#
Magnetotransport Studies of Encapsulated Topological Insulator Bi_{2}Se_{3} Nanoribbons

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{2}Se

_{3}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 measurements show improved charge transport characteristics as reduced nanoribbon/substrate interface carrier densities compared to the values obtained for the as-grown nanoribbons on SiO

_{2}substrates.

## 1. Introduction

^{15}cm

^{−3}has been reported in single crystals of BiSbTeSe

_{2}[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].

_{2}Se

_{3}have been reported to be nearly ideal 3D-TIs, practically without any bulk conduction, and with exceptionally high carrier mobilities [14,15]. However, Bi

_{2}Se

_{3}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 Bi

_{2}Se

_{3}nanoribbons.

_{2}Se

_{3}and Bi

_{2}Te

_{3}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 Al

_{2}O

_{3}[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 Bi

_{2}Se

_{3}nanoribbons, where the accumulation layer is formed at the nanoribbon/substrate interface [14,17], other approaches have to be considered.

_{2}Se

_{3}nanoribbons. The choice of selecting ZnO as an encapsulation 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 stoichiometry of Bi

_{2}Se

_{3}, 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 Bi

_{2}Se

_{3}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 chemical potential using a back-gate. These findings are important for the implementation of 3D-TI-nanoribbon-based topological quantum devices.

## 2. Materials and Methods

_{2}Se

_{3}nanoribbons were grown on glass substrates using catalyst-free physical vapor deposition (PVD). The growth procedure is described in detail elsewhere [22]. As-grown nanoribbons were mechanically transferred to prepatterned Si/300 nm SiO

_{2}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.

_{2}chips. ZnO-encapsulated Bi

_{2}Se

_{3}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 Bi

_{2}Se

_{3}and ZnO/Bi

_{2}Se

_{3}nanoribbons. After developing the resist, the samples were etched for 60 s in H

_{2}O/HCl/H

_{2}O

_{2}/CH

_{3}COOH 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.

^{+}/I

^{−}(see Figure 2a) was used as the current electrodes to ensure a uniform flow of current in the nanoribbon, while the remaining electrodes V

_{1}to V

_{8}were employed as the voltage probes. Longitudinal resistance R

_{xx}was recorded using, for example, electrode pair V

_{3}/V

_{7}while the transversal resistance R

_{xy}was measured across the pair V

_{5}/V

_{6}. For this particular nanoribbon device, voltage electrodes V

_{1}to V

_{4}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 SiO

_{2}.

_{2}Se

_{3}nanoribbons, 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

_{2}Se

_{3}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 Bi

_{2}Se

_{3}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 Bi

_{2}Se

_{3}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 Bi

_{2}Se

_{3}, BiO

_{x}(see Figure 1b), which is always present on surfaces of Bi

_{2}Se

_{3}[19].

_{2}Se

_{3}and ZnO/Bi

_{2}Se

_{3}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 ${R}_{xx}\left(B\right)$, additionally impacting the ${R}_{xy}\left(B\right)$ dependence.

_{2}Se

_{3}nanoribbons with thicknesses of ~30–40 nm is about ~3.5 × 10

^{18}cm

^{−3}, and it increases to ~9 × 10

^{18}cm

^{−3}for the 28-nanometer-thin nanoribbon. This peculiar ${n}_{3D}\left(t\right)$ dependence of the catalyst-free PVD-grown Bi

_{2}Se

_{3}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 × 10

^{13}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 ${n}_{3D}\left(t\right)$ for the as-grown ribbons is similar to those previously reported in the literature.

_{2}Se

_{3}nanoribbons are close to those determined for the as-grown nanoribbons with thicknesses of ~30–40 nm, and are also about ~3.5 × 10

^{18}cm

^{−3}. A pronounced increase of ${n}_{3D}$ 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 Bi

_{2}Se

_{3}nanoribbons.

_{2}Se

_{3}nanoribbon on h-BN is plotted in Figure 3a. The applied back-gate voltage directly affects the nanoribbon bottom surface/substrate interface, and at higher ${V}_{g}$ values, some parts of the nanoribbon bulk as well. The slope of the ${n}_{2D}({V}_{g})$ gives an indication of the capacitance of this field-effect device, and C ≈ 6.2 × 10

^{−5}F/m

^{2}. In order to effectively deplete the majority of the initial carriers of ~9 × 10

^{12}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 ${n}_{2D}({V}_{g})$ data are helpful for the study of the properties of the nanoribbon/substrate interface. The ${R}_{xx}\left({V}_{g}\right)$ data of the same ribbon reflect the ${n}_{2D}({V}_{g})$ characteristics (see inset of Figure 3a). The absence of maxima or saturation in the ${R}_{xx}\left({V}_{g}\right)$ indicates that the Fermi energy ${E}_{F}$ remained above the Dirac point in the entire measured ${V}_{g}$ range. To tune the ${E}_{F}$ to the Dirac point, which is important for accessing the charge carriers exclusively from the surface Dirac states, ultra-thin (t ~ 10 nm) Bi

_{2}Se

_{3}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 SiO

_{2}could be used ($\epsilon ~3\u20134$), or, alternatively, one could choose a SrTiO

_{3}substrate, in which the relative dielectric constant at low temperatures is in the order of 10

^{3}–10

^{4}.

^{12}cm

^{−2}and the mobility ${\mu}_{1}=$ 3530 cm

^{2}/Vs, while the carrier density and mobility of band 2 are ${n}_{2}=$ 4.74 × 10

^{12}cm

^{−2}and ${\mu}_{2}=$ 990 cm

^{2}/Vs, respectively. These parameters of the two bands are similar to those estimated for other ZnO-encapsulated Bi

_{2}Se

_{3}nanoribbons (see Table 1).

^{2}/Vs is more than three times larger than the value of ${\mu}_{2}$. For nanoribbon A1b, where the ${\mu}_{1}$ is 4700 cm

^{2}/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 Bi

_{2}Se

_{3}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 ${n}_{TSSdH}$~2.4 × 10

^{12}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 bottom surface/interface ${n}_{BS,Int.}$ carrier density at ${V}_{g}$ = 0 V would be then ${n}_{1}-{n}_{TSSdH}$ ≈ 4 × 10

^{12}cm

^{−2}, which would not be very different from all the ZnO/Bi

_{2}Se

_{3}nanoribbons transferred onto the h-BN (4.03, 3.84 and 4.78 × 10

^{12}cm

^{−2}for the nanoribbons A3t, D3b, and A1b, respectively). These low values corroborate that the ZnO encapsulation of Bi

_{2}Se

_{3}nanoribbons mitigates the creation of an accumulation layer.

^{12}cm

^{−2}. At ${V}_{g}$ = 0 V, the ${n}_{2}$ is 4.74–5.31 × 10

^{12}cm

^{−2}(see Table 1), and if rescaling to the 3D values: 1.46–1.64 × 10

^{18}cm

^{−3}. Peculiarly enough, the second frequency of the aforementioned SdH oscillations of the nanoribbon A1b (Figure S2, SI), with the highest ${\mu}_{2}$, gives 1.44 × 10

^{18}cm

^{−3}. This value is close to the 3D bulk carrier densities determined from band 2.

## 4. Conclusions

_{2}Se

_{3}nanoribbons and the use of h-BN as a substrate help to improve the nanoribbon/substrate interface properties. Thin layers of crystalline ZnO have no degrading impact on the overall transport characteristics of Bi

_{2}Se

_{3}nanoribbons. The 3D charge carrier densities for nanoribbons of different thicknesses are of the same order as the values determined 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 Bi

_{2}Se

_{3}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 Bi

_{2}Se

_{3}nanoribbons stays preserved if ZnO is used as an encapsulation layer. This approach of all-around encapsulation in combination with ultra-thin Bi

_{2}Se

_{3}nanoribbons, transferred to mono or few layer h-BN substrates, would be beneficial to controllably achieve ambipolar transport in Bi

_{2}Se

_{3}.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, H.; Liu, C.-X.; Qi, X.-L.; Dai, X.; Fang, Z.; Zhang, S.-C. Topological insulators in Bi
_{2}Se_{3}, Bi_{2}Te_{3}and Sb_{2}Te_{3}with a single Dirac cone on the surface. Nat. Phys.**2009**, 5, 438–442. [Google Scholar] [CrossRef] - Hsieh, D.; Xia, Y.; Wray, L.; Qian, D.; Pal, A.; Dil, J.H.; Osterwalder, J.; Meier, F.; Bihlmayer, G.; Kane, C.L.; et al. Observation of Unconventional Quantum Spin Textures in Topological Insulators. Science
**2009**, 323, 919–922. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hasan, M.Z.; Kane, C.L. Colloquium: Topological insulators. Rev. Mod. Phys.
**2010**, 82, 3045–3067. [Google Scholar] [CrossRef][Green Version] - Fu, L.; Kane, C.L. Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator. Phys. Rev. Lett.
**2008**, 100, 096407. [Google Scholar] [CrossRef][Green Version] - Fu, L.; Kane, C.L. Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B
**2009**, 79, 161408. [Google Scholar] [CrossRef][Green Version] - Manousakis, J.; Altland, A.; Bagrets, D.; Egger, R.; Ando, Y. Majorana qubits in a topological insulator nanoribbon architecture. Phys. Rev. B
**2017**, 95, 165424. [Google Scholar] [CrossRef][Green Version] - Shiomi, Y.; Nomura, K.; Kajiwara, Y.; Eto, K.; Novak, M.; Segawa, K.; Ando, Y.; Saitoh, E. Spin-Electricity Conversion Induced by Spin Injection into Topological Insulators. Phys. Rev. Lett.
**2014**, 113, 196601. [Google Scholar] [CrossRef][Green Version] - Khokhriakov, D.; Hoque, A.M.; Karpiak, B.; Dash, S.P. Gate-tunable spin-galvanic effect in graphene-topological insulator van der Waals heterostructures at room temperature. Nat. Commun.
**2020**, 11, 3657. [Google Scholar] [CrossRef] - Yasuda, K.; Mogi, M.; Yoshimi, R.; Tsukazaki, A.; Takahashi, K.S.; Kawasaki, M.; Kagawa, F.; Tokura, Y. Quantized chiral edge conduction on domain walls of a magnetic topological insulator. Science
**2017**, 358, 1311–1314. [Google Scholar] [CrossRef][Green Version] - Xue, L.; Zhou, P.; Zhang, C.X.; He, C.Y.; Hao, G.L.; Sun, L.; Zhong, J.X. First-principles study of native point defects in Bi
_{2}Se_{3}. AIP Adv.**2013**, 3, 052105. [Google Scholar] [CrossRef][Green Version] - Kunakova, G.; Surendran, A.P.; Montemurro, D.; Salvato, M.; Golubev, D.; Andzane, J.; Erts, D.; Bauch, T.; Lombardi, F. Topological insulator nanoribbon Josephson junctions: Evidence for size effects in transport properties. J. Appl. Phys.
**2020**, 128, 194304. [Google Scholar] [CrossRef] - Xu, Y.; Miotkowski, I.; Liu, C.; Tian, J.; Nam, H.; Alidoust, N.; Hu, J.; Shih, C.-K.; Hasan, M.Z.; Chen, Y. Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator. Nat. Phys.
**2014**, 10, 956–963. [Google Scholar] [CrossRef][Green Version] - Hong, S.S.; Cha, J.J.; Kong, D.; Cui, Y. Ultra-low carrier concentration and surface-dominant transport in antimony-doped Bi
_{2}Se_{3}topological insulator nanoribbons. Nat. Commun.**2012**, 3, 757. [Google Scholar] [CrossRef][Green Version] - Kunakova, G.; Galletti, L.; Charpentier, S.; Andzane, J.; Erts, D.; Léonard, F.; Spataru, C.D.; Bauch, T.; Lombardi, F. Bulk-free topological insulator Bi
_{2}Se_{3}nanoribbons with magnetotransport signatures of Dirac surface states. Nanoscale**2018**, 10, 19595–19602. [Google Scholar] [CrossRef][Green Version] - Kunakova, G.; Bauch, T.; Palermo, X.; Salvato, M.; Andzane, J.; Erts, D.; Lombardi, F. High-Mobility Ambipolar Magnetotransport in Topological Insulator Bi
_{2}Se_{3}Nanoribbons. Phys. Rev. Appl.**2021**, 16, 024038. [Google Scholar] [CrossRef] - Brahlek, M.; Kim, Y.S.; Bansal, N.; Edrey, E.; Oh, S. Surface versus bulk state in topological insulator Bi
_{2}Se_{3}under environmental disorder. Appl. Phys. Lett.**2011**, 99, 012109. [Google Scholar] [CrossRef][Green Version] - Veyrat, L.; Iacovella, F.; Dufouleur, J.; Nowka, C.; Funke, H.; Yang, M.; Escoffier, W.; Goiran, M.; Eichler, B.; Schmidt, O.G.; et al. Band Bending Inversion in Bi
_{2}Se_{3}Nanostructures. Nano Lett.**2015**, 15, 7503–7507. [Google Scholar] [CrossRef][Green Version] - Brahlek, M.; Koirala, N.; Bansal, N.; Oh, S. Transport properties of topological insulators: Band bending, bulk metal-to-insulator transition, and weak anti-localization. Solid State Commun.
**2015**, 215–216, 54–62. [Google Scholar] [CrossRef][Green Version] - Kong, D.; Cha, J.J.; Lai, K.; Peng, H.; Analytis, J.G.; Meister, S.; Chen, Y.; Zhang, H.-J.; Fisher, I.R.; Shen, Z.-X.; et al. Rapid Surface Oxidation as a Source of Surface Degradation Factor for Bi
_{2}Se_{3}. ACS Nano**2011**, 5, 4698–4703. [Google Scholar] [CrossRef][Green Version] - Lang, M.; He, L.; Xiu, F.; Yu, X.; Tang, J.; Wang, Y.; Kou, X.; Jiang, W.; Fedorov, A.V.; Wang, K.L. Revelation of Topological Surface States in Bi
_{2}Se_{3}Thin Films by In Situ Al Passivation. ACS Nano**2012**, 6, 295–302. [Google Scholar] [CrossRef] [PubMed] - Ngabonziza, P.; Stehno, M.P.; Myoren, H.; Neumann, V.A.; Koster, G.; Brinkman, A. Gate-Tunable Transport Properties of In Situ Capped Bi
_{2}Te_{3}Topological Insulator Thin Films. Adv. Electron. Mater.**2016**, 2, 1600157. [Google Scholar] [CrossRef][Green Version] - Andzane, J.; Kunakova, G.; Charpentier, S.; Hrkac, V.; Kienle, L.; Baitimirova, M.; Bauch, T.; Lombardi, F.; Erts, D. Catalyst-free vapour–solid technique for deposition of Bi2Te3and Bi2Se3nanowires/nanobelts with topological insulator properties. Nanoscale
**2015**, 7, 15935–15944. [Google Scholar] [CrossRef] - Singh, A. Growth, Structural and Electrical Characterization of Topological Dirac Materials. Ph.D. Thesis, University of Cambridge, Cambridge, UK, 28 June 2018. [Google Scholar]
- Ghosh, R.; Kundu, S.; Majumder, R.; Roy, S.; Das, S.; Banerjee, A.; Guria, U.; Bera, M.K.; Subhedar, K.M.; Chowdhury, M.P.; et al. One-pot synthesis of multifunctional ZnO nanomaterials: Study of superhydrophobicity and UV photosensing property. Appl. Nanosci.
**2019**, 9, 1939–1952. [Google Scholar] [CrossRef] - Ashcroft, N.W.; Mermin, N.D. Solid State Physics; Harcourt College Publishers: San Diego, CA, USA, 1976. [Google Scholar]
- Bansal, N.; Kim, Y.S.; Brahlek, M.; Edrey, E.; Oh, S. Thickness-Independent Transport Channels in Topological InsulatorBi
_{2}Se_{3}Thin Films. Phys. Rev. Lett.**2012**, 109, 116804. [Google Scholar] [CrossRef] [PubMed][Green Version] - Qu, D.-X.; Hor, Y.S.; Xiong, J.; Cava, R.J.; Ong, N.P. Quantum Oscillations and Hall Anomaly of Surface States in the Topological Insulator Bi
_{2}Te_{3}. Science**2010**, 329, 821–824. [Google Scholar] [CrossRef] [PubMed] - Kunakova, G.; Meija, R.; Andzane, J.; Malinovskis, U.; Petersons, G.; Baitimirova, M.; Bechelany, M.; Bauch, T.; Lombardi, F.; Erts, D. Surface structure promoted high-yield growth and magnetotransport properties of Bi
_{2}Se_{3}nanoribbons. Sci. Rep.**2019**, 9, 11328. [Google Scholar] [CrossRef] [PubMed][Green Version]

**Figure 1.**(

**a**) Schematic representation of catalyst-free PVD-synthesized free-standing Bi

_{2}Se

_{3}nanoribbons on glass substrate; (

**b**) false-colored HR-TEM image of a Bi

_{2}Se

_{3}nanoribbon after encapsulation with a thin layer of ZnO.

**Figure 2.**(

**a**) SEM image of a Bi

_{2}Se

_{3}nanoribbon Hall-bar device; (

**b**) Hall resistance ${R}_{xy}\left(B\right)$ for the ZnO/Bi

_{2}Se

_{3}nanoribbon device A3t (see Table S1), measured at back-gate voltage ${V}_{g}$ = 0 V. The inset shows anti-symmetrized ${R}_{xy}\left(B\right)$ 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 Bi

_{2}Se

_{3}and ZnO/Bi

_{2}Se

_{3}nanoribbons, plotted versus the nanoribbon thickness. In the case of the ZnO/Bi

_{2}Se

_{3}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 3.**(

**a**) Charge carrier density ${n}_{2D}(={n}_{3D}t)$ as a function of the back-gate voltage ${V}_{g}$. Here, ${n}_{2D}$ is calculated from the anti-symmetrized ${R}_{xy}\left(B\right)$ data in the 0–2.5 T range. ${R}_{xy1}$ and ${R}_{xy2}$ 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/m

^{2}. In the inset—longitudinal resistance ${R}_{xx}$ as a function of the ${V}_{g}$; (

**b**) conductance tensor element ${G}_{xy}\left(B\right)$ at different applied ${V}_{g}$, fitted with the two-carrier model, inset shows fitted ${G}_{xx}\left(B\right)$ curves; (

**c**) from the two-carrier model extracted parameters of the two bands: carrier densities ${n}_{1}$; ${n}_{2}$, and mobilities ${\mu}_{1}$; ${\mu}_{2}$ (in the inset) versus the back-gate voltage. All the data shown correspond to the ZnO/Bi

_{2}Se

_{3}nanoribbon A3t.

Surfaces (Band 1) | Bulk (Band 2) | Top Surface * | Bulk * | ||||
---|---|---|---|---|---|---|---|

ZnO/Bi_{2}Se_{3} NR on h-BN: | t_{NR}, nm | ${\mathit{n}}_{1}$ | ${\mathit{\mu}}_{1}$ | ${\mathit{n}}_{2}$ | ${\mathit{\mu}}_{2}$ | ${\mathit{n}}_{2\mathit{D},\mathit{S}\mathit{d}\mathit{H}}$ | ${\mathit{n}}_{3\mathit{D},\mathit{S}\mathit{d}\mathit{H}}$ |

A3t | 29 | 6.43 × 10^{12} | 3540 | 4.74 × 10^{12}/1.64 × 10^{18} | 930 | ||

A1b | 35 | 7.18 × 10^{12} | 4700 | 5.31 × 10^{12}/1.52 × 10^{18} | 2052 | 2.40 × 10^{12} | 1.44 × 10^{18} |

D3b | 34 | 6.24 × 10^{12} | 4800 | 4.99 × 10^{12}/1.46 × 10^{18} | 1350 | ||

Bi_{2}Se_{3} NR on SiO_{2},sample E5 [14] | 30 | 15.0 × 10^{12} ** | 2.40 × 10^{12} | ||||

Bi_{2}Se_{3} NR on SiO_{2},sample BR3-10R2 [14] | 63 | - | 2.50 × 10^{12} | 1.70 × 10^{18} | |||

Bi_{2}Se_{3} NR on SiO_{2},sample E [17] | 79 | 13.0 × 10^{12} * | 2.90 × 10^{12} | 6.60 × 10^{17} | |||

Bi_{2}Se_{3} NR on STO,sample B51-10 [15] | 9 | 5.55 × 10^{12} ** | 1232 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kunakova, G.; Kauranens, E.; Niherysh, K.; Bechelany, M.; Smits, K.; Mozolevskis, G.; Bauch, T.; Lombardi, F.; Erts, D. Magnetotransport Studies of Encapsulated Topological Insulator Bi_{2}Se_{3} Nanoribbons. *Nanomaterials* **2022**, *12*, 768.
https://doi.org/10.3390/nano12050768

**AMA Style**

Kunakova G, Kauranens E, Niherysh K, Bechelany M, Smits K, Mozolevskis G, Bauch T, Lombardi F, Erts D. Magnetotransport Studies of Encapsulated Topological Insulator Bi_{2}Se_{3} Nanoribbons. *Nanomaterials*. 2022; 12(5):768.
https://doi.org/10.3390/nano12050768

**Chicago/Turabian Style**

Kunakova, Gunta, Edijs Kauranens, Kiryl Niherysh, Mikhael Bechelany, Krisjanis Smits, Gatis Mozolevskis, Thilo Bauch, Floriana Lombardi, and Donats Erts. 2022. "Magnetotransport Studies of Encapsulated Topological Insulator Bi_{2}Se_{3} Nanoribbons" *Nanomaterials* 12, no. 5: 768.
https://doi.org/10.3390/nano12050768