Abstract
How the surface state (SS) develops and how the spin transport in a curved cylindrical topological insulator nanowire have attracted theoretical attention recently. However, experimental confirmation for the SS in such a real modeling system still remains insufficient. Here we carried out a systematic comparative study on the cylindrical singlecrystal Bi_{2}Te_{3} nanowires of various diameters and report unambiguously dual evidence for the Dirac SS. Both the predicted anomalous AharonovBohm (AB) quantum oscillations with a period of h/e in H_{//} and the 1/2shifted Shubnikovde Haas (SdH) oscillations (i.e., γ = −1/2) in H_{⊥} were indentified below 1.4 K. In addition, AltshulerAronovSpivak (AAS)like oscillations with a period of h/2e and ordinary SdH oscillations with γ = 0 were also resolved. These data provide clear evidence of coexistence of the nontrivial topological Dirac state and trivial electron state on the surface of topological insulator nanowire.
Introduction
Topological insulator (TI) is a rapidly growing field of research in condensed matter physics^{1,2,3}. It is characterized by a full insulating gap in the bulk and gapless spinresolved surface states (SS) in which the spin of the electrons is locked perpendicular to its momentum by strong spinorbit interaction. These spin helical properties of the Dirac fermions in SS have made them relevant for applications on improved spintronic devices and potentially useful for quantum computing^{4,5,6,7}. While the topologically nontrivial surface state has been unambiguously indentified by angleresolved photoemission spectroscopy (ARPES) in Bi_{2}X_{3} (X = Te or Se) compounds^{8,9,10,11,12,13}, direct probing the topological nature by electrical transport is still a major challenge^{14,15,16,17,18,19,20,21}. This is because the electrical transport measurement is a bulk sensitive experiment, even small imperfections in the asgrown nearstoichiometric crystals will result in a metallic behavior in bulk and thus overwhelm or mask the surface contribution^{20,21}. In order to overcome the material's obstacles and enhance the surface contribution, a number of efforts have been made recently by growing bulk singlecrystals with compositional gradient^{15}, chemical doping^{16,22,23} or gatevoltage tuning of the chemical potential in ultrathin films^{24,25,26}. Recognition of the 2D surface state in 3D crystal was mostly based on the observation of angular dependent Shubnikovde Haas (SdH) quantum oscillations or quantum Hall (QH) effect in high magnetic fields^{15,16}.
Topological insulator nanowire with perfectly insulating bulk and curved twodimensional metallic surface realizes an ideal hollow cylinder and thus exhibits more advantages for detection of the SS using transport measurement^{17,18,19,27}. A key or probably clearcut transport signature closely related to the nontrivial surface Dirac electrons or the surface curvature induced Berry's phase in a TI nanowire is the anomalous AharonovBohm (A–B) effect with a period of φ_{0} = h/e flux quantum (i.e., twice the conventional period for an ordinary metallic hollow cylinder) when applying a magnetic field (H_{//}) along the length of the cylinder and meanwhile, the oscillations at zero flux φ_{0} = 0 have a minimum (0AB) or maximum (πAB) depending on the doping level^{28,29,30}. In the case of weak antilocalization and strong disorderinduced diffusive motion from topological trivial surface electrons away from the Dirac point, an ordinary AltshulerAronovSpivak (AAS) effect with a period of h/2e and a minimum in MR at zero flux φ_{0} = 0 will appear^{31}. While the anomalous AB or AASlike oscillations were reported in both Bi_{2}Se_{3} and Bi_{2}Te_{3} nanoribbons previously^{17,18,27}, no evidence of topological SS was reported in a curved cylindrical TI nanowire of different diameters. It is still not clear how the SS develops and how the spin transports in such a real curved quasi1D wire.
It was well known that, in a 2D metal, the SdH oscillations are due to the successive emptying of the Landau levels (LLs) as the magnetic field (H) is increased, where the LL index n is related to the extremal crosssection, S_{F}, of the Fermi surface by ^{16}. For the quadratic Schrodinger spectrum, there are nfilled LLs below the Fermi energy, E_{F}, when the applied fields equal to H_{n}. By contrast, in the Dirac case, there have n + 1/2 filled LLs between, E_{F} and the Dirac point at E = 0, wherein the conduction band and the valence band each contribute half of the state in the n = 0 LL and thus result in an important 1/2shift of the spectrum at ultra quantum limit. In other words, the plot of 1/H_{n} vs. LL index number n intercepts the naxis at the value of γ = −1/2, whereas the interception γ = 0 in the Schrodinger case. Therefore, the observation of the 1/2shifted SdH oscillations is considered to be another criterion for the topological nature of the surface Dirac states in TI^{32,33}. Unfortunately, such a 1/2shifted SdH spectrum has not been identified in a curved ultrathin TI wire yet.
Here we carried out a systematic comparative study on cylindrical singlecrystal Bi_{2}Te_{3} nanowires of various diameters (40 nm, 100 nm and 320 nm) fabricated by templateassisted electrodeposition, and, for the first time, we report unambiguously dual evidence for the Dirac SS in the wires. Both the predicted anomalous AB oscillations with a period of h/e in H_{//} and the 1/2shifted SdH oscillations (i.e., γ = −1/2) in H_{⊥} were indeed observed clearly below 1.4 K. In addition, AASlike quantum interference oscillations with a period of h/2e and ordinary SdH oscillations with γ = 0 were also resolved. These data provide clear evidence of coexistence of the nontrivial topological Dirac states and trivial electron states on the surface of TI nanowires. Interestingly, when the wire diameter increases, both AB and SdH quantum oscillations were considerably suppressed and finally unresolved in 320 nm wires and instead, the universal conduction fluctuation (UCF)like behavior was seen though the similar positive MR behavior remains. These results demonstrated that the topological surface states in ultrathin wires are extreme robust regardless of the surface oxidation of the wire and the data also led to the unique situation for detection of the coexistence of the nontrivial topological and trivial metallic surface states in the ultrathin wire due to the enhanced surface contribution. We anticipated that our experimental data will inspire more sophistical theoretical and experimental considerations on onedimensional (1D) ultrathin TI nanowires, which have not been well explored, such as the possible helical Luttinger liquid^{30} that was ever described as the edge mode of the 2D quantum spin hall (QSH) topological insulator.
Results
All of Bi_{2}Te_{3} nanowires used in this work were synthesized by electrochemical deposition via customermade porous anodic aluminum oxide (AAO) membrane. The wire diameter was exactly controlled by the pore size of the template so that we are able to carry out a systematic comparative study on wires of various diameters by selecting the templates with proper pore size. While the diameter of each wire along its length is uniform, it shows variations from wire to wire within an uncertainty of ~20%, verified by both scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Fig. 1 (a) and the inset show, respectively, the low magnification SEM and TEM images from the smallest diameter wires we studied. The majority of the nanowires displays a length of 8–15 μm and a diameter of 40–50 nm. Highresolution TEM and the selected area electron diffraction pattern on a randomly selected nanowire revealed singlecrystal morphology (Fig. 1b and the inset). An oxidation layer of approximately ~5.0 nm as indicated in Fig. 1(b), which was probably formed after the nanowires were released from the membrane, is visible on the surface. Therefore, the actual diameter of the nanowires inside the oxidation shell is about 30–40 nm. All of the samples fabricated under the same controlled conditions showed very similar structure, verified by XRD measurement on the nanowire arrays (see Supplementary Fig. S1), where the (110) diffraction is always the dominant peak in the spectra.
Standard 4probe transport measurements on an individual nanowire were carried out with a physical property measurement system (PPMS, Quantum Design Inc.) cryostat equipped with a dilution refrigerator insert and a 16 T superconducting magnet. Four Ptelectrodes were patterned on an individual wire using focusedion beam (FIB) technique (see Fig. S2 in supplementary materials). There is always a possibility of Ga or Pt implantation on the wire during the process, the ion beam imaging was therefore suspended during the process and the deposition current was set below 30 pA (prior to the Pt deposition, the contact areas were milled for 5 second with a beam current of 10–30 pA in order to remove the surface oxidation, then the four Pt electrodes were deposited subsequently with the same beam current; the extended leads were made by a relative large current beam based on the stripe areas). It was found that the maximum spreading or diffusion distance of the actual Pt along the wire is less than 300 nm under the mentioned deposition parameters verified through a profile analysis of the TEM energy dispersive Xray spectroscopy (EDS) studies^{34}. The Ga^{+} implantation or the damageinduced defects on the wire were expected to be near the contact areas within ~300 nm. The wire far away from the contacts is supposed to be less effected due to the natural protection of the 5 nm surface oxidation. Especially, the distance (L) between the inner edges of the two voltage electrodes were kept much larger than the spreading distance of Pt or Ga, they are, respectively, 5.4, 4.0, 4.2 μm for 40 nm, 100 nm and 320 nm wires used in this work, respectively.
Figs. 2(a) shows resistance (R) versus temperature (T) of three diameter wires measured at a zero magnetic field. Fig. 2 (b) is the variation, ΔR/R_{0}, of the MR versus H_{⊥} for 100 nm, 320 nm wires at 2 K and 40 nm wire at 2.5 K. The RT curves of 100 nm and 320 nm wires show very similar behavior, i.e., a resistance hump near 220 K in highT range and an upturn below 14 K. In contrast, the 40 nm wire displays a nonmetallic transport behavior with a weak Tdependence over the temperature range of 14–300 K and then turns up below about 14 K. The hump around 220 K and the shallow minimum in R vs. T curves were usually found in TI – bulk crystals when the carrier density decreases, such as n < 10^{17} cm^{−3} ^{15,20}. When n > 10^{17} cm^{−3}, a good metallic behavior was attributed to the contribution of the bulk conductivity. The broad hump of the resistance in large diameter wires was considered to be the competition of the conductivity between the surface state and the bulk. When the temperature decreases, the contribution of the insulating bulk conductivity decreases sharply and thus the surface conductivity will be dominant in lowT range. The absence of the resistance hump in this 40 nm wire likely provides an indication that the surface contribution of the 40 nm wire dominates over the entire Trange due to the enhanced surface to volume ratio. The upturn feature of the resistance below 14 K in all three samples is probably from the electronelectron interactions^{35,36} due to the enhanced disordering in one or twodimensional metals. The positive MR with a sharp valley (or a cusp in conductivity) in lowH region, as shown in Fig. 2 (b) can be understood in terms of the weak antilocalization (WAL) model and such a positive MR behavior is a common feature in TI system due to the strong spinorbit coupling or the ee interaction^{35,36}. The most remarkable data we focused here are that the MR fluctuations or quantum oscillations were found to be enhanced with the decrease of the wire diameter, as shown in Fig. 2 (c) by subtraction of a fitted smooth background. The amplitude of the MR fluctuations or oscillations in 40 nm wire at 2.5 K was found to be 8 and 40 times larger than those in 100 nm and 320 nm wires obtained at 2 K, respectively (we have no the 2.5 K data for comparison). To understand the nature of these MR oscillations intensified in ultrathin nanowire, we focus our attention on the data of 40 nm wire.
Figs. 3 (a) and 3 (b), respectively, show the R vs. H_{//} and R vs. H_{⊥} curves of 40 nm ultrathin wire at different T. Both curves display remarkable MR oscillations at temperatures below 4.0 K. Compared with the well recognized oscillation spectra in H_{⊥} orientation, the quantum oscillations in parallel H_{//} direction become relatively weak but definitely resolvable and all tiny features are reproducible when scanning the field from 16 T to −16 T or vice versa.
Discussion
Fig. 4 (a) shows the variations of the resistance, ΔR, vs. H_{//} measured at different T after subtraction of a background by fitting the original data with a polynomial function (each curve was shifted up by adding a certain constant value for clarity; the fitted background curves were shown in Fig. S3). The big bump near 6 T is probably from the MR effect of the bulk contribution in parallel H and thus was omitted by the subtraction. It is noticed that the significant minima of the MR oscillations indicated by the vertical lines are equal gaped. In other words, the MRoscillation spectra are periodic with H_{//} and have a period of about ΔH_{//} = 4.45 T. Such a period corresponds to the AB oscillations from a 35 nm diameter metallic hollow cylinder evaluated from the formula of ΔH_{//}(πd^{2})/4 = Φ_{0}, with d the wire diameter and Φ_{0} = h/e the magnetic flux quanta. As described above, the estimated value, d~35 nm, for a cylinder is indeed, as expectedly, on the order of the actual wire diameter of 30–40 nm without the oxidation layer verified by TEM study. A fact that the minima in resistance exactly fall on the multiple integer of Φ_{0} provides an unambiguous evidence that the observed quantum oscillations in parallel H_{//} are the consequence of the ordinary 0AB effect due to the metallic surface states of the cylindrical wire. As expected theoretically^{28,29} that the 0AB effect with a period of Φ_{0} can be realized at doping large enough that the resistance is less than the quantum resistance h/e^{2}. In our case, there is no reason to expect that the Fermi energy coincides exactly with the Dirac point in surface state.
Besides the 0AB effect, we also noticed a doublepeak feature in the oscillation spectra, where tiny dips were found to superimpose on the most of the broad peaks of the 0AB oscillations. Although the dips at the odd multiples of Φ_{0}/2 are relatively weak and smeared out with the increase of temperatures, the doublepeak feature is at least well resolved below 1.4 K and reproducible with Hscan from 16 T to 16 T. There are two possibilities for these tiny dips. (1) They are the consequence of the weak π–AB oscillations with a period of Φ_{0} but the minima at each odd multiple of Φ_{0}/2 due to the massless Dirac carriers on the SS of the TIwire induced by the topological Berry's phase, as predicted by the theories^{28,29}. (2) They are the normal AAS effect of the weak topological trivial electrons with a period of Φ_{0}/2, where the dips at even multiples of Φ_{0}/2 are exactly at the same positions with the 0AB effect and thus cannot be recognized. It is difficult to verify either scenario suggested above being more adequate from the present data. However, our observation, at least, clearly demonstrated that the topological surface state is not destroyed by the surface oxidation of the wire and, in contrast, it becomes more robust with the decrease of the wire diameter. We have to mention that the AB oscillations wellrecognized in 40 nm diameter wire were not resolved clearly in 100 nm and 320 nm larger diameter wires although the SdH oscillations or universal conductance fluctuations (UCF) were definitely observable in perpendicular field as shown in Fig. 2 (c). This is because the quantum oscillations were enhanced with the decrease of wire diameter and their amplitude in perpendicular field is much larger than that in parallel field.
Fig. 4 (b) shows the variation of the resistance, ΔR, as a function of H_{⊥} at different T after the subtraction of a fitted smooth background (each curve was shifted up for clarity by adding a constant value). Compared with the Roscillations in H_{//}, the amplitude of the oscillation spectra in H_{⊥} become more significant and, especially, some resolvable fine structures, such as the tiny kinks, are visible at 0.2 K. The influences of the AB oscillations in H_{⊥} orientation can be completely excluded because the AB spectrum is expected only in parallel field. It was seen that the oscillation spectra in H_{⊥} do not display periodic behavior with H_{⊥}. However, when we plot the variations of the resistance, ΔR, as a function of 1/H_{⊥} at different T as shown in Fig. 5 (a), the spectra do display a periodic behavior with 1/H_{⊥} in the high field regime if defining each minima, together with the tiny kinks resolved at 0.2 K as marked specifically by the dashed lines. The periodicity of the oscillations is about Δ(1/H_{⊥}) = 0.036T^{−1}. Such periodic feature of the conduction spectra as a function of 1/H_{⊥} is generally considered to be a direct signature of the SdH oscillations.
To verify these quantum oscillations in H_{⊥} is truly from the SdH effect, Fig. 5 (b) plots the integer LL index, n (open squares) vs. 1/H_{⊥} at the minima or kinks of the SdH spectrum and the data defined from the maxima are also shown additionally in the plot as the solid squares (shifted by 1/2 in LL index). It was clearly seen that the curve (A) nicely falls on a straight line. While both two dimensional electron gas (2DEG) in conventional semiconductors and in 2D Dirac electron system have a linear n vs. 1/H_{⊥} dependence, the different Berry's phase would make the intercept zero for regular 2DEG and nonzero for Dirac system at ultra quantum limit. Clearly, the bestfit straight line intercepts the naxis at the value of γ = −0.41± 0.1, almost close to the ideal value of γ = −1/2 than 0 or 1. Such a 1/2shifted SdH effect in high H_{⊥} regime provides unambiguously transport evidence for the surface Dirac spectrum in TI due to the nontrivial Berry's phase.
From Fig. 5 (b), the best fit of the straight line gives a Fermi crosssection areas, S_{F}, of 30.7 T (i.e., 3.1 × 10^{17} m^{−2}). The Fermi wave vector, and the 2D carrier density, , can be, therefore, estimated to be respectively, 0.055Å^{−1} and 4.9 × 10^{12} cm^{−2}. All of these values estimated from 40 nm Bi_{2}Te_{3} nanowire are well on the same order of those obtained in the surface states of Bi_{2}Te_{3} crystals^{16,18,32,33} and Bi_{2}Se_{3} nanoribon^{19}.
In order to fully understand the surface SdH oscillations, it might be useful to directly compare the MR data with the theoretical expression for the SdH oscillations of a 2DEG system, where the general formula is described as^{19},
H_{F} is the frequency of the SdH oscillations in 1/H_{⊥} and A, μ and β × 2π are respectively the temperature dependent amplitude, carriers mobility and the Berry's phase. Using the H_{F} extracted from the slope of the curve (A) in Fig. 5 (b), the best fit, as shown by the solid red curve in Fig. 6 (a), results in β = 0.49 ± 0.01, A = 39.01 ± 6.81 Ω and μ = 0.33 ± 0.07 m^{2}/Vs, respectively. For 2D Dirac electrons, the Berry's phase of π should be β = 0.5, the fitted value of β = 0.49 from eq.(1) is in good agreement with the expectation for surface Dirac electrons. Since the mobility, and k_{F} = 0.055 Å^{−1}, the electron mean free path, , in the surface Dirac states is estimated to be 119.6 nm. Hence, the metallicity parameter, , is then estimated to be ~66, which is also in excellent agreement with those obtained from the SS of high quality Bi_{2}Te_{3} bulk crystals^{16}.
However, one may notice that the amplitude of the SdH spectrum was poorly described by eq.(1) in low field regime, such as the initial three big peaks cannot be described and the predicted minima at n = 5 and 6 shrink to tiny kinks. A probable origin is that there also exists an additional set of SdH oscillations superimposed on the surface Dirac spectrum. Indeed, the three broad peaks in 1/H_{⊥} spectrum in low field regime, as indicated by the solid lines in Fig. 5 (a), are equal gaped, indicating a nature of another set of SdH oscillations. The LL index, n vs. 1/H_{⊥} dependence (shifted by 1/2) by defining the maxima of three broad peaks is shown in Fig. 5 (b) as the solid circles in curve (B) (the data defined from the minima are also additionally shown in the curve as the open circles). The bestfit straight line of the curve (B) passes exactly through the zero point of naxis with the ideal value γ = 0. The best fit of the straight line gives a Fermi crosssection area, S_{F}, of 8.0 T (i.e., 0.77 × 10^{17} m^{−2}). The Fermi wave vector, k_{F} and surface carrier density n_{2D} are, therefore, evaluated to be respectively, 0.016 Å^{−1} and 2.56 × 10^{12} cm^{−2}. Similarly, the initial three SdH peaks in low field regime at T = 0.2 K can be well described with three fitting parameters of β = 0.9 ± 0.01, A = 37.99 ± 9.23 Ω and μ = 0.61 ± 0.13 m^{2}/Vs, as shown by the solid green curve in Fig. 6 (b). Hence, the conventional electron meanfree path, and the metallicity parameter, , are then respectively ~64.1 nm and 10. For conventional 2DEG, the Berry's phase of 2π should be β = 1.0, the fitted value of β is ~0.9, again in agreement with our expectation for a massive fermions. These data clearly indicated that this set of the SdH oscillations with a relative large period of Δ(1/H_{2}) = 0.128 T^{−1} is less dependent on the topological nontrivial surface Dirac carriers, but probably has a nature of the trivial carriers in the surface states away from the Dirac point. The magenta solid curve in Fig. 6 (c) is the sum of the two set of the SdH oscillations, which almost manifasts the main feature of the experimental data. Back to the previous data in parallel H_{//}, the tiny dips superimposed on the broad peaks of the 0AB spectra might have the same origin due to the trivial electrons in the SS, instead of the πAB effect. All of the data support the coexistence of the nontrivial topological Dirac state and trivial electron state on the surface of TI wires^{37}.
One may comment on why the SdH oscillations were not detected in H_{//}. To account for this issue, let's estimate the magnetic lengths, at n = 1. From Fig. 5 (b), the 1/H_{1} of both SdH spectra are respectively 0.05 T^{−1} and 0.116 T^{−1} and thus we get ~5.7 and 8.7 nm, respectively. Both values are larger than the thickness of the topological surface states which were considered to be on the order of ~2 nm or less. In other words, all of the radii of the electron cyclotron orbits at LLs with n ≥ 1 exceed the thickness of the surface states and therefore omits the possible SdH oscillations of the SS in H_{//}.
Finally, we have to emphasize that the positive MR behavior with a steep valley in low H regime is a common feature for all of the TIwires while their RT curves might display variations from wire to wire. In our three diameter nanowire samples, we observed the hump and the upturn or the shallow minimum in RT curves, but the estimated 2D density n_{2D} ~4.9 × 10^{12} cm^{−2}, is almost 4 times larger than the density measured in other Bi_{2}Te_{3} nanoribbons^{18} and Bi_{2}Te_{3} bulk^{16} having a metallic behavior. Actually, we have not very satisfied explanation on why our nanowires with a relative high carrier density display the hump, upturn and the nonmetallic behavior. However, a possible understanding is the inhomogeneity of defects or impurities along the wire created by the process of nanofabrication for the electrodes, especially near the contact area, where the ee interactions might be dominant due to the strong disordering. This means that the MR behavior actually echoes the intrinsic surface property of the TIwires and are directly related to the metallic surface state, while the resistivity is a consequence of the combinations of all band charge carriers interacted with their environment. Secondly, the 0AB and the SdH oscillations are always visible in all of 40 nm wires we investigated, in contrast, only UCF can be seen in large diameter wires (see Fig. 2c). Thirdly, the topological TI surface state in 40 nm wire was found to be robust and still survive regardless of the surface oxidation. This data is also consistent with the previous observations by Peng et al.^{38} that the Dirac cone of the surface states can be clearly seen in monthsold samples exposing to air for a few days and in samples with controlled surface contaminations of CO and O_{2} gas molecules by Liu et al.^{39}. A fact that the quantum oscillation phenomena were enhanced considerably with the decrease of wire diameter indicates that the Dirac point which usually closes to the valence band in Bi_{2}Te_{3} bulk samples was fortunately lifted up to the midgap region due to the surface oxidationinduced disorder in ultrathin wires^{39}. In other words, the small diameter Bi_{2}Te_{3} wires with a natural surface oxidation might be a nice candidate for the detection of TI surface states and the potential application for electronic devices. A very interesting scenario for checking the theoretical model in 1D TI wire as suggested by Bardarson et al.^{28} is that, by varying the chemical potential of the surface states of the TI, the minimum of the resistance should shift back and forth between Φ = 0 and Φ = π or, alternatively, change the period of the resistance oscillations from Φ_{0} to Φ_{0}/2 by increasing the surface disorder. It might be possible to realize the switching behavior between 0 and π–AB oscillations by reducing the wire diameter continuously by considering the surface bandbanding and the size confinement effect.
In summary, we provide unambiguously dual transport evidence of topological surface Dirac states in 40 nm Bi_{2}Te_{3} singlecrystal nanowire by measurement of both AB oscillations with a period of Φ_{0} in H_{//} and the 1/2shifted SdH oscillations in H_{⊥}. Both types of the quantum oscillations are expected only from the Dirac spectrum of the topological surface states. In addition, our data also showed that the AAS effect with a period of Φ_{0}/2 and the ordinary SdH quantum oscillations coexisted with the anomalous 0AB and 1/2shifted SdH oscillations in the surface states of the wire. The nature of these ordinary quantum oscillations might be the consequence of the conventional electrons confined to the same region of space or due to the inhomogeneity of defects or disordering alone the wire, which are probably tunable for application on future electronics.
Methods
Synthesis
Bi_{2}Te_{3} nanowires used in this work were synthesized by AAO templateassisted electrodeposition. The solution was prepared by dissolving 10 mM Te (powder: 99.9998% purity) and 7.5 mM Bi (shots: 99.999% purity) elements into concentrated nitric acid (69.1%) and the solution was then diluted to 1 M final concentration with distilled water. The synthesis of nanowires was carried out using a threeelectrode system at a constant potential of −62 mV, relative to an Ag/AgCl reference electrode at room temperature. A pure Ptwire was used as the counter electrode and Au film evaporated on one side of the AAO membrane prior to the electrodeposition was used as the working electrode. Freestanding nanowires were obtained by dissolving the membrane with 2 M aqueous NaOH solution, followed by several cycles of cleaning process via centrifugation.
Device fabrication and characterization
To make standard fourprobe devices on an individual Bi_{2}Te_{3} Nanowire for transport measurement, we dispersed the nanowires onto a silicon substrate with a 1 μm thick Si_{3}N_{4} insulating layer. Then, the sample was transferred into FEI SEM/FIB dual beam system for the deposition of Ptelectrodes. The size of the four Ptstripe electrodes has a nominal width of 100 nm and a thickness of 150 nm deposited from a precursor gas of (methylcyclopentadienyl)trimethyl platimum (CH_{3})_{3}CH_{3}C_{5}H_{4}Pt. Usually, the film by FIBinduced Pt deposition is amorphous consisting of Pt, C, Ga or O depending on the deposition condition. The resistivity of the FIBdeposited Pt stripes varies from 70 to 700 μΩ.cm, almost 12 orders higher than that for a Pt bulk, but the contact resistance between the Pt electrode and TI wire is almost transparent with a resistance less than 10 Ω. While the maximum spreading or diffusion distance of the actual Pt along the wire is on the order of 300 nm, the distance (L) between the inner edges of the two voltage electrodes for all of the studied samples was kept larger than 4 μm, which is much longer than the spreading distance.
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Acknowledgements
We acknowledge fruitful discussions with Prof. H. W. M. Chan, Zhong Fang, Lin He, Jianxin Li, Ying Liu and Yi Zhou. This work was supported by the National Key Basic Research of China, under Grant Nos. 2011CBA00111 and 2010CB923403; the National Nature Science Foundation of China, Grant Nos. 11174292, No. 11104281 and No. 11104280; Dr Tian also thanks the support of the Hundred Talents Program of the Chinese Academy of Science and the Center for Nanoscale Science (Penn State MRSEC) funded by NSF under Grant No. DMR0820404, USA.
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M.T. supervised the research and contributed to the analysis. M.T., W.N., H.D. and J.W. synthesized the Bi_{2}Te_{3} nanowires and fabricated the devices. W.N., Z.Q. and H.D. carried out the transport measurement in high magnetic field and performed structural analysis. M.T. and W.N wrote the paper, together with help of all other coauthors.
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Tian, M., Ning, W., Qu, Z. et al. Dual evidence of surface Dirac states in thin cylindrical topological insulator Bi_{2}Te_{3} nanowires. Sci Rep 3, 1212 (2013). https://doi.org/10.1038/srep01212
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DOI: https://doi.org/10.1038/srep01212
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