Citation: Kunakova, G.; Kauranens,
E.; Niherysh, K.; Bechelany, M.; Smits,
K.; Mozolevskis, G.; Bauch, T.;
Lombardi, F.; Erts, D.
Magnetotransport Studies of
Encapsulated Topological Insulator
Bi2Se3 Nanoribbons. Nanomaterials
2022, 12, 768. https://doi.org/
10.3390/nano12050768
Academic Editors: Yanquan Geng,
Emmanuel Brousseau, Bo Xue,
Jingran Zhang and Jiqiang Wang
Received: 27 January 2022
Accepted: 20 February 2022
Published: 24 February 2022
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nanomaterials
Article
Magnetotransport Studies of Encapsulated Topological
Insulator Bi2Se3 Nanoribbons
Gunta Kunakova 1,* , Edijs Kauranens 1, Kiryl Niherysh 1,2 , Mikhael Bechelany 3 , Krisjanis Smits 4 ,
Gatis Mozolevskis 4, Thilo Bauch 5, Floriana Lombardi 5 and Donats Erts 1
1 Institute of Chemical Physics, University of Latvia, 19 Raina Blvd., LV-1586 Riga, Latvia;
edijs.kauranens@lu.lv (E.K.); kiryl.niherysh@lu.lv (K.N.); donats.erts@lu.lv (D.E.)
2 Research and Development Department, Integrated Micro- and Nanosystems, Belarusian State University of
Informatics and Radioelectronics, P. Brovki Str. 6, 220013 Minsk, Belarus
3 Institut Européen des Membranes, IEM, UMR 5635, University of Montpellier, ENSCM, CNRS,
34095 Montpellier, France; mikhael.bechelany@umontpellier.fr
4 Institute of Solid State Physics, University of Latvia, Kengaraga 8, LV-1063 Riga, Latvia; smits@cfi.lu.lv (K.S.);
gatis.mozolevskis@cfi.lu.lv (G.M.)
5 Quantum Device Physics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University
of Technology, SE-41296 Goteborg, Sweden; thilo.bauch@chalmers.se (T.B.);
floriana.lombardi@chalmers.se (F.L.)
* Correspondence: gunta.kunakova@lu.lv
Abstract: The majority of proposed exotic applications employing 3D topological insulators require
high-quality materials with reduced dimensions. Catalyst-free, PVD-grown Bi2Se3 nanoribbons are
particularly promising for these applications due to the extraordinarily high mobility of their surface
Dirac states, and low bulk carrier densities. However, these materials are prone to the formation
of surface accumulation layers; therefore, the implementation of surface encapsulation layers and
the choice of appropriate dielectrics for building gate-tunable devices are important. In this work,
all-around ZnO-encapsulated nanoribbons are investigated. Gate-dependent magnetotransport mea-
surements show improved charge transport characteristics as reduced nanoribbon/substrate interface
carrier densities compared to the values obtained for the as-grown nanoribbons on SiO2 substrates.
Keywords: Bi2Se3 nanoribbons; ZnO; magnetotransport
1. Introduction
Three-dimensional topological insulators (3D-TIs) are among the major materials
in the class of topological materials. 3D-TIs have attracted significant research interest
due to their unusual surface properties. Carriers originating from topological surface
states exhibit a Dirac cone in the band structure [1] and charge transport via these states is
protected against backscattering from non-magnetic impurities [2,3]. If proximitized with
an s-wave superconductor, superconductivity induced in the topological surface states is
unconventional and predicted to host Majorana fermions [4,5]. The exploitation of these
exotic surface properties is advantageous for a variety of applications, for example, in
topological quantum computing [6], spintronics [7,8], and in the development of new-
concept electronic devices [9]. The surface states of TIs are metallic while the bulk of the
material, which is expected to be an insulator, is highly doped due to the formation of
native defects [10]. This aspect remains the main challenge in accessing the surface-state
charge transport, hampering progress towards the development of applications beyond
fundamental studies.
Owing to their large surface-to-volume ratio, 3D-TI nanowires and nanoribbons are
promising candidates with which to achieve truly topological surface-state-dominated
charge transport without any contribution from the bulk. Their nanosized geometry pro-
vides even more functionalities because of the low number of transport modes [11], which
Nanomaterials 2022, 12, 768. https://doi.org/10.3390/nano12050768 https://www.mdpi.com/journal/nanomaterials
Nanomaterials 2022, 12, 768 2 of 8
is particularly important for probing Majorana states [6]. Remarkable improvements in
material quality have been demonstrated in 3D-TIs doped with native-defect-compensating
substitutions. Nearly insulating bulk with a charge carrier density of ~1015 cm−3 has
been reported in single crystals of BiSbTeSe2 [12] (BSTS), but this approach is not fully
successful in nanowires and nanoribbons. Here, precise and reproducible concentrations of
dopants are challenging to obtain, and they are achieved at the expense of charge carrier
mobility [13].
Nanoribbons of Bi2Se3 have been reported to be nearly ideal 3D-TIs, practically with-
out any bulk conduction, and with exceptionally high carrier mobilities [14,15]. However,
Bi2Se3 is prone to the formation of surface accumulation layers [16]; this is particularly
evident in thin nanoribbons, where the thickness is comparable with the Debye screening
length [14,17,18]. The majority of the proposed 3D-TI-nanoribbon-based electronic devices
require good tunability of their chemical potential for accessing surface Dirac carriers in
a controlled manner. This can be achieved by employing electrostatic gating techniques.
However, additional trivial carriers with large densities form at the nanoribbon surfaces,
or at the interface with the substrate, which cannot be effectively depleted by common
electrostatic gating techniques. Therefore, more effort is needed to prevent the uncontrolled
formation of surface accumulation layers in Bi2Se3 nanoribbons.
The use of surface-capping layers for Bi2Se3 and Bi2Te3 has proven to be beneficial
to protect against environmental doping [19] and to probe surface state transport. Widely
used capping layer materials are Te or Se, and the oxide layers of ZnO or Al2O3 [13,20,21],
deposited on the top surface of the material. This allows more efficient electrostatic tuning
of the Fermi level [21], while in the case of Bi2Se3 nanoribbons, where the accumulation
layer is formed at the nanoribbon/substrate interface [14,17], other approaches have to
be considered.
In this work, we used atomic layer deposition (ALD) to fabricate all-around ZnO-
capped or -encapsulated Bi2Se3 nanoribbons. The choice of selecting ZnO as an encapsula-
tion layer material was based on the fact that thin layers of high-quality ZnO are possible
to grow at moderate temperatures. This is particularly important for preserving the stoi-
chiometry of Bi2Se3, as elevated temperatures may cause the unwanted out-diffusion of
Se, which increases the doping of the bulk. Comparative magnetotransport studies of
individual encapsulated and as-grown Bi2Se3 nanoribbons from the same batch synthesis
show that the encapsulation layer of ZnO helps to minimize the impact of the accumulation
layer at the nanoribbon/substrate interface and improves the tunability of the chemi-
cal potential using a back-gate. These findings are important for the implementation of
3D-TI-nanoribbon-based topological quantum devices.
2. Materials and Methods
Free-standing Bi2Se3 nanoribbons were grown on glass substrates using catalyst-
free physical vapor deposition (PVD). The growth procedure is described in detail else-
where [22]. As-grown nanoribbons were mechanically transferred to prepatterned Si/
300 nm SiO2 chips by bringing the chip and the glass substrate into contact with each other.
The glass substrate with the remaining free-standing nanoribbons was then covered with
2 nm of ZnO, using ALD at ~100 ◦C, in a home-built set-up.
Flakes of hexagonal boron nitride (h-BN) were exfoliated from h-BN single crystals (2D
semiconductors) and transferred to prepatterned Si/300 nm SiO2 chips. ZnO-encapsulated
Bi2Se3 nanoribbons were then transferred to the chips partially covered with thin flakes of
h-BN. Standard electron beam lithography processing was used to define electrical contacts
to individual Bi2Se3 and ZnO/Bi2Se3 nanoribbons. After developing the resist, the samples
were etched for 60 s in H2O/HCl/H2O2/CH3COOH solution [23] at room temperature to
remove the surface oxide layer, and layers of Ti (3 nm) and Au (80 nm) were evaporated
shortly after the etching to ensure formation of ohmic contacts.
Charge transport measurements were conducted in a Physical Property Measurement
System (PPMS) Dynacool, equipped with a 9 T magnet, at a base temperature of 2 K. In
Nanomaterials 2022, 12, 768 3 of 8
magnetoresistance measurements, a magnetic field B was applied perpendicularly to the
nanoribbon surface. Electrode pair I+/I− (see Figure 2a) was used as the current electrodes
to ensure a uniform flow of current in the nanoribbon, while the remaining electrodes V1
to V8 were employed as the voltage probes. Longitudinal resistance Rxx was recorded
using, for example, electrode pair V3/V7 while the transversal resistance Rxy was measured
across the pair V5/V6. For this particular nanoribbon device, voltage electrodes V1 to V4
are positioned where the nanoribbon is on top of the h-BN flake (~30 nm in thickness),
while the other voltage electrodes are located on the nanoribbon part, which is in direct
contact with the SiO2.
In order to determine whether the ZnO had covered the free standing Bi2Se3 nanorib-
bons, the nanoribbons were transferred to Cu grids and imaged through high-resolution
transmission electron microscope (HR-TEM Technai, Fei, Eindhoven, Netherland).
3. Results and Discussion
Simplified schematics illustrating the free-standing nanoribbons and encapsulation
with a thin ZnO layer are shown in Figure 1a. The HR-TEM studies of the ZnO/Bi2Se3
nanoribbons reveal a crystalline layer, with a thickness of ~2 nm, at the nanoribbon surfaces.
In total, five different nanoribbons of various geometries were examined, and a crystalline
surface layer was formed in all of them. The d-spacing value estimated from the lattice
fringes of Bi2Se3 is 0.21 nm, which is in good agreement with the previous studies [22].
The d-spacing value determined for the ZnO of 0.28 nm corresponds to (100) planes of
hexagonal wurtzite [24]. The interface between the Bi2Se3 and ZnO is separated by a layer
of amorphous material, with a thickness of ~1.5–2 nm. This layer corresponds to native
oxide of Bi2Se3, BiOx (see Figure 1b), which is always present on surfaces of Bi2Se3 [19].
Figure 1. (a) Schematic representation of catalyst-free PVD-synthesized free-standing Bi2Se3 nanorib-
bons on glass substrate; (b) false-colored HR-TEM image of a Bi2Se3 nanoribbon after encapsulation
with a thin layer of ZnO.
One of the fabricated nanoribbon Hall-bar devices used in the magnetotransport
measurements is depicted in Figure 2a. The measured Rxy(B) at zero back-gate voltage is
shown in Figure 2b. In order to minimize the error from misaligned electrodes, the data
were anti-symmetrized as a function of the magnetic field (see inset of Figure 2b). The
Rxy(B) dependences for all the measured nanoribbons were nonlinear. The absolute value
of the slope calculated from the high magnetic field range 7–9 T was always smaller than
the value determined from the 0–2.5 T range. This nonlinearity points to the charge carriers
originating from two or more carrier bands characterised by different densities/mobilities.
Nanomaterials 2022, 12, 768 4 of 8
The initial carrier density n3D can be calculated from the low or high magnetic field slope
of Rxy(B) as:
1
n3De
= t
dRxy
dB
× w
wh
. (1)
Here, t is the nanoribbon thickness, w is the nanoribbon width, wh is the distance
between the Hall contacts, and e is the elementary charge. The calculated values for the 2D
carrier densities (n2D = n3D·t) from both the 0–2.5 T and 7–9 T regions for the as-grown
and ZnO-encapsulated nanoribbons from the same batch synthesis are listed in Table S1
(see Supplementary Information (SI)). The values estimated from the 7–9 T range are about
20–30% higher than those obtained from the 0–2.5 T range.
Figure 2. (a) SEM image of a Bi2Se3 nanoribbon Hall-bar device; (b) Hall resistance Rxy(B) for the
ZnO/Bi2Se3 nanoribbon device A3t (see Table S1), measured at back-gate voltage Vg = 0 V. The inset
shows anti-symmetrized Rxy(B) data with linear fit in the 0–2.5 T range (black solid curve), and in
the 7–9 T range (black dashed curve); (c) Hall carrier density of Bi2Se3 and ZnO/Bi2Se3 nanoribbons,
plotted versus the nanoribbon thickness. In the case of the ZnO/Bi2Se3 nanoribbons, total thickness t
is reduced by 4 nm, accounting for the two ~2 nm thick ZnO layers. Gray data points correspond to
the data from [14]; here, the carrier density is calculated from the same magnetic field range (0–2.5 T).
Figure 2c shows the n3D of the as-grown Bi2Se3 and ZnO/Bi2Se3 nanoribbons, plotted
as a function of the nanoribbon thickness. The data correspond to the values calculated from
the 0–2.5 T range, since in high magnetic fields, some nanoribbons showed the presence of
Shubnikov–de Haas oscillations in Rxx(B), additionally impacting the Rxy(B) dependence.
The charge carrier density n3D for the as-grown Bi2Se3 nanoribbons with thicknesses
of ~30–40 nm is about ~3.5 × 1018 cm−3, and it increases to ~9 × 1018 cm−3 for the
28-nanometer-thin nanoribbon. This peculiar n3D(t) dependence of the catalyst-free PVD-
grown Bi2Se3 nanoribbons has been reported previously [14]. The increased 3D charge
carrier density for nanoribbons of thicknesses below ~30 nm is due to the accumulation
layer of a large carrier density of ~1.3 × 1013 cm−2 (see Table 1), formed at the nanoribbon’s
bottom surface/substrate interface [14]. Figure 2c also includes the values of the carrier
densities reported in [14] (gray points). In this work, the obtained n3D(t) for the as-grown
ribbons is similar to those previously reported in the literature.
The n3D values for the ZnO-encapsulated Bi2Se3 nanoribbons are close to those deter-
mined for the as-grown nanoribbons with thicknesses of ~30–40 nm, and are also about
~3.5× 1018 cm−3. A pronounced increase of n3D of the thin ZnO-encapsulated nanoribbons
(t < 30 nm) is not observed, indicating that the overall carrier density in the accumulation
layer could be smaller compared to the as-grown Bi2Se3 nanoribbons.
The charge carrier density n2D as a function of the back-gate voltage Vg for a 28-
nanometer-thin ZnO-encapsulated Bi2Se3 nanoribbon on h-BN is plotted in Figure 3a.
Nanomaterials 2022, 12, 768 5 of 8
The applied back-gate voltage directly affects the nanoribbon bottom surface/substrate
interface, and at higher Vg values, some parts of the nanoribbon bulk as well. The
slope of the n2D(Vg) gives an indication of the capacitance of this field-effect device, and
C ≈ 6.2 × 10−5 F/m2. In order to effectively deplete the majority of the initial carriers of
~9 × 1012 cm−2, one would need to apply approximately twice as high a voltage to the
back-gate, which is not feasible for this device. Nevertheless, the n2D(Vg) data are helpful
for the study of the properties of the nanoribbon/substrate interface. The Rxx
(
Vg
)
data of
the same ribbon reflect the n2D(Vg) characteristics (see inset of Figure 3a). The absence of
maxima or saturation in the Rxx
(
Vg
)
indicates that the Fermi energy EF remained above
the Dirac point in the entire measured Vg range. To tune the EF to the Dirac point, which
is important for accessing the charge carriers exclusively from the surface Dirac states,
ultra-thin (t ~ 10 nm) Bi2Se3 nanoribbons would be needed. Another aspect for improving
the gate tunability is the thickness and permittivity of the gate dielectric, i.e., a thinner
dielectric layer than the 32 nm of h-BN on 300 nm of SiO2 could be used ( ε ∼ 3–4), or,
alternatively, one could choose a SrTiO3 substrate, in which the relative dielectric constant
at low temperatures is in the order of 103–104.
Figure 3. (a) Charge carrier density n2D(= n3Dt) as a function of the back-gate voltage Vg. Here, n2D
is calculated from the anti-symmetrized Rxy(B) data in the 0–2.5 T range. Rxy1 and Rxy2 represent the
Hall resistances measured using two different pairs of transversal electrodes, on the same nanoribbon.
Black dashed line is the linear fit, and the capacitance estimated from the slope is 6.2 × 10−5 F/m2. In
the inset—longitudinal resistance Rxx as a function of the Vg; (b) conductance tensor element Gxy(B)
at different applied Vg, fitted with the two-carrier model, inset shows fitted Gxx(B) curves; (c) from
the two-carrier model extracted parameters of the two bands: carrier densities n1; n2, and mobilities
µ1; µ2 (in the inset) versus the back-gate voltage. All the data shown correspond to the ZnO/Bi2Se3
nanoribbon A3t.
Since the Rxy(B) curves clearly indicate the presence of charge carriers from several
carrier bands, we analysed the magnetotransport data using the two-carrier model.
Here, the conductance tensor elements Gxy and Gxx as a function of the magnetic field
can be written as [25,26]:
Gxy(B) = eB
(
n1µ21
1 + µ21B
2
+
n2µ22
1 + µ22B
2
)
(2a)
Gxx(B) = e
(
n1µ1
1 + µ21B
2
+
n2µ2
1 + µ22B
2
)
(2b)
with parameters n1, n2 and µ1, µ2 representing the carrier densities and mobilities of the
two bands, respectively. Gxy and Gxx from the measured resistances are calculated as:
Nanomaterials 2022, 12, 768 6 of 8
Gxy(B) = −
R′xy
R′2xy + R′2xx
(3a)
Gxx(B) = − R
′
xx
R′2xy + R′2xx
(3b)
R′xy is the Hall resistance, corrected considering the geometry of a nanoribbon Hall-
bar device, and is equal to Rxy w/wc. R′xx is the sheet resistance, equal to Rxx w/L. The
calculated conductance tensor elements as a function of magnetic field for different applied
back-gate voltages are fitted with Equations (2a) and (2b) and plotted in Figure 3b. For
the nanoribbon A3t, the extracted value of the charge carrier density of band 1 is n1 =
6.43 × 1012 cm−2 and the mobility µ1 = 3530 cm2/Vs, while the carrier density and
mobility of band 2 are n2 = 4.74 × 1012 cm−2 and µ2 = 990 cm2/Vs, respectively. These
parameters of the two bands are similar to those estimated for other ZnO-encapsulated
Bi2Se3 nanoribbons (see Table 1).
The extracted carrier density values n1 and n2 of the two bands change with the
applied back-gate voltage. The value n1 scales linearly with the applied back-gate voltage
and is reduced by ~50% at Vg = −100 V. Instead, n2 is practically insensitive to Vg in the
0–−50 V range, while at Vg > −50, V starts to decrease more rapidly.
Table 1. Summary of the carrier densities (cm−2) and mobilities (cm2/Vs) extracted from the two-
band analysis and from the SdH oscillations for ZnO-encapsulated Bi2Se3 nanoribbons on h-BN and
SiO2 substrates, and comparison with the literature data (refs. [14,15,17]).
Surfaces (Band 1) Bulk (Band 2) Top Surface * Bulk *
ZnO/Bi2Se3 NR on
h-BN: tNR, nm n1 µ1 n2 µ2 n2D, SdH n3D, SdH
A3t 29 6.43 × 1012 3540 4.74 × 1012/1.64 × 1018 930
A1b 35 7.18 × 1012 4700 5.31 × 1012/1.52 × 1018 2052 2.40 × 1012 1.44 × 1018
D3b 34 6.24 × 1012 4800 4.99 × 1012/1.46 × 1018 1350
Bi2Se3 NR on SiO2,
sample E5 [14] 30 15.0 × 10
12 ** 2.40 × 1012
Bi2Se3 NR on SiO2,
sample BR3-10R2 [14] 63 - 2.50 × 10
12 1.70 × 1018
Bi2Se3 NR on SiO2,
sample E [17] 79 13.0 × 10
12 * 2.90 × 1012 6.60 × 1017
Bi2Se3 NR on STO,
sample B51-10 [15] 9 5.55 × 10
12 ** 1232
* Extracted from analysis of the SdH oscillations. ** These values account only carrier density of the nanoribbon
bottom surface/substrate interface.
In what follows, we discuss a possible scenario that would account for this behaviour.
Band 1 is affected by the back-gate voltage much more strongly; therefore, the carrier
density n1 can most likely be associated with the surface states. As the nanoribbons are
fully encapsulated by the ZnO protection layer, the mobilities of the nanoribbon top and
bottom surfaces can be expected to have similar values, and carriers from both surfaces
would appear in the same channel (n1) of the two-band model. The bulk mobilities are
typically reported to be of much lower values [27], and the µ1 of 3530 cm2/Vs is more than
three times larger than the value of µ2. For nanoribbon A1b, where the µ1 is 4700 cm2/Vs,
SdH oscillations with two dominating frequencies are observed (see Figure S2, SI). One of
the frequencies of ~99 T is similar to that observed in the catalyst-free PVD-grown Bi2Se3
nanoribbons, which have previously been reported to represent the surface Dirac states
from the nanoribbon top surfaces [14,22,28]. This gives the carrier density of the nanoribbon
top surface of nTS SdH~2.4 × 1012 cm−2. The carriers from the top surface are most likely
insensitive to the back-gate voltage, as the nanoribbon is of a relatively large thickness. The
Nanomaterials 2022, 12, 768 7 of 8
bottom surface/interface nBS, Int. carrier density at Vg = 0 V would be then n1 − nTS SdH ≈
4 × 1012 cm−2, which would not be very different from all the ZnO/Bi2Se3 nanoribbons
transferred onto the h-BN (4.03, 3.84 and 4.78 × 1012 cm−2 for the nanoribbons A3t, D3b,
and A1b, respectively). These low values corroborate that the ZnO encapsulation of Bi2Se3
nanoribbons mitigates the creation of an accumulation layer.
Band 2 with carrier density n2 can be assumed to correspond to the bulk carriers.
Above −50 V, when the bottom surface/interface carriers are partly depleted, a fraction of
the bulk carriers also starts to be affected by the back-gate voltage, and at Vg = −100 V, the
n2 is reduced to ~3.5 × 1012 cm−2. At Vg = 0 V, the n2 is 4.74–5.31 × 1012 cm−2 (see Table 1),
and if rescaling to the 3D values: 1.46–1.64 × 1018 cm−3. Peculiarly enough, the second
frequency of the aforementioned SdH oscillations of the nanoribbon A1b (Figure S2, SI),
with the highest µ2, gives 1.44 × 1018 cm−3. This value is close to the 3D bulk carrier
densities determined from band 2.
4. Conclusions
To conclude, the application of a ZnO encapsulation layer to topological insulator
Bi2Se3 nanoribbons and the use of h-BN as a substrate help to improve the nanorib-
bon/substrate interface properties. Thin layers of crystalline ZnO have no degrading
impact on the overall transport characteristics of Bi2Se3 nanoribbons. The 3D charge carrier
densities for nanoribbons of different thicknesses are of the same order as the values de-
termined for as-grown nanoribbons with thicknesses of 30–40 nm. The reduced surface
carrier density extracted from two-band Hall analysis points towards a reduction in the
interface accumulation layer when encapsulating Bi2Se3 nanoribbons with a thin ZnO
layer. Moreover, the ZnO-encapsulated nanoribbons show excellent Hall mobility. The
presence of the Shubnikov–de Haas oscillations confirms that the high quality of catalyst-
free PVD-grown Bi2Se3 nanoribbons stays preserved if ZnO is used as an encapsulation
layer. This approach of all-around encapsulation in combination with ultra-thin Bi2Se3
nanoribbons, transferred to mono or few layer h-BN substrates, would be beneficial to
controllably achieve ambipolar transport in Bi2Se3.
Supplementary Materials: The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/nano12050768/s1.
Author Contributions: Conceptualization, G.K.; investigation E.K. and K.N.; resources K.S., G.M.,
T.B., F.L., D.E. and M.B.; writing—review and editing, G.K., T.B., F.L. and D.E. All authors have read
and agreed to the published version of the manuscript.
Funding: This research was funded by the Latvian Council of Science, project “Highly tunable
surface state transport in topological insulator nanoribbons”, No. lzp-2020/2-0343, and by the
European Union’s Horizon 2020 research and innovation program, Grant Agreement No. 766714/
HiTIMe.Institute of Solid-State Physics, University of Latvia as the Center of Excellence has received
funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-
2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data presented are available on request from the corresponding
author.
Conflicts of Interest: The authors declare no conflict of interest.
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