Bi2Te3

Letter pubs.acs.org/NanoLett

Solvothermal Synthesis of Lateral Heterojunction Sb2Te3/Bi2Te3 Nanoplates Fucong Fei,† Zhongxia Wei,† Qianjin Wang,‡ Pengchao Lu,† Shuangbao Wang,‡ Yuyuan Qin,† Danfeng Pan,† Bo Zhao,† Xuefeng Wang,§ Jian Sun,† Xinran Wang,§ Peng Wang,‡ Jianguo Wan,† Jianfeng Zhou,‡ Min Han,§ Fengqi Song,*,† Baigeng Wang,*,† and Guanghou Wang†

Downloaded by UNIV OF NEBRASKA-LINCOLN on September 1, 2015 | http://pubs.acs.org Publication Date (Web): August 27, 2015 | doi: 10.1021/acs.nanolett.5b01987

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National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and College of Physics, Nanjing University, Nanjing 210093, P. R. China ‡ National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and Department of Material Science and Engineering, Nanjing University, Nanjing 210093, P. R. China § National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, P. R. China S Supporting Information *

ABSTRACT: A lateral heterojunction of topological insulator Sb2Te3/Bi2Te3 was successfully synthesized using a two-step solvothermal method. The two crystalline components were separated well by a sharp lattice-matched interface when the optimized procedure was used. Inspecting the heterojunction using high-resolution transmission electron microscopy showed that epitaxial growth occurred along the horizontal plane. The semiconducting temperature-resistance curve and crossjunction rectification were observed, which reveal a staggered-gap lateral heterojunction with a small junction voltage. Quantum correction from the weak antilocalization reveals the well-maintained transport of the topological surface state. This is appealing for a platform for spin filters and onedimensional topological interface states. KEYWORDS: topological insulator, solvothermal synthesis, bismuth telluride, antimony telluride, heterojunction, transport

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progress in the production of LHJs in two-dimensional materials has shed light on this topic.14−20 Here, we report the successful preparation of Sb2Te3/Bi2Te3 LHJs. Sb2Te3 and Bi2Te3 are both TI materials with 5−20 quintuple layers.21−23 High-resolution (HR) transmission electron microscopy (TEM) images of the LHJ interface showed that epitaxial growth occurred. Electrical rectification was observed in the cross-junction transport in the LHJ devices, indicating the onset of an interior electric field across the junction interface. Weak antilocalization and its robust coupling were found, showing that topological transport was well maintained. Preparation of the LHJ Using the Two-Step Route. The first step of the synthesis produced Bi2Te3 nanoflakes.24 These nanoflakes were then dispersed in the coating solution that was intended to prepare Sb2Te3 nanoflakes. Both these crystals had been shown to be TIs when they are more than six quintuple layers (nanometers) thick.21,23 The solution concentrations and annealing periods have been optimized to achieve

ateral heterojunctions (LHJs) play a more interesting role than vertical ones in the heterojunction physics of topological insulators (TIs) because in a vertical TI heterojunction a surface is eliminated, killing a surface state (SS), whereas a new interface state is generated between two well-maintained SS regions in the same plane in a TI-based LHJ.1−9 Such LHJ and interface states may accommodate novel electronic physics for Dirac Fermions.1,2,4−6,10−13 For example, aligning the working functions of the two crystals in a LHJ will tune the eigenvalues of the spin helicity of the SS between +1 and −1, allowing the LHJ to be used in quantum information devices.1,2 Spintronic devices can also be implemented in such a TI-based LHJ. It has been proposed that quantum spin Hall edge states will arise and accumulate spins according to the distinct behaviors of the two TIs when a Landau quantization magnetic field is applied.1,2 A spin-filtered state will therefore be expected along the interface. The ability to control the SS and the bulk electrons separately also points to some new physics of LHJs. LHJs also have an advantage of gate-tunable rectification than the traditional three-dimensional heterojunctions.14 It has been proposed to implement such idea by fractional gating,1 but no experiments have yet been described in which the growth of such a TI-based LHJ has been achieved. Recent © XXXX American Chemical Society

Received: May 20, 2015 Revised: August 25, 2015

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DOI: 10.1021/acs.nanolett.5b01987 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Successful preparation of lateral heterojunctions of topological insulators. (a) Transmission electron microscopy (TEM) image of the asprepared heterojunction nanoplates. The hexagonal morphology indicated that the nanoplates crystallized well. (b) Scanning TEM (STEM) image of the heterojunction nanoplates, in which the contrast of the inner region was enhanced using atomic contrast in the STEM image. (c) Powder XRD pattern of the products. Black and red spectrum shown in the lower panel are peaks information from standard JCPDS cards No. 15-0874 (Sb2Te3) and No. 15-0863 (Bi2Te3), respectively. (d) STEM image of a typical nanoplate (inset) and corresponding EDS spectrum of the spots marked in inset, respectively. (e) STEM image of a typical plate for 2D EDX mapping measurement. (f) and (g) Mapping data of Sb and Bi, respectively, from the rectangle marked in (e). (h) EDX line profile from mapping data of the Sb and Bi. (i) Schematic diagram of lateral epitaxial growth of the Bi2Te3−Sb2Te3 heterostructures.

For investigating how sharp the interface was, 2D energy dispersive spectra mapping was carried out near the interface. Figure 1e−h showed the result, where Figure 1f and g were the mapping data of Sb and Bi respectively from the rectangle marked in Figure 1e. One may find the sharp transition from a Bi-rich to Sb-rich region. In Figure 1h, we can see the line profile from mapping data of the two elements, where the width of transition region is well less than 3 nm, near the resolution limit of the STEM machine. We are therefore convinced that the desired LHJ with nanometer-scale sharp interface was successfully prepared using the two-step route shown schematically in Figure 1i. Lateral Epitaxial Growth between the Two TIs. Atomic force microscopy images of the flakes were acquired and inspected carefully, which excluded the possibility that Sb2Te3 formed a coating on the top surface of the Bi2Te3. There was a hexagonal interface between the two regions in each flake, as shown in Figure 2a, and the interface was 1 nm thicker than the other areas of the flake. We believe that this was because the chemically active interface absorbed some mobile contaminants.25 The inner crystal and the margin crystal were both 16 nm thick, as shown by the scanning profile along the blue line. The possibility of a core/shell structure was thus excluded. This was also confirmed because no obvious cross-doping was found in energy dispersive spectroscopy imaging in Figure 1f and g. In fact, Bi2Te3/Sb2Te3 core−shell structures were formed when water was excluded from the mixture used to perform the

the proper thickness. These crystals were selected so that lateral expitaxy could be achieved, because the crystals have similar space groups and lattice constants. The successfully synthesized TI LHJs were Bi2Te3 nanoplates surrounded by Sb2Te3 margins. Low magnification TEM images of the material were shown in Figure 1a, in which regular hexagonal shapes and shiny fringes (from electronic interference) can be seen, indicating a good degree of crystallinity. The inner plates could be identified by the pale contrast in Figure 1a. The poor contrast between the two components was enhanced by acquiring a scanning TEM image using the high-angle angular dark-field mode, in which atomicweight-dependent electronic scattering leads to intense atomic contrast. The inner flakes could be seen clearly in Figure 1b since the heavier elements (Bi) were enriched in the inner crystals rather than the marginal ones. The X-ray diffraction pattern of the prepared sample (dry powder) is shown in Figure 1c, and all the peaks could be assigned according to the reference spectrum (the lower panel; JCPDS cards 15-0874 and 15-0863). The peaks were therefore believed to be for Sb2Te3 and Bi2Te3, which were the intended products. The strong peaks of two candidates were resolved well, indicating the nice phase separation. The energy dispersive spectra for a single LHJ flake were shown in Figure 1d (the flake was shown in the inset). The two regions were respectively found to be composed of Bi2Te3 and Sb2Te3. B


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Figure 2. Evidence for lateral epitaxial growth of the Bi2Te3/Sb2Te3 heterojunctions. (a) Linear profile along the line marked in the inset (the atomic force microscopy image). The thickness was found to be 16 nm. The inner and outer crystals had the same thicknesses, excluding the possibility that core−shell structures were formed. The scale bar in inset represents 500 nm. (b) High-resolution (HR) TEM image of positions near the LHJ interface. HR-TEM image of the (c) inner Bi2Te3 and (d) outer Sb2Te3 zones. The insets show the fast Fourier transform patterns. The hexagonal lattice fringes showed that the lattice spacings of 0.22 and 0.214 nm applied to the (112̅0) planes of the crystals. (e) Magnified view of the region outlined by the dashed square in (b) This region was the interface between the two crystalline regions. Continuous lattice fringes can be seen across the heterostructure interface. The arrow marks a dislocation and the two yellow dashed lines mark bent lattice planes, both phenomena being caused by the lattice mismatch. The scale bar represents 2 nm.

Figure 3. Electrical transport and its staggered band diagram. (a) Resistance versus temperature for a typical device. The inset showed a schematic of the device. (b) Current−voltage (I−V) curve of a Bi2Te3−Sb2Te3 heterojunction near zero voltage, indicating the onset of the junction field. (c) Temperature dependence of I−V asymmetry, defined as the mean ΔV value. ΔV is the voltage difference between corresponding positive and negative currents. (d) Calculated bandgap configuration of the two materials. The two band structures were aligned according the calculated Fermi level. (e) Proposed band diagram for the lateral heterojunction.

second step of the synthesis and when larger amounts of TeO2 and SbCl3 were used (Supporting Information, Figure S1) and such core−shell structures synthesized by similar solvothermal method have been reported before.26 The well-limited lateral growth in our sample can be attributed to the guiding behavior of the surfactant template. It can also be attributed to the fact that the surface energy can be reduced during the lateral growth while less surface energy is saved in the van der Waals epitaxial growth along vertical direction.20

The HRTEM images showed that a good standard of epitaxial growth occurred. HRTEM images of positions near the LHJ flake interface are shown in Figure 2b, and parallel lattice fringes can be seen in both the inner and marginal crystals. Different lattice spacings (0.22 nm and 0.214(3) nm) were found in the two regions of the LHJ, as shown in Figure 2c and 2d, despite their having similar hexagonal fast Fourier transformation (FFT) patterns (shown in the insets). These spacings were respectively found to be for the (1120̅ ) planes of C


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Figure 4. The magnetoresistance transport: well-maintained topological surface states. (a) Magnetoresistance of the device up to 8 T. The inset is the Hikami−Larkin−Nagaoka fitting curve for weak antilocalization near the zero field. (b) Transport parameters of the crossing-LHJ devices. The red points are the reference data.

current−voltage asymmetry for the interior field in the junction and found that voltage asymmetry was greatly reduced from voltages of 3 mV with the increasing temperature, and disappeared when the temperature was higher than 30 K, as is shown in Figure 3c. Taking the Boltzmann constant (∼2.5 meV at 30K) into consideration, our observations confirm that there was a small but robust junction voltage of ∼3 mV. We proposed that the produced LHJ was a heterostructure with a staggered bandgap, as shown in Figure 3e. The LHJ was an n−n junction. We fabricated two probe FET devices of single Bi2Te3 and Sb2Te3 nanoplates on silicon subtract with dielectric SiO2 layer and measure the resistance under different back gate voltage. We found that both Bi2Te3 and Sb2Te3 are ntype because resistance raises under negative gate bias. The Fermi level was quite near the bottom of the conduction band (5−10 meV) in the bulk gap of ∼160 meV, as determined from the thermally activated conductivity (Figure 3a). The interior voltage drop across the junction was found to be around 3 meV, and the width of the junction region was subject to the carrier diffusion constants, which were not determined. The carriers’ density was higher than 1012 cm−2, which were mostly surface carriers and cannot be eliminated yet by a SiO2 back gate.27 The system still requires delicate optimization to allow a p−n junction to be formed between the two SS regions, or intense gate of SrTiO3.28 In Figure 3d, by the first-principle calculations, we obtained the band structures of the two semiconductors and aligned them in the same frame according to the intrinsic Fermi level (see whole-scale band structure diagram in Supporting Information, Figure S2). We can see the bandgap of Bi2Te3 is slightly larger than that of Sb2Te3. Its conduction band minimun is also a few millielectronvolts higher. Therefore, the n−n type LHJ scenario with a staggered bandgap is confirmed. It is notable that gallium contamination and platinum diffusion is a very problem in FIB fabricating progress. We used several solutions to reduce the gallium contamination. First, we used the least possible current and voltage value of the ion beam, under the premise of good conduction, to minimize the contamination and ion injection. Then, we used marks deposited by electron beam previously near the samples to locate the samples rather than used ion beam to directly “see” where the sample was. Therefore, only the electrodes area could be contaminated by gallium. During the deposit process, a Pt gun jetted organic matter containing platinum to the whole substrate during deposit progress, and it is understandable that some organic matter adsorbs on samples. In initial fabrication,

the two crystals.22 The similar lattice spacings allowed fine epitaxial growth between the two crystals as seen. Higher magnification image along the LHJ interface (Figure 2e) showed that the two sets of atomic fringes evolved smoothly from left to right. The subtle lattice mismatch solved by a dislocation, which was finally found as shown in the figure and marked by the arrow. It is therefore clear that lateral epitaxial growth occurred and that the LHJ had a lattice-matched abrupt interface. n−n Type LHJ with a Staggered Bandgap. We fabricated some two-probe devices across the LHJ, as shown schematically in the inset of Figure 3a. The as-prepared nanoflakes were generally covered with a thin layer of organic surfactant, which protected the flakes from being oxidized but also prevented electrical transport. The presence of such a surfactant layer was believed to cause insulating failure of the devices. We made use of the insulating organic coating while the device was being fabricated using focused ion beams. We tentatively dug the LHJ surface and removed the organic layer for 5 nm in the selected region with a diameter of 100 nm, leaving the surface therein bare to allow a contact to be fabricated. Pt electrodes were prepared on the bare areas, using a Pt nanogun, to complete the device. This produced flying leads across the junction as shown in the inset of Figure 3a. Perfectly linear current−voltage (I−V) curves were found, at least at room temperature, indicating that successful Ohmic contacts had been produced. The temperature dependence of the resistance of a typical device under 500 nA source current was shown in Figure 3a and the direction of current was marked in the inset, showing that the resistance increased from 100 kΩ to around 600 kΩ as the temperature decreased. This indicates that the device behaved as a semiconductor and that the Fermi level was aligned with the bandgaps of both crystals. The signature of cross-junction transport was found at low temperatures. The linear current−voltage curve changed as the temperature decreased. A rectification effect occurred at 5 K, as shown in Figure 3b. The transport current quickly increased to 5 nA when the positive voltage was 2 mV, but the transport current remained well below 1 nA when a negative bias voltage was applied. This was a typical rectification effect, indicating the onset of an interior electrical field across the LHJ interface. The current increased abruptly and quickly at −3 mV when the voltage was decreased, indicating that the threshold voltage was small, ∼ 3 mV. This threshold voltage is very small, and we concluded that it was because Bi2Te3 and Sb2Te3 have similar band structures. We looked for temperature-dependent D


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absence of deionized water in the second step. The products were examined by HRTEM using a FEI TECNAI F20 transmission electron microscope equipped with a 200 kV electron gun and an energy dispersion spectrometer. Atomic force microscopy images were acquired using an NT-MDT atomic force microscope. An ARL X’TRA X-ray powder diffractometer was used to determine the crystal structure. Coarse electrodes were fabricated using ultraviolet lithography technique and the focused ion beam deposited tiny Pt contacts were fabricated in a FEI Helios Nanolab 600i dual beam system. Electrical transport measurements were performed in a Cryomagnetics cryostat equipped with a Stanford Research Systems SR830 digital lock-in amplifier, Keithley 4200 and Agilent 2635 meters, and a Cryomagnetics 9T C-Mag system. A temperature of 2 K and a magnetic field of 8 T were achieved during the measurements. The electronic band structure calculations were performed within the framework of density functional theory (DFT) using the WIEN2k code,43 with a full-potential linearized augmented plane-wave and local orbitals (FPLAPW+lo) basis. The Perdew−Becke−Erzenhof (PBE)44 parametrization of the generalized gradient approximation (GGA) had been adopted as the exchange-correlation function. Experimental lattice parameters were used for the rhombohedral crystal structure (a = 4.40 Å and c = 30.53 Å for Bi2Te3, a = 4.28 Å and c = 30.52 Å for Sb2Te3). A 10 × 10 × 10 mesh for BZ sampling and 8 for the plane wave cutoff parameter RMTKmax were used, where R is the minimum LAPW sphere radius and Kmax is the plane-wave vector cutoff. The spin−orbit coupling (SOC) had also been taken into account.

the devices were always not conductive because of the presence of surfactant layer. This phenomenon, from another perspective, proves that this kind of organic adsorbate containing platinum is not conductive and be separate by surfactant layer from contacting the TI samples. Therefore, we believe that this kind of Pt adsorbate does not affect the transport measurement and the properties of our samples. Well-Maintained Topological Transport of the LHJ. The topological SS were found well maintained after the magnetoresistance (MR) of the device was measured at 2 K and at up to a field of 8 T. A crossover was seen from a low-field parabolic MR to an increasing high-field linear MR, as shown in Figure 4a. Such a trend has been found widely in the Dirac systems, in which low-field MR has been attributed to classical MR and high-field linearity has been attributed to a high g factor or quasilinear dispersion.29−35 It was interpreted by the mobility fluctuations of Dirac Fermions.36 Using the Kohler’s rule, the classical parabolic MR gave the carriers’ mobility of a few hundred square centimeters per volt and a carrier concentration of more than 7 × 1012 cm−2. An abrupt decrease in the resistance was found near the zero field, and this was attributed to weak antilocalization, which has recently been regarded to be a signature of SS transport.27,37,38 We fitted a line to the zero-field MR curve using the Hikami−Larkin− Nagaoka formula as shown in the inset of Figure 4a,39,40 and this gave a dephasing length of 83 nm and an alpha value of 0.42. This near-half alpha value indicated that the device had a single transport channel or electronic state. This can be understood because all SSs are coherently coupled because their electronic dephasing lengths are much larger than their thicknesses.41 Please see Figure 4b for more measured transport parameters of our crossing-junction devices. The two red points in Figure 4b showed the measurement for two reference samples without a junction, which were prepared using the same solution. One can see all the data fell in the similar regime to the reported TI devices. This means our device had a dephasing length close to those obtained in samples without a junction.27,38 All these observations point to the fact that the transport through the topological SS is well maintained in our LHJ samples.42 In summary, a two-step solvothermal method was used to successfully synthesize LHJ samples based on Bi2Te3 and Sb2Te3 TIs. The LHJ had a lattice-matched abrupt interface and an interior crossjunction voltage of 3 mV. The LHJ could be further optimized because the junction voltage drop was small and the Fermi level was inappropriate (because the two materials have similar band structures). These further improvements could result in the successful use of the LHJ in spin filters and IS devices. Material and Methods. All of the LHJ flakes used in this study were prepared using a simple two-step solvothermal technique. The first step was preparing Bi2Te3 nanoflakes.24 Powdered Bi2O3 (0.466 g), TeO2 (0.48 g), and NaOH (1 g) were dissolved in ethylene glycol (50 mL) containing polyvinylpyrrolidone (PVP) surfactant (0.8 g). The solution was annealed at 180 °C in an autoclave for 12 h. The second step was introducing 8 mL of the first product to the coating solution, which was prepared by dissolving powdered SbCl3 (0.228 g), TeO2 (0.24 g), and NaOH (0.9 g) in a mixture of ethylene glycol (38 mL) and deionized water (4 mL) containing PVP (0.8 g). The second step was completed by annealing the mixture at 195 °C in an autoclave for 24 h. Core−shell structures, rather than LHJs, were produced in the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b01987. STEM image and energy dispersive X-ray spectrum of Bi2Te3/Sb2Te3 core−shell structures, the whole-scale band structure diagram of Bi2Te3 and Sb2Te3. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Fax +86-25-83595535. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the National Key Projects for Basic Research in China (Grant Nos. 2013CB922103, 2011CB922103, and 2015CB921202), the National Natural Science Foundation of China (Grant Nos. 91421109, 11023002, 11134005, 61176088, 51372112, 2117109, 11474147, 51372112, and 11574133), the NSF of Jiangsu Province (Grant Nos. BK20130054 and BC2013118), the PAPD project, and the Fundamental Research Funds for the Central Universities for financially supporting this work. Part of the calculations were performed on the supercomputer in the High Performance Computing Center of Nanjing University. Technical assistance provided by Prof. Li Pi and Mingliang Tian from the Hefei High Field Center is acknowledged. Insightful E


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of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi2Te3 and Sb2Te3. Phys. Rev. Lett. 2009, 103, 146401. (22) Zhang, H.; Liu, C.-X.; Qi, X.-L.; Dai, X.; Fang, Z.; Zhang, S.-C. Topological insulators in Bi2Se3 Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 2009, 5, 438−442. (23) Wang, G.; Zhu, X.-G.; Sun, Y.-Y.; Li, Y.-Y.; Zhang, T.; Wen, J.; Chen, X.; He, K.; Wang, L.; Ma, X.; et al. Topological Insulator Thin Films of Bi2Te3 with Controlled Electronic Structure. Adv. Mater. 2011, 23, 2929−2932. (24) Kong, D.; Koski, K. J.; Cha, J. J.; Hong, S. S.; Cui, Y. Ambipolar Field Effect in Sb-Doped Bi2Se3 Nanoplates by Solvothermal Synthesis. Nano Lett. 2013, 13, 632−636. (25) Jensen, P. Growth of nanostructures by cluster deposition: Experiments and simple models. Rev. Mod. Phys. 1999, 71, 1695− 1735. (26) Liang, L.-X.; Deng, Y.; Wang, Y.; Gao, H.-L. Epitaxial formation of core−shell heterostructured Bi2Te3@Sb2Te3 hexagonal nanoplates. J. Nanopart. Res. 2014, 16, 2138. (27) Chen, T.; Chen, Q.; Schouteden, K.; Huang, W.; Wang, X.; Li, Z.; Miao, F.; Wang, X.; Li, Z.; Zhao, B.; et al. Topological transport and atomic tunnelling−clustering dynamics for aged Cu-doped Bi2Te3 crystals. Nat. Commun. 2014, 5, 5022. (28) 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, 2151−2155. (29) Wang, W.; Du, Y.; Xu, G.; Zhang, X.; Liu, E.; Liu, Z.; Shi, Y.; Chen, J.; Wu, G.; Zhang, X. Large Linear Magnetoresistance and Shubnikov-de Hass Oscillations in Single Crystals of YPdBi Heusler Topological Insulators. Sci. Rep. 2013, 3, 2181. (30) Huynh, K.; Tanabe, Y.; Tanigaki, K. Both Electron and Hole Dirac Cone States in Ba(FeAs)2 Confirmed by Magnetoresistance. Phys. Rev. Lett. 2011, 106, 217004. (31) Liang, T.; Gibson, Q.; Ali, M.; Liu, M.; Cava, R.; Ong, N. P. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2. Nat. Mater. 2014, 14, 280−284. (32) Tang, H.; Liang, D.; Qiu, R.; Gao, X. Two-dimensional Transport Induced Linear Magneto-Resistance in Topological Insulator Bi2Se3 Nanoribbons. ACS Nano 2011, 5, 7510−7516. (33) Assaf, B.; Cardinal, T.; Wei, P.; Katmis, F.; Moodera, J. F.; Heiman, D. Linear magnetoresistance in topological insulator thin films: Quantum phase coherence effects at high temperatures. Appl. Phys. Lett. 2013, 102, 012102. (34) Wang, X.; Du, Y.; Dou, S.; Zhang, C. Room Temperature Giant and Linear Magnetoresistance in Topological Insulator Bi2Te3 Nanosheets. Phys. Rev. Lett. 2012, 108, 266806. (35) Gao, B.; Gehring, P.; Burghard, M.; Kern, K. Gate-controlled linear magnetoresistance in thin Bi2Se3 sheets. Appl. Phys. Lett. 2012, 100, 212402. (36) Narayanan, A.; Watson, M. D.; Blake, S. F.; Bruyant, N.; Drigo, L.; Chen, Y. L.; et al. Linear Magnetoresistance Caused by Mobility Fluctuations in n-Doped Cd3As2. Phys. Rev. Lett. 2015, 114, 117201. (37) Lu, H. Z.; Shi, J. R.; Shen, S. Q. Competition between weak localization and antilocalization in topological surface states. Phys. Rev. Lett. 2011, 107, 076801. (38) 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.; et al. Gate-Voltage Control of Chemical Potential andWeak Antilocalization in Bi2Se3. Phys. Rev. Lett. 2010, 105, 176602. (39) Hikami, S.; Larkin, A. I.; Nagaoka, Y. Spin-orbit interaction and mangetoresistance in the two dimensional random system. Prog. Theor. Phys. 1980, 63, 707−710. (40) We estimate the contact resistance by measuring a gold wire contacted by the similar FIB fabrication. Considering the fact that our device is of good Ohmic contact and the device’s resistance increases over 5 times with the decreasing temperature, the contact resistance therefore is believed to be less than 20% in the low-temperature measurement. Such estimation gives an error of 0.01 for the alpha value of 0.42 in the HLN fitting.

discussions with Prof. Dajun Shu, Xiangang Wan, and Yong Zhou from Nanjing University are also acknowledged.


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Nano Letters


(41) Li, Z. G.; Garate, I.; Pan, J.; Wan, X. G.; Chen, T.; Ning, W.; Zhang, X. O.; Song, F. Q.; Meng, Y. Z.; Hong, X. C.; et al. Experimental evidence and control of the bulk-mediated intersurface coupling in topological insulator Bi2Te2Se nanoribbons. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 041401(R). (42) Further nonlocal probe measurements along the interface is ongoing, which may resolve the spin polarization of the interface state. (43) Blaha P., Schwarz K., Madsen G. K. H., Kvasnicka D., Luitz J. WIEN2k, An Augmented Plane Wave 1 LO Program for Calculating Crystal Properties; Vienna: TU Wien, 2001. (44) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865.

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Bi2Te3

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