Quantitative analysis of weak antilocalization effect of topological

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Quantitative analysis of weak antilocalization effect of topological surface states in topological insulator BiSbTeSe

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Hui Li, Huan-Wen Wang, Yang Li, Huachen Zhang, Shuai Zhang, Xing-Chen Pan, Bin Jia, Fengqi Song, and Jiannong Wang Nano Lett., Just Accepted Manuscript • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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Quantitative analysis of weak antilocalization effect of topological surface states in topological insulator BiSbTeSe2 Hui Li1, Huan-Wen Wang1, Yang Li1, Huachen Zhang1, Shuai Zhang2,3, Xing-Chen Pan2,3, Bin Jia2,3, Fengqi Song2,3, Jiannong Wang1,4* 1Department

of Physics, the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China 2National

Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing, 210093, China 3Collaborative

Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China 4William

Mong Institute of Nano Science and Technology, the Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China * Correspondence and requests for materials should be addressed to J. W. (email: [email protected], Tel: (852) 2358 7497, Fax: (852) 2358 1652).

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Abstract. Quantitative analysis of the weak antilocalization (WAL) effect of topological surface states in topological insulators is of tremendous importance. The major obstacle to achieve accurate results is how to eliminate the contribution of the anisotropic magnetoconductance of bulk states when the Fermi level lies in bulk bands. Here, we demonstrate that we can analyze quantitatively and accurately the WAL effect of topological surface states in topological insulator, BiSbTeSe2 (BSTS), by measuring the anisotropic magnetoconductance. The anomalous conductance peaks induced by the WAL effect of topological surface states of BSTS together with the anisotropic magnetoconductance of bulk states have been observed. By subtracting the anisotropic magnetoconductance of bulk states, we are able to analysis the WAL effect of topological surface states using Hikami-Larkin-Nagaoka expression. Our findings offer an alternative strategy for the quantitative exploration of the WAL effect of topological surface states in topological insulators. Keywords: Topological insulators, Topological surface states, Weak antilocalization effect, Anisotropic magnetoconductance, Hikami-Larkin-Nagaoka expression

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Topologically protected surface states with gapless and helical Dirac cone is the most remarkable property of three-dimensional (3D) topological insulators.1-3 Electrons’ spin in topological surface states is locked to its momentum, which gives rise to a nontrivial  Berry phase after completing a time-reversed self-crossing path adiabatically in the quantum diffusion regime.4,5 This non-trivial  Berry phase could lead to quantum correction to the classical electronic conductivity in low magnetic fields (B-fields), manifesting itself as a weak antilocalization (WAL) effect.6-10 The observations of WAL effect of topological surface states have been wide reported in 3D topological insulators recently.

11-16

In general, assuming the

magnetoconductance of bulk states being isotropic, the WAL effect of 2D topological surface states has been analyzed quantitatively using Hikami-Larkin-Nagaoka (HLN) equation after subtracting the magnetoconductance of bulk states measured in the parallel orientations (B-field applied parallel to the current). 17 However, recent studies show that the magnetoconductance of bulk states is highly anisotropic.

18-20

Therefore, an

alternative method, which can eliminate the contribution of bulk state more accurately, is highly desirable for analyzing the WAL effect of topological surface states quantitatively. In this study, we show an alternative approach for the quantitative analysis of the WAL effect of topological surface states in a more accurate way by measuring anisotropic magnetoconductance of topological insulator BiSbTeSe2 (BSTS). The anomalous conductance peaks in the parallel orientations are observed in anisotropic magnetoconductance curves, which are originated from the WAL effect of topological surface states of BSTS. By subtracting the anisotropic magnetoconductance of bulk states, the WAL effect of topological surface states can be well described by the HLN expression. Fig. 1a shows the optical image of a typical BSTS device. The width w is about 6.7 μm, and the distance l between two voltage-probe for Vxx measurement is about 2 μm. The temperature (T) dependence of the longitudinal resistance (Rxx) of the BSTS device is shown in Fig. 1b. With decreasing temperature, the device changes from a metallic behavior to an insulating one, with a minimum resistance appearing around 220 K. Fig. 3


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1(c) shows the magnetoresistance (MR), defined as

, of

BSTS device measured at 2 K with the angle θ between the applied magnetic field (Bfield) and z-direction (see inset) being set at 0o and 90o. A sharp resistance cusp in the low B-fields appears in both perpendicular orientation (θ = 0o, BI, black curve in Fig. 1c) and parallel orientation (θ = 90o, B//I, red curve in Fig. 1c), which is a signature of the WAL effect in topological insulators. The observation of the WAL effect in both orientations suggests existing of a three-dimensional component of the WAL effect in BSTS device. It implies that both topological surface states and bulk states contribute to the WAL effect. However, when the B-field further increases above 3.4 T, the MR measured in parallel orientation decreases, and a negative MR up to about -7.5% at 16 T is observed. In contrast, the MR increases monotonically in the perpendicular orientation with a positive MR of about 30% at 16 T. The negative MR in the parallel orientation is also observed in our previous studies.11,16 However, its possible origins remain a challenge and is currently still under investigation. Following previous approach11 and assuming the WAL effect from bulk states being isotropic, the WAL effect induced by the topological surface states of BSTS can be revealed

by

subtracting

the , where

Fig. 1(d) shows

contribution

of

bulk

states

using

is the longitudinal sheet magnetoconductance.

as a function of normal component of B-fields, i.e. Bcosθ, measured

in the low B-fields at 2 K and at different tilting angles. All the curves coincide with each other at very low B-fields, indicating a 2D nature of the WAL effect induced by the topological surface states. This coincidence of the Gxx curves also indicate that the Zeeman effect could be neglected in our devices (see Supplementary Information section 1 for details). Generally, in a strong spin-orbit interaction regime when the inelastic scattering time

is much longer than the spin-orbit scattering time

scattering time

, the quantum correction to the 2D magnetoconductivity can be

described by the HLN equation:17,21 where e is the elementary charge,

and the elastic

, is the reduced Planck constant, 4


is the digamma

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function of argument z, and

is the phase coherence characteristic field with

being the phase coherence length. The  equals to 1, 0, -1/2 for the orthogonal, unitary, and symplectic cases, respectively.17,22 For the WAL effect induced by topological surface states in topological insulators, the  should be equal to -1/2 for one topological surface state due to the existence of non-trivial  Berry phase.15,23 However, the  can vary from -0.5 to -1.0 when the top and bottom surface states are weakly coupled.24 The red curve in Fig. 1d shows the HLN fitting result with  = -0.6 and

= 240 nm,

suggesting there is mainly one surface state contributing to the 2D WAL effect in our BSTS device. Fig. 2a shows the anisotropic magnetoconductance (AMC) of the BSTS device measured in out-of-plane (x-z plane, see inset of Fig. 1b) tilting at 2 K and at 2 T. The measured longitudinal sheet conductance Gxx(θ) shows a 180° periodic angular dependence with the longitudinal sheet conductance minima and maxima appearing at perpendicular orientation (θ = 0o, 180o) and parallel orientation (θ = 90o, 270o), respectively. A sharp conductance peak emerges when the device is in parallel orientations. The conventional AMC follows an expression given by curve in Fig. 2a), as discussed in our previous studies.25 The

and

(red are the measured

conductance in the parallel and perpendicular orientations, respectively. As it can be seen, the observed sharp conductance peak in the parallel orientations cannot be accounted for. On the other hand, we notice that such a conductance peak was ascribed to the 2D topological surface state induced feature following a curve in Fig. 2a).26 The

and

relationship (green

are the measured conductance in the parallel and

perpendicular orientations, respectively. However, as shown in Fig. 2a, the sharp conductance peaks observed in our BSTS devices also deviate from this relationship. We believe that the anomalous conductance peaks are due to the WAL effect of topological surface states of the BSTS device. To analyze quantitatively the measured anomalous AMC in our BSTS device, we propose to include both the conventional AMC term and 2D surface states WAL contribution, which is then given by, 5


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(1) + We consider the first term in Equation (1) is the AMC originating from the BSTS bulk states and take the measured

value in the analysis because in parallel orientation

there is no contribution from 2D surface states while

is a fitting parameter. The

second term is the correction of the WAL effect of the 2D surface states of BSTS. The red curve in Fig. 2b is the fitting results using Equation (1) with 0.59 and

= 1.012 mS,  = -

= 163 nm. The AMC of bulk states, i.e. the first term in Equation (1), is

plotted as the blue curve in Fig. 2b. As it can be seen, the Equation (1) has an excellent agreement with experimental measurements, indicating the observed anomalous conductance peaks in BSTS in the parallel orientations is indeed originating from the WAL effect of the 2D topological surface states of BSTS. Fig. 2c shows the

,

which is the difference between Gxx(θ) in Fig. 2b and the blue curve in Fig. 2b (the first term of Equation (1)), at 2 K and at 2 T. It is clear, the

can be well fitted by the

HLN expression (the second term of Equation (1)) with  = -0.6 and

= 163 nm (red

curve in Fig. 2c). This analysis demonstrates that the measurements of AMC of topological insulators provide an alternative path to the quantitative analysis of the WAL effect of topological surface states. It is noted that the

estimated from Fig. 2b and Fig.

2c (163 nm) is smaller than that from Fig. 1d (about 240 nm). Such a large discrepancy is due to the anisotropic magnetoconductance of bulk states of topological insulator, which has not been considered in the fitting of Fig. 1d. In addition, the surface states contribution ratio, defined as

, is very small (~ 2.8% at 2 T), as shown in

Fig. 2d. Such a small surface states contribution ratio further demonstrates that the fully elimination of the contribution of anisotropic magnetoconductance of bulk states is necessary for the accurate analysis of the WAL effect of the surface states. The magnitude of surface state contribution ratio increases monotonically with increasing B-

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fields and is up to about 3.8% at 8 T (Fig. 2d), which is due to the gradually enhanced WAL effect of surface states with increasing B-fields. Fig. 3a shows the measured AMC of the BSTS device at 2 T and at different temperatures indicated. With increasing temperature, the AMC magnitude, defined as , decreases monotonically (see Supplementary Information section 2). The anomalous conductance peaks in the parallel orientations become invisible at and above 50 K. This temperature dependence of anomalous conductance peaks is consistent with the temperature dependence of WAL effect in MR measurements as shown in Fig. 3b. The WAL effect is clearly visible at temperatures below 20 K and eventually disappear above 50 K. This further indicates that the WAL effect of the 2D topological surface states is responsible to the occurrence of the anomalous conductance peaks in the parallel orientations of AMC in topological insulator BSTS. Besides, the magnitude of surface states contribution ratio decreases from ~ 2.8% to ~ 1.6% as temperature increases from 2 K to 20 K, as shown in Fig. 3c. To verify further that the origin of the anomalous conductance peaks in parallel orientations of AMC curves in BSTS is from the WAL effect of topological surface states, we have measured the magnetotransport behavior of a BSTS device with tunable carrier densities using ionic liquid gating technique (see Methods for experimental details). A schematic device is presented in the inset of Fig. 4a. Fig. 4a shows the Rxx-T curves of the device measured at various gate bias (VG) indicated. When applying a positive gate voltage (VG = 1 V or 2 V) or zero gate voltage (VG = 0 V), the BSTS device exhibit a metallic transport behavior in general. The small resistance upturn below 35 K is likely due to electron-electron interaction.12,16.27 However, when a negative gate voltage is applied (VG = -2 V), the BSTS device shows an insulating behavior similar to that observed in Fig. 1b, which is probably due to topological surface states dominated the transport properties. The sheet carrier density estimated from the linear fitting of the Hall measurements (Fig. 4b) at different VG is summarized in Fig. 4c. As it can be seen, the electron density decreases monotonically from about 2.4×1012 /cm2 at VG = 2 V to about 0.8×1012 /cm2 at VG = -2 V. This suggests that the Fermi level moves down towards the Dirac point and the weight of the topological surface states transport increases as VG 7


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decreases, which is consistent with the angle-resolved photoemission spectroscopy (ARPES) measurements (see Supplementary Information section 3 for details). As a result, the Rxx-T dependences change from metallic to insulating as VG decreases from 2 V to -2 V as shown in Fig. 4a. The MR curves of the BSTS devices measured in the perpendicular orientation and at various VG are plotted in Fig. 4d. An evident WAL effect with a sharp resistance cusp in low B-fields is observed when VG = -2 V (green curve in Fig. 4d), which is believed to be originated from topological surface states of the BSTS. The WAL effect can be well fitted by the HLN equation with  = -0.53 and

of about

211 nm (see inset). On the other hand, the characteristics of the MR curves is almost the same as VG changes from 0 V to 2 V. It shows a quadratic B-field dependence in low Bfields (< 3 T), but a roughly linear B-field dependence in high B-fields (> 8 T). Fig. 5a shows the VG dependent AMC measurements of BSTS device at T = 2 K and B = 3 T. Similar to the previous observations in Fig. 2a, the sheet conductance Gxx shows a 180° periodic angular dependence. However, the anomalous conductance peaks in parallel orientations only occur at VG = -2 V, which is consistent with the WAL effect occurrence in the MR measurements in Fig. 4d. This indicates further that the anomalous conductance peaks in AMC curves indeed originate from the WAL effect of topological surface states. Fig. 5b and 5c show the measured AMC at VG = -2 V and 3 T together with fitting results using Equation (1) with

= 0.307 mS,  = -0.47 and

= 237.8 nm (solid

curves). The AMC of bulk states, i.e. the first term in Equation (1), is plotted as the blue curve in Fig. 5b. The

, which is the difference between Gxx(θ) in Fig. 5b and the

blue curve in Fig. 5b (the first term of Equation (1)), can be well fitted by the HLN expression (the second term of Equation (1)) with  = -0.47 and

= 237.8 nm (red curve

in Fig. 5c). It is noted that the fitting results using Equation (1) yield  = -0.47 and

=

237.8 nm, which are close to the value obtained from the WAL effect fitting in the inset of Fig. 4d because of the relatively large surface states contribution ratio of about 8.53%. In contrast, the anomalous conductance peaks are invisible at VG= 0, 1 V, and 2 V, but AMC curves can be well fitted by the first term of Equation (1) (the red curves in Fig. 5a), because bulk states of the BSTS dominate the magnetotransport behavior. 8


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In conclusion, we have performed systematic studies of the quantitative and accurate analysis of the WAL effect of topological surface states in topological insulator, BiSbTeSe2 (BSTS) devices by measuring anisotropic magnetoconductance. The anomalous conductance peaks in the parallel orientations originating from the WAL effect of topological surface states of BSTS together with the anisotropic magnetoconductance of bulk states have been observed. The WAL effect of topological surface states has been quantitatively and accurately analyzed further using HLN expression by eliminating the contribution of the anisotropic magnetoconductance of bulk states. Our findings provide an alternative avenue for the quantitative exploration of the WAL effect of topological surface states in topological insulators in a more accurate way.

Devices

fabrication

and

magnetoresistance

measurements.

To

study

the

magnetotransport properties, a Hall-bar geometry were patterned through standard electron-beam lithography and lift-off techniques. Au/Cr electrodes with thickness of 100 nm/10 nm were deposited using thermal evaporation methods. The magnetotransport properties of the devices were then measured in a Quantum Design Physical Property Measurement System using standard lock-in technique. Ionic gating of BSTS devices. The ionic gel was prepared by following the previous studies.28-30 0.3 g LiClO4 (Sigma Aldrich) and 1g PEO (Mw = 100,000, Sigma Aldrich) powder were dissolved in 15 ml anhydrous methanol (Alfa Aesar) by stirring overnight at 50 °C. After dropping the electrolyte on the devices, the devices were then annealed at 360 K in vacuum for half an hour to release tension and remove moisture before the gate sweep.

References (1) Fu, L.; Kane, C. L.; Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 2007, 98, 106803. (2) Hasan M. Z.; Kane C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 2010, 82, 3045.

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(3) Qi, X. L.; Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 2011, 83, 1057. (4) Lu, H. Z.; Shi, J.; Shen, S. Q. Competition between weak localization and antilocalization in topological surface states. Phys. Rev. Lett. 2011, 107, 076801. (5) Xu, Y.; Miotkowski, I.; Chen, Y. P. Quantum transport of two-species Dirac fermions in dual-gated three-dimensional topological insulators. Nat. Commun. 2016, 7, 11434. (6) Bergmann, G. Weak localization in thin films: a time-of-flight experiment with conduction electrons. Phys. Rep. 1984, 107, 1-58. (7) McCann, E.; Kechedzhi, K.; Fal’ko, V. I.; Suzuura, H.; Ando, T.; Altshuler, B. L. Weak-localization magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 2006, 97, 146805. (8) Garate, I.; Glazman, L. Weak localization and antilocalization in topological insulator thin films with coherent bulk-surface coupling. Phys. Rev. B 2012, 86, 035422. (9) Li, H.; He, H.; Lu, H.Z.; Zhang, H.; Liu, H.; Ma, R.; Fan, Z.; Shen, S.Q.; Wang, J. Negative magnetoresistance in Dirac semimetal Cd3As2. Nat. Commun. 2016, 7, 10301. (10) Gopal, R. K.; Singh, S.; Mandal, A.; Sarkar, J.; Mitra, C. Topological delocalization and tuning of surface channel separation in Bi2Se2Te Topological Insulator Thin films. Sci. Rep. 2017, 7, 4924. (11) He, H. T.; Wang, G.; Zhang, T.; Sou, I. K.; Wong, G. K.; Wang, J. N.; Lu, H. Z.; Shen, S. Q.; Zhang, F. C. Impurity effect on weak antilocalization in the topological insulator Bi2Te3. Phys. Rev. Lett. 2011, 106, 166805. (12) Liu, H. C.; Lu, H. Z.; He, H. T.; Li, B.; Liu, S. G.; He, Q. L.; Wang, G.; Sou, I. K.; Shen, S.Q.; Wang, J. Tunable interaction-induced localization of surface electrons in antidot nanostructured Bi2Te3 thin films. ACS Nano 2014, 8, 9616-9621. (13) Tu, N. H.; Tanabe, Y.; Satake, Y.; Huynh, K. K.; Le, P. H.; Matsushita, S. Y.; Tanigaki, K. Large-Area and Transferred High-Quality Three-Dimensional Topological Insulator Bi2–xSbxTe3–ySey Ultrathin Film by Catalyst-Free Physical Vapor Deposition. Nano Lett. 2017, 17, 2354-2360.

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(14) Liu, Y.; Tang, M.; Meng, M.; Wang, M.; Wu, J.; Yin, J.; Zhou, Y.; Guo Y.; Tan C.; Dang W.; Huang, S. Xu, H. Q.; Wang Y.; Peng, H. Epitaxial growth of ternary topological insulator Bi2Te2Se 2D crystals on mica. Small 2017, 13, 1603572. (15) Shrestha, K.; Chou, M.; Graf, D.; Yang, H. D.; Lorenz, B.; Chu, C. W. Extremely large nonsaturating magnetoresistance and ultrahigh mobility due to topological surface states in the metallic Bi2Te3 topological insulator. Phys. Rev. B 2017, 95, 195113. (16) Zhang, H.; Li, H.; Wang, H.; Cheng, G.; He, H.; Wang, J. Linear positive and negative magnetoresistance in topological insulator Bi2Se3 flakes. Appl. Phys. Lett. 2018, 113, 113503. (17) Hikami, S.; Larkin, A. I.; Nagaoka, Y. Spin-orbit interaction and magnetoresistance in the two dimensional random system. Prog. Theor. Phys. 1980, 63, 707-710. (18) Wang, J.; Li, H.; Chang, C.; He, K.; Lee, J. S.; Lu, H.; Sun Y.; Ma X.; Samarth, N.; Shen, S.Q.; Xue, Q.; Xie, M.; Chan, M. H. W.; Anomalous anisotropic magnetoresistance in topological insulator films. Nano Research, 2012, 5, 739-746. (19) Sulaev, A.; Zeng, M.; Shen, S. Q.; Cho, S. K.; Zhu, W. G.; Feng, Y. P.; Eremeev, S.V.; kawazoe, Y.; Shen, L.; Wang, L. Electrically tunable in-plane anisotropic magnetoresistance in topological insulator BiSbTeSe2 nanodevices. Nano Lett. 2015, 15, 2061-2066. (20) Wiedmann, S.; Jost, A.; Fauqué, B.; van Dijk, J.; Meijer, M. J.; Khouri, T.; Pezzini, S.; Grauer, S.; Schreyeck, S., Brune, C.; Buhmann, H.; Molenkamp, L. W.; Hussey, N. E. Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator Bi2Se3. Phys. Rev. B 2016, 94, 081302. (21) McCann, E.; Kechedzhi, K.; Fal’ko, V. I.; Suzuura, H.; Ando, T.; Altshuler, B. L. Weak-localization magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 2006, 97, 146805. (22) Dyson F. J. Statistical theory of the energy levels of complex systems. I. J. Math. Phys. 1962, 3, 140-156. (23) Chen, J.; Qin, H. J.; Yang, F.; Liu, J.; Guan, T.; Qu, F. M.; Zhang, G. H.; Shi, J. R.; Xie, X. C.; Yang, C. L.; Wu, K. H.; Li, Y. Q.; Lu, L. Gate-voltage control of 11


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chemical potential and weak antilocalization in Bi2Se3. Phys. Rev. Lett. 2010, 105, 176602. (24) Zhang, G.; Qin, H.; Chen, J.; He, X.; Lu, L.; Li, Y.; Wu, K. Growth of topological insulator Bi2Se3 thin films on SrTiO3 with large tunability in chemical potential. Adv. Funct. Mater. 2011, 21, 2351-2355. (25) Li, H.; Wang, H. W.; He, H.; Wang, J.; Shen, S. Q. Giant anisotropic magnetoresistance and planar Hall effect in the Dirac semimetal Cd3As2. Phys. Rev. B 2018, 97, 201110. (26) Tang, H.; Liang, D.; Qiu, R. L.; Gao, X. P. Two-dimensional transport-induced linear magneto-resistance in topological insulator Bi2Se3 nanoribbons. ACS Nano 2011, 5, 7510-7516. (27) Wang, J.; DaSilva, A. M.; Chang, C. Z.; He, K.; Jain, J. K.; Samarth, N.; Ma, X. C.; Xue, Q. K.; Chan, M. H. W. Evidence for electron-electron interaction in topological insulator thin films. Phys. Rev. B 2011, 83, 245438. (28) Fullerton-Shirey, S. K.; Maranas, J. K. Effect of LiClO4 on the structure and mobility of PEO-based solid polymer electrolytes. Macromolecules 2009, 42, 2142– 2156. (29) Efetov, D. K.; Kim, P. Controlling electron–phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 2010, 105, 256805. (30) Yu, Y.; Yang, F.; Lu, X. F.; Yan, Y. J.; Cho, Y. H.; Ma, L.; Niu, X.; Kim, S.; Son, Y.-W.; Feng, D.; Li, S.; Cheong, S.-K.; Chen, X. H.; Zhang, Y. Gate-tunable phase transitions in thin flakes of 1T-TaS2. Nat. Nanotech. 2015, 10, 270.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Zeeman effect on the topological surface states in BiSbTeSe2 system, temperature dependence of the AMC magnitude, ARPES measurements of the BiSbTeSe2 single crystals, the estimation of error bar of the surface states contribution ratio, and references 12


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Author contributions J.W. conceived the project; S.Z., B.J., and Q.S grown the BSTS bulk single crystals; H.L. fabricated BSTS devices and performed magnetotransport experiments with support from Y.L. and H.Z.; X.P. performed the ARPES measurements. H.-W.W. provided theoretical support; All authors analyzed experimental data and wrote the manuscript.

Acknowledgements This work was supported in part by the Research Grants Council of the Hong Kong SAR under Grant Nos. 16301418 and C6013-16E.

Additional information Competing financial interests: The authors declare no competing financial interests.

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Figure Captions Figure 1. BSTS devices and magnetotransport characteristics. (a) The optical image of the BSTS device. (b) The measured resistance (R) as a function of temperature (T) at zero magnetic field. (c) The magnetoresistance (MR) measured at 2 K with applied magnetic field (B) direction changing from perpendicular ( = 0o) to parallel ( = 90o) to the current (I) direction in the x-z plane. (d) Magnetoconductance as a function of the normal component of B-fields measured in the low B-fields at 2 K and at different tilting angles  . The solid red line is fitting curve using Hikami-Larkin-Nagaoka (HLN) equation. Figure 2. B-field dependence of anisotropic magnetoconductance (AMC) in x-z plane titling. (a) The angular dependence of the longitudinal sheet conductance Gxx at T = 2 K and B = 2 T. The green solid line is the fitting curve using relationship. The red solid line is the fitting curve of the first term of Equation (1) using measured

and

values. (b) The angular dependence of the longitudinal sheet

conductance Gxx at B = 2 T and T =2 K. The red solid line is the fitting curve using Equation (1) with

= 1.012 mS,  = -0.59 and

= 163 nm. The blue solid line is the

fitting curve of the first term of Equation (1) using measured

value and fitted

value

of about 1.012 mS. (c) The angular dependence of the Gxx, which is the difference between Gxx(θ) in Figure 2(b) and the blue curve in Figure 2(b) (the first term of Equation (1)), at T = 2 K and B = 2 T. The red solid line is the fitting curve using HLN expression with  = -0.59 and contribution ratio,

= 163 nm. (d) B-fields dependence of the surface states , at T = 2 K. The estimation of the standard error for

the surface states contribution ratio is detailed in the Supplementary Information section 4.

14


Page 15 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3. Temperature dependence of anisotropic magnetoconductance (AMC) in xz plane titling. (a) The AMC of BSTS device at 2 T and at different temperatures indicated. The red solid lines are the fitting curves using Equation (1), where  = -0.59 and

is of 163 nm, 118 nm and 76 nm for T = 2 K, 10 K, and 20 K, respectively, and

 = 0 for T ≥ 50 K. (b) Magnetoresistance curves measured at different temperatures indicated, where the weak antilocalization effect of the BSTS at low B-fields is observed at T < 50 K. (c) The surface states contribution ratio,

, as a function of

temperature measured at B = 2 T. The estimation of the standard error for the surface states contribution ratio is detailed in the Supplementary Information section 4. Figure 4. Gate voltage tunable magnetotransport properties of BSTS device. (a) The R-T curves of BSTS device at zero magnetic field and at different gate voltages. (b) The Hall resistance (Rxy) as a function of B-fields measured at different gate voltages. The red lines are the linear fitting results. (c) The carrier density of the BSTS device as a function of gate voltage. (d) Magnetoresistance (MR) curves of BSTS devices at low B-fields and at different gate voltages. Inset shows the WAL effect measured in the low B-fields at VG = -2 V and T = 2 K. The solid red line is fitting curve using HLN expression with  = 0.53 and

of about 211 nm.

Figure 5. Gate voltage tunable AMC of BSTS device. (a) The AMC curves of the BSTS device at 3 T, 2 K and at different gate voltages indicated. The red solid lines are the fitting curves using Equation (1) with measured 0.47,

and fitted

= 0.307 mS,  = -

of about 237.8 nm for VG = -2 V and  = 0 for others gate voltages. (b) The

angular dependence of the longitudinal sheet conductance Gxx for VG = -2 V. The red solid line is the fitting curve using Equation (1) with

= 0.307 mS,  = -0.47 and

of

about 237.8 nm. The blue solid line is the fitting curve of the first term of Equation (1) using measured

value and fitted

value of 0.307 mS. (c) The angular dependence of

the Gxx, which is the difference between Gxx(θ) in Figure 5(b) and the blue curve in 15


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5(b) (the first term of Equation (1)). The red solid line is the fitting curve using HLN expression with  = -0.47 and

of about 237.8 nm.

16


Page 16 of 22

Page 17 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 1

17


Nano Letters

b

T=2K

d 4.0

1.02

Gxx() (mS)

1.02 B = 2 T

1.01

c

0.99

Gxx() (S)

0.98

1.00

G//G/(G+(G//-G) cos )

0.98

2 K, 2 T

1st term of Eq. 1 - Measured

0

90

180

 (o )

270

360

T=2K

3.8

1.00 Eq. 1 - Fitting 1st term of Eq. 1 - Fitting

0

2 K, 2 T

-10

Gxx()/Gxx()100%

a

Gxx() (mS)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 22

3.6 3.4 3.2 3.0

-20 2.8 -30

Gxx

0

90

2nd term of Eq. 1 - Fitting

180

270

360

 (o )

Figure 2

18


2.6

2

4

6 B (T)

8

Page 19 of 22

a

B=2T

b

200 K

Out-of-plane 6

1.30

5

1.25 100 K 1.20

4

MR (%)

300 K

3

50 K

1 0 -2

1.15

1.10

20 K

1.05

10 K

1.00

2K

0

90

180

270

B I

T= 2K 10 K 20 K 50 K 100 K 200 K 300 K

2

c Gxx()/Gxx()100%

Gxx (mS)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

-1

0 B (T)

1

2 B=2T

2.8 2.4 2.0 1.6

360

0

4

8

12 T (K)

 (o)

Figure 3

19


16

20

Nano Letters

a

b 40

VG

Rxy ()

880 800

0V 1V 2V -2 V

20 0 -20

c 2.4 n (/cm-2)

a

720

VG = -2 V

100

VG = 0 VG = 1 V

40

Gxx (e2/h)

MRxx (%)

d

80 60

-6 -3 0 3 B (T)

160

50

100 T (K)

150

0

200

1.6 1.2

6

0V 1V

-0.4  = -0.53 l = 211 nm

-0.8 -0.4

B I -16

2K -2 -1 0 1 2 VG (V)

-2 V, 2 K

80

VG = 2 V 0

0.0

(1012)

2.0

0.8

-40

Rxx ()

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 22

-8

Figure 4

20


0.0 B (T)

0 B (T)

0.4

2V -2 V

8

16

Page 21 of 22

b 0.32

2 K, 3 T

5.5 5.0

Gxx() (mS)

a

2V

4.5

0.30

0.28 Eq. 1 - Fitting

-2 V, 3 T


4.0 3.5

1V

c

0V

Gxx() (S)

Gxx (mS)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

-2 V

0.30

0 -10 -20 Gxx

-30 0

90

180  (o)

270

360


0

90

180

( ) o

Figure 5

21


270

360

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Page 22 of 22

Quantitative analysis of weak antilocalization effect of topological

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