed description, see Ref. 27. The
workflows perform density functional theory [29] (DFT) calculations using the
Vienna Ab-initio Simulation Package[30, 31] (VASP), which uses plane-wave
basis sets within the projector-augmented-wave method[32, 33], with the
Perdew-Burke-Erzenerhof[34] (PBE) functional.

The generated defect set consists of extrinsic $s$\- and $p$-elements
configured in single and double-defect configurations, considering
combinations of substitutional and interstitial placements with possible
vacancies. While it fully covers the extrinsic single-site defects and
intrinsic-extrinsic pairs, it does not include every double-extrinsic pair due
to the large amount of possible interstitial combinations. In total, 52 600
defect configurations are considered in this search. However, defects sharing
the same stoichiometry will likely have the most stable configuration realized
at ambient conditions. Therefore, only defects lying on the defect hull[35,
25], i.e. being the most energetically favored within the same stoichiometry,
were considered further.

Searching for defects with advantageous properties for quantum applications,
we consider the diamond NV center as an ideal starting point. Following its
favorable properties, we search the screened defects for spin triplet ground
states, excluding single substitutionals and interstitials. Next, we narrow
the search further by an upper bound on the formation energy ($<$ 6 eV),
eliminating defects that are unlikely to form at high concentrations compared
to other lattice defects, such as carbon and silicon vacancies. Finally,
besides favorable spin properties and stability, the most interesting
advantage would be emission in the telecom range. Hence, we finish the
filtering by choosing defects with a zero-phonon line (ZPL) in the range of
0.5 eV to 1.1 eV, taking the screening accuracy into account[36]. The final
result is a group of five vacancy-substitution clusters, summarized in Table
1.

Period | 2 | 3
---|---|---
Defect | VSiNC | VSiOC | VSiFC | VSiSC | VSiClC
ZPL (eV) | 0.79 | 0.92 | 1.09 | 0.55 | 0.64
Dipole Moment (Debye) | 11.9 | 12.7 | 0.8 | 8.5 | 13.0
Maximal Formation Energy (eV) | 4.52 | 2.22 | 3.23 | 4.87 | 5.85
Table 1: The defects fulfilling all search criteria of a potential defect
emitter with similarity to the diamond NV center. They were chosen based on
having a maximal formation energy below 6 eV, a spin triplet ground state, and
a ZPL from 0.5 eV to 1.1 eV. Elements are grouped based on the period of the
extrinsic component.

We note the presence of the SiC NV center (VSiNC) among the filtered search
results as a defect with a likeness to the NV center, known to be stable and
with a strong luminescence. The inclusion of this defect in the search results
confirms our choice of parameters, while it can act as a reference for the
predicted quantities. Interestingly, the search results systematically consist
of a silicon vacancy and dopant bonding on the carbon site. Bonding on the
silicon site was observed among stable defects but with significantly higher
formation energies. Furthermore, we observe a trend of increasing ZPL with
each increasing element group within the same period. As the SiC NV center is
known to emit in the infrared[37], defects in the same period are unlikely to
yield transitions in the telecom region. However, turning to the third period
clusters, the two defects with sulfur and chlorine components are shown to
have ZPLs lower than the NV center and with the expected systematic screening
error of approximately 0.2 eV[36] would fall into the vicinity of 0.8 eV (1550
nm) where fiber-optic attenuation is minimal. Choosing between sulfur and
chlorine clusters, the VSiClC features the largest dipole moment, implying
higher radiative emission rates. Therefore, one can expect it to be comparably
bright to the SiC NV center, if not brighter.

In summary, the screening yields several attractive candidates worthy of
further investigation. In terms of bright telecom emission, we deem the VSiClC
cluster, which we refer to as the chlorine vacancy in analogy to the NV
center, to be the most promising candidate, and the remainder of this paper is
primarily devoted to the detailed characterization of this defect.

##  III Characterization Methods

For the more detailed DFT calculations, we use a basis set with a 420 eV
cutoff energy, applying the Heyd–Scuseria–
Ernzerhof[38] (HSE06) functional on 576 atom (6x6x2) 4H-SiC supercells at
$\Gamma$-point, with a convergence threshold on the forces of 0.01 eVÅ-1.
Excited states are obtained according to the $\Delta$SCF approach[39, 40].
Excited state structures are here converged to an energy difference of $5\cdot
10^{-5}$ eV.

The relative stability of the various charge and spin states is examined via
the thermodynamic formation energies

$E^{q,S}_{\text{form}}(E_{F})=E^{q,S}_{\text{defect}}-E_{\text{bulk}}-\sum_{i}n_{i}\mu_{i}+qE_{\text{F}}+E_{\text{corr}}^{q}\text{,}$
(1)

where $E^{q,S}_{\text{defect}}$ denotes the total energy of the defect state
of (reduced) charge $q$ and spin state $S$, while $E_{\text{bulk}}$ is the
energy of the defect-free host system. The $n_{i}$ and $\mu_{i}$ denote the
change in chemical components to form the defect and respective chemical
potential. The chemical potentials are here taken in the rich abundance limit,
assuming the 0 K crystalline structures of each element. Finally, the electron
potential energy of the charge state ($qE_{F}$) is added with a charge
correction term $E_{\text{corr}}^{q}$ to account for finite size coloumbic
effects. We employ the charge correction developed by Freysoldt et al.[41].
Binding energies are calculated to provide a sense of the defect structural
stability. Here, defect binding energies are defined as

$H^{b}[AB]=E_{\text{form}}[A]+E_{\text{form}}[B]-E_{\text{form}}[AB]\text{,}$
(2)

where the formation energy of the lowest lying defect state is considered for
the defect decomposition $(\text{AB}\to\text{A}+\text{B})$. In evaluating the
binding energies, we consider combinations of every stable component defect
identified in the defect screening.

We treat the vibrational contribution to the photoluminescence according to
Huang-Rhys theory of photon emission[42, 43]. Within this theory, we estimate
the phononic coupling strength and the implied ratio of zero-phonon emission,
in terms of the Huang-Rhys factor $S$ and Debye-Waller factor $W$. With the
coupling strength to each phonon mode, we reconstruct the phonon sideband. In
practice, we make use of the Pyphotonics toolbox[43].

The system phonon modes are obtained via the method of finite displacements.
However, as the defect significantly lowers the host crystal symmetry,
complete phonon characterization may involve an excessive number of
computations. Therefore, we perform the full set of phonon calculations on a
single defect configuration of high symmetry. Otherwise, we employ a single-
phonon approximation for an estimation of the average phonon coupling[44]. We
use the Phonopy package[45, 46], to construct displaced geometries, build the
dynamical matrix of the system, and calculate the phonon eigenmodes. The PBE-
functional is used within the phonon calculation framework, with the ground
state structure converged to less than $10^{-7}$ eVÅ-1 in forces.

Properties of the defect electron spin is also examined if the concerned
ground state hosts unpaired spins. In particular, we approximate the zero-
field-splitting (ZFS) with the spin dipole-dipole interaction using the method
in Ref. 14, and we calculate the hyperfine structure of the lattice sites
according to the method in Ref. 47, as implemented in VASP.

With a model Hamiltonian constructed with the spin parameters obtained from
mentioned methods (see explicit formulation in Supplemental Materials), we
investigate the coherence of the electron spin of the defect using the
generalized cluster-correlation expansion (gCCE) approach, as implemented in
the PyCCE toolbox[48]. We provide hyperfine values calculated as previously
described, up to a distance of 12 Å to the defect, including at least the
third-nearest neighbor spins. For more distanced spins, we neglect the fermi-
contact term and include only the dipole-dipole interaction term. The gCCE-
method is applied using a maximum bath-spin distance of 50 Å, and a maximum
separation of cluster spins of 10 Å. We use second order cluster expansion
(gCCE-2) to obtain converged results and ensemble average over 250 bath spins
configurations, each calculated with a Monte-Carlo bath state averaging using
100 bath states.

##  IV Results

###  IV.1 Chlorine Vacancy Structure & Ground States

a)

b)

Figure 1: The structure of the ClV defect in 4H-SiC. a) The four different
nonequivalent defect configurations of 4H-SiC. b) The defect-local structure
in the _hh_ configuration together with the $10^{-9}$ Å-1 isosurface spin
density of the occupied $a_{1}$ level.

The ClV center consists of a silicon vacancy and a substitutional chlorine ion
located on the neighboring carbon site. In 4H-SiC, a double-defect cluster is
constructed in four nonequivalent lattice configurations labeled _hh_ , _kk_ ,
_hk_ , and _kh_ by the local environment of the defect sites (see Fig. 1). The
_hh_ and _kk_ configurations are on-axis, meaning the defect axis aligns with
the _c_ -axis, making the defect C3v symmetric. The off-axis configurations
lower the symmetry of the crystal further to C1h. The six dangling bonds of
the silicon and carbon sites create localized defect states that appear in the
band gap. For the most relevant states of the defect, the band gap states are
for the on-axis (off-axis) configurations a lower $e$ state ($a^{\prime}$ and
$a^{\prime\prime}$ states) and a higher $a_{1}$ ($a^{\prime}$) state in the
spin-up channel, while in the spin-down channel an additional $a_{1}$
($a^{\prime}$) state is found to be the lowest-lying state in the gap. The
only exception is the double-positive charge state, where the otherwise band-
gap-present states are lowered into the valence band (see Fig. 2). The other
dangling bond states are found deep within the valence or conduction bands and
are, therefore, not considered.

a) b) Figure 2: The Kohn-Sham electronic band structure of relevant charge
states, evaluated at the $\Gamma$-point. a) The band structure of double-
positive, single-positive, and neutral charge states of the _hh_
configuration. b) The single-positive state band structure of the off-axis
configurations, illustrating the band splitting due to the off-axis symmetry
breaking.

Fig. 2 shows the Kohn-Sham band structures and occupations of charge states,
excluding the negative states. The _hh_ configuration is taken as
representative of the defect. Note that the off-axis configurations will split
the otherwise degenerate defect states due to their lower symmetry, as shown
in Fig. 2(b). The most stable spin configurations are a triplet for the
single-positive charge state and doublets for the double-positive and neutral
charge states. However, the single-positive state may also exhibit a meta-
stable spin-singlet state, which by our calculations, lies 100 meV and 64 meV
higher in energy for the on- and off-axis configurations, respectively. The
defect states are mainly centered on the neighboring carbons with a small
contribution on the chlorine, as shown in Fig. 1(b). This qualitative
localization feature is shared by both the SiC divacancy and NV center[49,
50].

Figure 3: The formation energy of the lowest lying spin-charge states of the ClV defect. Colored regions mark the approximate region of relative stability of each state. State Transition | _hh_ | _kk_ | _hk_ | _kh_
---|---|---|---|---
(2$+|+$) | 1.07 | 1.05 | 1.19 | 1.14
($+|$0) | 1.76 | 1.73 | 1.73 | 1.69
(0$|-$) | 2.00 | 1.87 | 1.92 | 1.76
($-|$2$-$) | 3.01 | 2.96 | 2.99 | 3.01
Table 2: The ionization levels of the ClV charge states, in eV.

Fig. 3 shows the formation energy and Table 2 summarizes the ionization levels
within the band gap. Previous studies have considered additionally positive
charge states of the defect on the level of the local density
approximation[51]. However, these are likely to lack occupied defect orbitals
in the band gap, hence are less interesting from the perspective of possible
photon emitter states. In turn, the positive charge state, featuring several
deep defect Khon-Sham levels in the band gap where optical transitions may
occur, has a sizable stability region. The (2$+|+$) varies from 1.05 to 1.19
eV $+$ $E_{\text{V}}$ and the ($+|$0) varies from 1.69 to 1.76 eV $+$
$E_{\text{V}}$. In contrast, the neutral charge state is only stable in a
smaller region between 1.69 to 1.92 eV $+$ $E_{\text{V}}$ and is greatly
affected by the relative stability of the surrounding charge states, severely
limiting this region of stability for the _kh_ configuration.

The defect structure shown in Fig. 1(a) is the lowest configuration for this
stoichiometry. Notably, the energy difference (taken from screening data)
between the studied structure and the relocation of the chlorine to the
silicon site is about 4.45 eV. Furthermore, the evaluation of binding energies
to various component separations of the ClV center, using the screened defect
data, shown in Fig. 4(a), indicates that the binding energy is greater than 7
eV. For assurance of accuracy, the formation energy is evaluated for the
lowest-lying separation with the HSE06 functional, which corresponds to the
silicon vacancy separated from the chlorine substitution site. As shown in
Fig. 4(b), the change in binding energy from the PBE-predicted values is
minimal.

a)

b)

Figure 4: The binding energies of the ClV defect compared to possible single-
defect separations, including three different identified chlorine interstitial
sites, in the _hh_ configuration. a) The formation energy of all identified
defect combinations and the ClV defect calculated with $\Gamma$-point PBE at
screening accuracy. b) The formation energies, $E_{\text{form}}$, and binding
energy, $H^{b}$, of the ClV and lowest-lying identified dissipation formation
(separated chlorine substitution and silicon vacancy), calculated with the
HSE06 functional.

###  IV.2 Optical Properties

Figure 5: The _hh_ band structure with studied transitions marked, where
$T^{+}_{\\{1,2,3\\}}$ and $T^{0}_{\\{1,2,3,4,5\\}}$ denote the studied
transitions in the positive and neutral charge state respectively. The
$T^{+}_{1}$, and other transitions involving a degenerate $e$ state, can
consist of two transitions, either to the $a^{\prime}$ or the
$a^{\prime\prime}$ states of the $e$ state split by a Jahn-Teller distortion
in the excited state or by structural symmetry reduction already present in
the _hk_ and _kh_ configurations. However, we mainly consider the transition
to the $a^{\prime\prime}$ state or the otherwise lowest-lying state.

Following the band structures of Fig. 2, the defect-to-defect transitions
exhibited in the positive and neutral charge states are labeled and
illustrated in Fig. 5. We note that there is no label for the transition
between the spin-down channel occupied $a^{\prime\prime}$ state to the lowest
unoccupied $a^{\prime}$ state in the neutral charge state. These states
originate from the same degenerate $e$ state from the positive charge state,
which is split in the neutral charge state by the symmetry breaking Jahn-
Teller effect. Furthermore, we note that the positive charge state shares the
electronic structure of the neutral divacancy and negative NV center[52]. The
optical cycle of those defects involves the transition between the occupied
$a_{1}$ state to the lowest lying unoccupied $e$ state[53]. Here, we report on
the corresponding transition in the ClV defect, which is denoted as
$T^{+}_{1}$. As summarized in Table 3, this transition is predicted to be
particularly bright from the notably low radiative lifetime on the order of 30
ns, comparable to the predicted value for the diamond NV center of 6.5 ns
using the same methodology[26]. However, in contrast to the previously
mentioned diamond and SiC defects which have been of high recent interest as
single-photon emitters, this defect is predicted to emit in the telecom range
with the ZPLs of the $T^{+}_{1}$ transition corresponding to wavelengths of
1330 nm, 1440 nm, 1490 nm and 1590 nm, respectively for the _hh_ , _kk_ , _hk_
and _kh_ configurations. As is shown and predicted from the symmetry
consideration of the transition, the emitted light will be polarized
perpendicular to the $c$-axis in the on-axis configurations and otherwise
likely to have mixed polarization. Additionally, we study two other
transitions labeled $T^{+}_{2}$ and $T^{0}_{2}$ belonging to the positive and
neutral ground state. Compared to the $T^{+}_{1}$ transition, these also
feature low lifetimes, but in separate ZPL ranges. In particular, the
$T^{+}_{2}$ is predicted to be in the visible spectrum while the $T^{0}_{2}$
is in the near-infrared region of 1100–1300 nm, most notable for being in the
second biological window[54], where attenuation through blood and tissue is
minimal. Transitions involving extended states in the valence or conduction
band are not studied in detail here, but are estimated from the ionization
levels indicated in Table 2 to have approximate bound-to-defect ZPLs of 1.7 eV
and defect-to-band ZPLs of 2.1 eV.

Transition | Config. |  ZPL (eV) |  Lifetime (ns) | $\theta$
---|---|---|---|---
T${}^{+}_{1}$ | $hh$ | 0.93 | 28.4 | $90.0^{\circ}$
$kk$ | 0.86 | 30.9 | $90.0^{\circ}$
$hk$ | 0.83 | 24.3 | $27.6^{\circ}$
$kh$ | 0.78 | 28.1 | $29.9^{\circ}$
T${}^{+}_{2}$ | $hh$ | 1.64 | 63 | $0.1^{\circ}$
$kk$ | 1.74 | 40 | $0.5^{\circ}$
$hk$ | 1.74 | 35 | 67.2∘
$kh$ | 1.76 | 81 | 79.1∘
T${}^{0}_{2}$ | $hh$ | 1.12 | 83.8 | $84.0^{\circ}$
$kk$ | 1.03 | 86.8 | $87.0^{\circ}$
$hk$ | 1.03 | 33.9 | $86.0^{\circ}$
$kh$ | 0.91 | 43 | $90.0^{\circ}$
Table 3: The properties of the particularly bright excited state transitions,
for the positive and the neutral charge state. The data includes zero-phonon
lines (ZPLs), the radiative lifetime of the state, and the polarization angle
($\theta$) between the transition dipole moment and the c-axis.

###  IV.3 Electron-Phonon Coupling

Config. |  $\Delta Q$ ($\text{amu}^{1/2}$Å) |  $\omega_{g}$ (meV) | $S$ | $W$
---|---|---|---|---
_hh_ | 0.96 | 32.22 | 3.55 | 2.88%
_kk_ | 1.02 | 30.82 | 3.85 | 2.12%
_hk_ | 1.17 | 28.70 | 4.69 | 0.92%
_kh_ | 1.11 | 29.84 | 4.43 | 1.19%

Table 4: The phonon-coupling properties of the $T^{+}_{1}$ transition assuming
a single-phonon approximation. Included is the single-phonon coordinate
displacement, $\Delta Q$, the effective single-phonon frequency estimated from
interpolated ground state energies, $\omega_{g}$, the obtained Huang-Rhys
factor, $S$, and corresponding Debye-Waller factor, $W$.

We investigate the vibrational coupling of electron transition, focusing on
the predicted telecom emission of the ClV+ state. As explained in Section III,
calculated phonons of the defect ground state of the _kk_ configuration is
used to qualitatively reconstruct the phonon sideband and quantify the overall
coupling to phonons via Huang-Rhys theory. The calculated sideband in Fig. 6
show discernible localized vibrational modes with a considerable contribution.
Bumps in the spectrum can be associated with groups of local modes making up
vibrational configurations with $a_{1}$ and $e$-state characteristics. In
particular, the oscillation of the chlorine ion within the defect axis and
perpendicular to the plane of reflection is a considerable component in the
most strongly coupled modes.

Figure 6: The phonon sideband of the $T^{+}_{1}$ transition for the _hh_
configuration, obtained after explicit phonon calculations and summation of
partial phonon-contributions to the transition. The Huang-Rhys factor and
corresponding quantum efficiency estimated from the multi-phonon coupling is
also included.

As for the expected size of the optical phonon coupling, a Huang-Rhys factor
of 3.53 was obtained for the _kk_ configuration corresponding to a Debye-
Waller factor of 2.9%. The zero-phonon contribution to the ClV luminescence is
therefore noted to be lower than that of the diamond NV center (3.2%[55]) and
the neutral divacancy (5.3%[23]), which may be attributed to the relatively
larger mass of the chlorine vacancy, as is majorly involved in the coupled
vibrational modes. However, it should be noted that integrated photonics
technologies available for SiC can increase this ratio considerably, with the
divacancy demonstrated to achieve an enhanced Debye-Waller factor of more than
75%[56] with Purcell enhancement in a crystal cavity. Estimated quantities for
all configurations are obtained in the single-phonon approximation and yield a
quantum efficiency of approximately 1-3% (see Table 4), where the off-axis
configurations are on the lower end of this estimate. However, it should be
noted that compared with the multi-phonon estimation of the _kk_ , there is an
overestimation of the Huang-Rhys factor in the single-phonon approximation. In
fact, results show that the single-phonon approximation underestimates the
contribution from low-frequency local modes at approximately 22 meV which are
the dominating factor to the total Huang-Rhys factor (see Supplemental
Material). On the other hand, the higher Huang-Rhys factors obtained in the
off-axis configurations are most likely explained by an increased structural
relaxation between ground and excited states, as indicated by the increased
coordinate differences, $\Delta Q$.

###  IV.4 Spin Properties

Config. |  $D$ (GHz) |  $E$ (MHz)
---|---|---
_hh_ | 1.93 | 0
_kk_ | 1.87 | 0
_hk_ | 1.90 | 209
_kh_ | 1.82 | 150
Table 5: Zero-field splitting parameters of the ClV$+$ $S=1$ ground state. The
$D$ and $E$ parameters are reported on the standard form of
$D=\frac{3}{2}D_{zz}$ and $E=\frac{1}{2}(D_{xx}-D_{yy})$ with the principal
components of the ZFS tensor $D_{xx}$, $D_{yy}$, $D_{zz}$.

We calculate the ZFS tensors of each ClV$+$ triplet configuration. Eigenvalues
of the tensor are reported in Table 5. We note the similarity in size of the
$D$-components to those of the divacancy ($D\approx 1.3$ GHz)[3] and NV center
($D\approx 2.9$ GHz)[57], which indicates that the ClV defect can be studied
and used with spin-resonance techniques, such as optically detected magnetic
resonance (ODMR), without considerable modification to experimental setups
calibrated to the resonance of similar defects. One can also note the
possibility of discerning the four configurations in spin-resonance-based
techniques because of the observable variation in $D$.

To determine the coupling of the defect electron spin to possible neighboring
spins, the hyperfine structure is calculated at the neighboring lattice sites.
These sites may feature 29Si and 13C doublet nuclear spins, which are found at
respective natural abundances of 4.4% and 1.1%. Furthermore, the chlorine site
of the defect will feature a quartet spin, but may be found as either 35Cl at
75.76% natural abundance or 37Cl at 24.24%. These sites are labeled as in Fig.
7, where we number the sites according to rising position along, and distance
to, the chlorine-to-vacancy axis. In the off-axis configurations, we
distinguish between the lattice sites lying on and off the C1h plane of
reflection, respectively denoted by primed and double-primed labels. In the
on-axis configurations, a unique labeling along the defect axis is enough due
to the rotational and reflection equivalence in the C3v symmetry. The
hyperfine coupling may also differ between the two chlorine isotopes according
to the difference in gyromagnetic ratio, which is reportedly 4.176 MHzT-1 for
35Cl and 3.476 MHzT-1 for 37Cl[58].

In Table IV.4, we report the results of the ClV+ ground state, assuming a 35Cl
isotope spin. Of particular note is the overall negativity of the chlorine
principal components, indicating anti-parallel coupling of the defect triplet
and nuclear quartet. Furthermore, the tensor is largely isotropic, but an
order of magnitude larger than that of the nitrogen spin in the diamond NV
center (approximately $-2$ MHz) [59]. Otherwise, the couplings to nearest
neighbor spins are quantitatively comparable to those reported from similar
ab-initio considerations for the NV center in diamond and the divacancy in
SiC[60]. We note the difference in coupling between carbon nearest neighbors
and silicon neighbors. the coupling indicates a primary localization of the
spin density toward the nearest neighbor carbons, in agreement with the
illustrated orbital of Fig. 1(b). Furthermore, as indicated by the hyperfine
strengths of next-nearest neighbors, the spin density appears to extend
perpendicular to the defect axis, coupling mainly to spins near the silicon
vacancy site.

Using the obtained hyperfine and ZFS values, we calculate the coherence time,
$T_{2}$, of the positive ClV center and obtain $T_{2}\approx 1.45$ ms at an
external field of 100 G. Once again, this is similar to what has been
calculated and demonstrated for the divacancy[61], known to have one of the
longest coherence times at natural abundance, and is close to the reported
$T_{2}$ of the SiC host 1.1 ms[62].

a)b) Figure 7: The _hh_ structure (a) with neighbor carbon and silicon sites,
and the _hk_ structure (b) along the defect axis, showing the broken C3v.
Labels follow the distance to the chlorine site, where the second index
increases with distance along the defect axis. Symmetrically equivalent sites
are not labeled, but primed quantities are introduced for the off-axis
configurations to emphasize the reduced symmetry.

Table 6: The diagonalized hyperfine parameters (in MHz) for neighbor lattice
sites of the ClV$+$ state. The diagonal components are sorted according to
$|A_{xx}|>|A_{yy}|>|A_{zz}|$, and $\theta$ defines the angle between principal
value $(A_{xx})$ and the defect symmetry axis. For second-nearest neighbor
sites and beyond, we provide a range of the observed hyperfine values larger
than 2 MHz.

Ion | Config. | $A_{xx}$ | $A_{yy}$ | $A_{zz}$ | $\theta$
---|---|---|---|---|---
35Cl | _hh_ | $-16.3$ | $-16.3$ | $-15.8$ | $90^{\circ}$
_kk_ | $-18.1$ | $-18.1$ | $-16.9$ | $90^{\circ}$
_hk_ | $-12.2$ | $-12.1$ | $-11.6$ | $85^{\circ}$
_kh_ | $-9.9$ | $-9.3$ | $-9.0$ | $107^{\circ}$
13C1,2 | _hh_ | 106 | 36.5 | 35.9 | 106∘
_kk_ | 98 | 29.4 | 28.7 | 73∘
_hk_ (C′) | 102 | 39.4 | 38.4 | 105∘
_kh_ (C′) | 96 | 36.8 | 36.3 | 106∘
_hk_ (C′′) | 107 | 34.4 | 33.8 | 107∘
_kh_ (C′′) | 98 | 30.1 | 29.6 | 106∘
29Si1,1 | _hh_ | 0.99 | 0.80 | 0.34 | 90∘
_kk_ | 0.65 | 0.63 | $-0.06$ | 56∘
_hk_ (Si′) | 0.58 | 0.56 | $-0.12$ | 90∘
_kh_ (Si′) | $-1.08$ | 0.28 | 0.12 | 68∘
_hk_ (Si′′) | 0.60 | 0.49 | $-0.41$ | 105∘
_kh_ (Si′′) | 1.10 | 0.89 | 0.18 | 92∘

Ion | $A_{xx},A_{yy},A_{zz}$
---|---
| _hh_ | _kk_ | _hk_ | _kh_
C3,2 | 4.9 – 10.5 | 5.4 – 11.1 | 4.9 – 10.6 | 5.0 – 10.8
C1,3 |  $|A|<$ 1 |  $-8.5$ – $-5.3$ |  $|A|<$ 2 | $|A|<1$
C2,3 | 3.2 – 7.4 | 0.9 – 2.7 | 3.3 – 7.7 | 3.4 – 8.6
Si2,2 | 9.4 – 11.8 | 10.5 – 12.4 | 8.7 – 12.2 | 6.9 – 13.8
Si4,2 |  $|A|<$ 1 |  $|A|<$ 1 |  $-3.6$ – $-0.5$ |  $-3.3$ – $-1.2$
Si1,3 | 11.6 – 12.1 | 12.8 – 13.4 | 9.7 – 12.7 | 9.9 – 14.5
Si1,4 |  $|A|<$ 2 | 2.4 – 2.7 |  $|A|<$ 2 | $|A|<2$

##  V Discussion

We have shown that the ClV exhibit bright optical emissions and have predicted
both qualitative and quantitative similarity to the diamond NV center.
However, one consequence of these similarities that has not been examined in
this paper is if there exists an optical cycle that populates one of the spin
substates. The convenience of the solid-state qubits and emitters currently
dominating the field is the presence of spin-dependent processes in excitation
and state relaxation that allow for optical cycles that effectively polarize
the spin state of the defect[50, 63]. In both NV centers (in diamond and SiC)
and the divacancy in SiC, these cycles have been enabled by a nonradiative
intersystem crossing (ISC) from the excited triplet state onto an excited
singlet state, which may de-excite onto the singlet ground state and
transition into the triplet ground state through another ISC. The spin
dependence of these processes finally favors the occupation of a particular
spin state. The ClV defect also displays a triplet in the positive state and
semi-stable singlet state that could accommodate a similar process. However,
describing such a cycle requires insight into the effect of spin-orbit
interaction on this defect, as well as the precise treatment of the singlet
shelving states. The latter step is notoriously difficult as the excited
shelving state displays high electron correlation and requires beyond-DFT
methods to describe accurately[50]. Such detailed characterization is
desirable but goes beyond the scope of the current work. However, assuming
such a spin initialization cycle exists, the defect qubit techniques of
similar defects could be generalized to the ClV defect. In addition, ODMR
measurements could similarly enable the myriad of sensing schemes developed
for the NV center. Given the ZFS parameters of the ClV electron spin, one may
assume that ODMR would be applicable at a microwave drive of similar size as
that of the NV center in diamond.

The most distinguishing feature of the ClV center is its bright emission in
telecom. However, there are also transitions in the infrared and visible
regions, which is rare in a single defect. However, the proximity of the
visible excitation (ca. 1.7 eV) is considerably close to the predicted ($+|$0)
ionization threshold and the accuracy in both ZPL and formation energies may
be approximately 0.1 eV[64, 65]. Therefore, it is difficult to say at this
level of theory whether one can reach the higher $a_{1}$ state without
considerable photoionization using a single-photon excitation. Interestingly,
the difference in excitation energy between the $T^{+}_{1}$ and $T^{+}_{2}$
transitions is about 0.9 eV, which indicates that one could resonantly excite
to the higher $a_{1}$ level via a two-photon process while avoiding
photoionization.

Spin-to-charge conversion has been a particularly successful method of spin
readout with majorly increased fidelity[66] based on distinguishing the spin
state from spin-selective charge conversions of the center. In this context,
we note the lack of likely localized defect transition in the ClV2+ state.
Therefore, the double-positive state could be considered to be dark with
respect to the predicted $T^{+}$ transitions, and a spin-to-charge readout to
this state may be effective, assuming a spin-selective photoionization can be
achieved and not suppressed by the ISC rate. Photoionization to the neutral
state, as demonstrated for the divacancy[2], can also be considered. However,
based on the (2$+|+$) and ($+|$0) ionization levels in Fig. 3 of ca. 1 eV and
1.7 eV from the valence band, photoionization with a two-photon process will
likely require secondary photon energies higher than for the initial
excitation wavelength at telecom energies.

Our spin property characterization clearly illustrates the similarity to the
divacancy and NV centers. Regarding hyperfine coupling to lattice spins, the
dominating source of spin decoherence at natural abundance in SiC, there is
close to no quantitative difference, and we expect coherence times to coincide
apart from the effect of the present chlorine spin. However, as indicated by
the calculated $T_{2}$ time of 1.45 ms, this defect can exhibit long coherence
times at natural abundance, shown to be close to or longer than the coherence
time of the divacancy, having the longest coherence time at natural abundance
among the known defects in SiC[61]. The longer coherence times could be
attributed to the chlorine spin coupling, adding an antiparallel contribution
to the otherwise spin-parallel mean field. These results are mainly valid at
$T=0$ K, but the temperature effects on the defect are vital to its
applicability as a qubit. The room-temperature properties of the diamond NV
center have been attributed to low spin-orbit interaction and high Debye
temperature of diamond[61], leading to millisecond room-temperature coherence
times[1]. While we do not include temperature effects in this work, we note
that room-temperature coherent control has been demonstrated for both the
divacancy[67] and the SiC NV center[4], achieving a room-temperature coherence
time of 24 $\mu$s. Given the ClV likeness to these defects and calculated
$T_{2}$ time in this work, it is plausible that the same room-temperature
properties can be achieved.

Finally, having shown the potential properties of this highly interesting
defect, the authors note that the ClV and other chlorine-related centers have
been largely unexplored in the field of quantum technology. Despite chlorine
being a central component in CVD growth of SiC crystals, there is a lack of
publications reporting chlorine centers with notable photoluminescence. This
may indicate that, despite chlorine and intrinsic defects being present during
the crystal growth process, a barrier or competing process prevents the
formation of the stable defect cluster. However, deep-level transient
spectroscopy measurements at high annealing temperatures in chlorine-implanted
p-type SiC have observed defect levels attributed to chlorine-related centers.
Notably, Ref. 68 predicts one such charge level of
$E_{\textsubscript{V}}+0.97$ eV that agrees with the ($2+|+$) level of the ClV
center presented in this paper. This results suggests that chlorine needs to
be implanted to create the ClV center.

##  VI Conclusions

In this work, we have done a large-scale search of the extrinsic defect space
within 4H-SiC using the workflow package ADAQ, identifying four defects that
are worthy of further investigation: The VSiOC, VSiFC, VSiSC and ClV centers.
We report in detail on the most intriguing defect, the ClV center, whose
predicted optical properties are promising for a future single-photon emitter.
Our hybrid-DFT calculations predict strong thermodynamic stability and bright
emission within three optical regions of major interest in single-photon nano-
devices, the visible, infrared, and telecom regions. Meanwhile, it shares many
structural and electronic state properties with defects that have dominated
the literature over the last decade. While its natural quantum efficiency is
on par with the NV center, it is offered greater opportunity for enhancement
using the SiC mature fabrication techniques and up-and-coming nanophotonics
technology. The overarching similarity between the ClV and other known defects
implies it should hold the properties of a state-of-the-art solid-state qubit,
with optical spin initialization and readout. Simultaneously, it exhibits
noteworthy coherence qualities. Apart from the presence of a quartet nuclear
spin in its vicinity for state storage and control, the triplet electron spin
coherence time is found to be one of the longest in natural abundance SiC.
Further investigation into its excited state spin properties and external
field sensitivity will tell more of its prospects for quantum sensing. The ClV
center has the qualities which made the diamond NV center a focal point of
solid-state quantum technologies. As it further addresses the demand for
telecom range emission, it offers an improved defect candidate for future
quantum technologies.

###### Acknowledgements.

We acknowledge support from the Knut and Alice Wallenberg Foundation (Grant
No. 2018.0071). Support from the Swedish Government Strategic Research Area
Swedish e-science Research Centre (SeRC) and the Swedish Government Strategic
Research Area in Materials Science on Functional Materials at Linköping
University (Faculty Grant SFO-Mat-LiU No. 2009 00971) are gratefully
acknowledged. JD and RA acknowledge support from the Swedish Research Council
(VR) Grant No. 2022-00276 and 2020-05402, respectively. We acknowledge PRACE
for awarding us access to MareNostrum at Barcelona Supercomputing Center
(BSC), Spain. The computations were also enabled by resources provided by the
National Academic Infrastructure for Supercomputing in Sweden (NAISS) and the
Swedish National Infrastructure for Computing (SNIC) at NSC and PDC partially
funded by the Swedish Research Council through grant agreements no. 2022-06725
and no. 2018-05973.

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