Ambipolar field effect in the ternary topological insulator (BixSb1–x)2Te3 by composition tuning

Ambipolar Field Effect in Topological Insulator Nanoplates of (BixSb1-x)2Te3 Desheng Kong1,+, Yulin Chen2,3,4,+, Judy J. Cha1, Qianfan Zhang1, James G. Analytis2,4, Keji Lai2,3, Zhongkai Liu2,3,4, Seung Sae Hong2, Kristie J. Koski1, Sung-Kwan Mo5, Zahid Hussain5, Ian R. Fisher2,4, Zhi-Xun Shen2,3,4, and Yi Cui1,* 1Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA, 2Department of Applied Physics, Stanford University, Stanford, California 94305, USA, 3Department of Physics, Stanford University, Stanford, California 94305, USA, 4Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA, 5Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.+These authors contributed equally to this work. Topological insulators represent a new state of quantum devices, The manipulation matter attractive to both fundamental physics and concentration in technological demonstrated in applications such as 1-11 quantum information processing spintronics and . In a topological topological this of carrier insulator study paves type and nanostructures the way for implementation of topological insulators in nanoelectronics insulator, the bulk energy gap is traversed by spin- and spintronics. momentum locked surface states forming an odd number Recently, binary sesquichalcogenides Bi2Te3, Sb2Te3 of surface bands that possesses unique electronic and Bi2Se3 have been identified as three-dimensional (3D) properties. However, transport measurements have often topological insulators with robust surface states consisting been dominated by residual bulk carriers from crystal of a single Dirac cone in the band spectra7-9. In these 6 defects 12-14 or environmental doping materials, which mask the topological surface states have been topological surface contribution. Here we demonstrate experimentally confirmed with surface sensitive probes (BixSb1-x)2Te3 as a tunable topological insulator system to such manipulate bulk conductivity by varying the as 8,9,16,17 ARPES and scanning microscopy/spectroscopy (STM/STS) Bi/Sb 18,19 tunneling .. Several recent composition ratio. (BixSb1-x)2Te3 ternary compounds are magnetotransport experiments have also revealed charge confirmed carriers originating from surface states as topological insulators for the entire 13,20-22 . However, 9,10,13 despite the substantial efforts in material doping composition range by angle resolved photoemission and 23,24 spectroscopy (ARPES) measurements and ab initio electric gating calculations. Additionally, we observe a clear ambipolar carriers of these materials, especially in nanostructures, gating effect similar to that observed in graphene 15 , manipulating and suppressing the bulk using are still challenging owing to impurities formed during nanoplates of (BixSb1-x)2Te3 in field-effect-transistor (FET) synthesis and extrinsic doping from exposure to the ambient environment *To whom correspondence should be addressed: yicui@stanford.edu (Y.C.) 1 12-14 . M b d c SSB M 0.2 -0.2 0 0.2 Γ M M Γ M SSB Γ K K Γ K M Γ M BVB K Γ 0.2 0 0.2 M Γ M M BVB K Γ M BVB 0 0.1 -0.2 SSB BCB K Γ 0 M K SSB -0.2 K 0.2 Γ Γ 0 M K -0.2 M K 0.2 Γ K 0 M BCB -0.2 Binding energy (eV) a Bulk p-type -0.2 K c Sb2Te3 Bulk p-type Γ 0 (Bi0.25Sb0.75)2Te3 Bulk insulator Γ k (1/Å) Quintuple Layer (Bi0.50Sb0.50)2Te3 Bulk n-type K 0.2 Bi / Sb (Bi0.75Sb0.25)2Te3 Γ Te Bi2Te3 Bulk n-type K b K a BCB BCB BVB SSB BVB SSB BVB SSB BVB SSB /BVB SSB /BVB BVB 0.3 0.4 0.5 -0.2 0 0.2 -0.2 0 0.2 -0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0 0.2 -0.2 0 0.2 -0.2 0 0.2 0.0 0.2 -0.2 0.0 0.2 -0.2 0.0 0.2 k (1/Å) 0.4 0 0.2 SSB Dirac point BVB 0.4 Energy (eV) Binding energy (eV) (Bi0.50Sb0.50)2Te3 0.2 0.0 -0.2 0.6 -0.2 0.2 0 0.2 0 -0.2 -0.4 k (1/Å) Figure 1. (BixSb1-x)2Te3 is a tunable topological insulator system with a single Dirac cone of surface states. a, Tetradymitetype type crystal structure of (BixSb1-x)2Te3 consists of quintuple layers (~ 1 nm in thickness) bonded by Van der Waals interactions. b, ARPES Fermi surface (FS) map (top row) and band dispersion along K-Γ-M (bottom row) directions from bulk single crystals with nominal compositions of Bi2Te3, (Bi0.25Sb0.75)2Te3, (Bi0.50Sb0.50)2Te3, (Bi0.75Sb0.25)2Te3 and Sb2Te3. By increasing Sb concentration, Fermi energy (EF) exhibits systematic downshift from the bulk conduction band (BCB) to the bulk valence band (BVB) through a bulk insulating state achieved in (Bi0.5Sb0.5)2Te3. The surface state band (SSB) consists of a single Dirac cone around the Γ point, forming a hexagram FS (top row) and Vshape dispersion in the band structure (bottom row). The apex of the V-shaped dispersion is the Dirac point. Note the shape of the Dirac cone (especially the geometry below the Dirac point, which hybridizes with the BVB) also varies with the Bi/Sb composition. For Bi:Sb ratio less than 50:50, as-grown materials become p-type; the EF resides below the Dirac point thus only the lower part of the Dirac cone is revealed in the ARPES measurement (while the V-shape dispersion inside bulk gap is not seen). The n-type SSB pocket on FS shrinks with increasing Sb concentration and eventually becomes a p-type pocket hybridized with the bulk band (BVB) in the Bi:Sb concentrations of 25:75 and 0:100. c, 3D illustration of the band structure of (Bi0.50Sb0.50)2Te3 with vanished bulk states on FS. SSB forms a single Dirac cone with hexagram FS. d, Corresponding band structure calculations near Γ point show qualitative agreement with ARPES measurements with gapless SSB consist of linear dispersions spanning the bulk gap are observed in all the compositions. The difference of EF between calculated and measured band structures reflects the carriers arising from defects and vacancies in the crystals. alloy sharing similar tetradymite structure with the parent Here we propose ternary sesquichalcogenide (BixSb1as a tunable 3D topological insulator system compound Bi2Te3 and Sb2Te3 (Fig. 1a). To verify the allowing us to engineer the bulk properties via the Bi/Sb topological nature of (BixSb1-x)2Te3, we performed ARPES composition ratio. (BixSb1-x)2Te3 is a non-stoichiometric measurements on the (0001) plane of (BixSb1-x)2Te3 bulk x)2Te3 2 yielding calculations (Fig. 1d) in which the linear SSB dispersion experimental Fermi surface (FS) topology maps and band around the Γ point in all compositions confirms their dispersions (Fig. 1b). Along with the broad electronic topological non-triviality. This is not surprising as the spin- spectra originating from the bulk states, the single Dirac orbit coupling strength (critical for the formation of cone that forms the topological surface state band (SSB) topological insualtors ) and the bulk energy gap in is revealed around the Γ point for all ternary compositions ternary (BixSb1-x)2Te3, with varying Bi/Sb ratios, are indicated by the hexagram FSs (top row) and the sharp comparable to the parent compounds Bi2Te3 and Sb2Te3. linear dispersion in the band spectra (bottom row). The Consequently, a quantum phase transition to an ordinary parent compounds, as-grown Bi2Te3 (n-type) and Sb2Te3 insulator does not occur with varying Bi/Sb ratios, single crystals of multiple compositions 1-3 (p-type), are highly metallic with Fermi energy, EF, located complementary to a recent study on the topological deep inside the bulk conduction band (BCB) and bulk trivial/non-trivial phase transition in the BiTl(S1–δSeδ)2 valance band (BVB), respectively, due to excessive system . 26 9 This non-triviality across the entire carriers arising from crystal defects and vacancies . With compositional range in ternary (BixSb1-x)2Te3 compounds increasing Sb concentration, EF systematically shifts demonstrates a rich material assemblage of topological downward (Fig 1b, bottom row). In particular, at a Bi/Sb insulators based on an alloy approach, which is an ratio of 1:1, i.e. (Bi0.50Sb0.50)2Te3, the bulk states attractive avenue to search for material candidates with completely disappear at EF with a vanished bulk pocket in improved properties. The compositional engineering of the bulk properties of the FS map and band dispersion. The surface Dirac cone topological of (BixSb1-x)2Te3 (Fig. 1c) noticeably exhibits clear 9,18,25 hexagonal warping, similar to that of pure Bi2Te3 insulators nanostructures. . can also be Single-crystalline applied to (BixSb1-x)2Te3 The experimentally observed ARPES measurements nanoplates are synthesized by means of a catalyst-free are qualitatively reproduced by ab initio band structure vapor-solid (VS) growth using a mixture of Bi2Te3 and a b c e 100 75 1120 0.5 μm _ _ xEDX _ _ 1210 2110 50 25 0 d f Bi Sb c 5 μm 1 nm Te Carrier Density (cm-2) 0 25 50 x 75 100 15 10 1014 1013 2×1012 p type n type 0 25 50 x 75 100 Figure 2. Characterization of (BixSb1-x)2Te3 nanoplates. a, Optical microscopy image of vapor-solid grown (Bi0.50Sb0.50)2Te3 nanoplates. b, A high-resolution TEM image of the edge of a (Bi0.50Sb0.50)2Te3 nanoplate (shown in the inset) reveals clear crystalline structure with top and bottom surfaces as (0001) atomic planes. c, A selected area diffraction pattern with sharp diffraction spots indicates that the nanoplate is a high-quality, single crystal. d, Bi, Sb and Te elemental maps obtained from an EDX scan. Overlaying the elemental maps reveals the morphology of the nanoplate, indicating the elements are fairly uniformly distributed without obvious precipitates. e, The composition, xEDX, in (BixSb1-x)2Te3 nanoplates calibrated by EDX spectra. f, The nanoplate area carrier density is chemically modulated by adjusting compositions as determined by the Hall effect. The average carrier concentration from multiple samples is shown as solid circles with error bars corresponding to the maximum deviation. A schematic diagram of the device structure is shown in the inset. 3 27 a 50 R (kΩ) Sb2Te3 powders as precursors. The growth method has been established in our previous work . Figure 2a shows 25 a typical optical microscopy image of as-grown (BixSb1x)2Te3 nanoplates on an oxidized silicon substrate (300nm SiO2/Si) possessing thicknesses of a few nanometers and lateral dimensions of micrometers. On these substrates, 4 μm thin layers of nanoplates are semitransparent and can be readily identified with thickness-dependent color and contrast 27 resembling the optical properties of graphene. b The single-crystalline nature of these nanoplates is revealed by the clear lattice fringes in high resolution 0 75 R H (Ω) transmission electron microscopy (TEM) images (Fig. 2b) and the sharp selected area electron diffraction spot pattern (Fig. 2c). Energy-dispersive X-ray spectroscopy 0 -75 (EDX) elemental mapping reveals Bi, Sb, and Te -150 -150 distributed across the entire nanoplate without detectable phase separation (Fig. 2d). Nanoplate -75 0 75 150 VG (V) elemental composition is calibrated by EDX spectra (Fig. 2e). To Figure 3. Ambipolar field effect in a ultrathin nanoplates of reflect the initial growth conditions, the nanoplates are (BixSb1-x)2Te3. a, Typical dependence of resistance, R, on gate labelled with nominal compositions. We fabricated six- voltage, VG, in a ultrathin (Bi0.50Sb0.50)2Te3 nanoplate (~5 nm in terminal hall bar devices on thin nanoplates with thickness) exhibiting a sharp peak in the resistance and thicknesses ranging from 5nm to 10nm for transport subsequent decay. Inset: an optical microscopy image of the measurements (shown schematically in the inset of Fig. FET device with a thickness of ~5 nm as determined by AFM. b, 2f). In Fig. 2f, we illustrate the dependence of carrier types Hall coefficient, RH, versus, Vg, for the same nanoplate. Each RH and areal carrier densities on composition measured by (solid circle) is extracted from the Hall trace between ±6T at a the Hall effect, which is consistent with the trend in bulk certain VG. At the VG of peak R, RH exhibits a sign reversal. crystals. Binary Bi2Te3 (n-doped) and Sb2Te3 (p-doped) nanoplates contain very high carrier densities of ~10 2 14 cm - FET devices. In ultrathin nanoplates (~5 nm), the typical . By adjusting the composition in ternary (BixSb1-x)2Te3 dependence of the resistance, R, on the gate voltage, VG, nanoplates, the carrier density systemically drops orders (Fig. 3a) exhibits a very sharp peak that is ~50 times of the of magnitude with the lowest density achieved in resistance at large VG far from the peak position. The Hall (Bi0.50Sb0.50)2Te3. In addition to the intrinsic defects formed coefficient, RH, reverses its sign when R approaches the during synthesis, the carrier concentration in chalcogenide maximum value (Fig. 3b). These behaviours resemble the topological insulators is often affected by extrinsic dopants 15 ambipolar field effect observed in graphene , which also contaminating the sample surfaces from atmospheric possesses 2D Dirac fermions. The gate voltage induces exposure12,13. For example, we have identified water as an an additional charge density and electrostatically dopes effective n-type dopant that is always present in ambient conditions (Supplementary Information, the nanoplate altering the nanoplate from an n-type Fig. S5). A conductor to a p-type conductor through a mixed state in systematic approach to modulate the carrier density is which both electrons and holes are present. For regions therefore essential for nanostructures to achieve low density since the extrinsic doping depends with only electrons or holes, R and |RH| decrease with on increasing gate-voltage-induced carrier concentration. In environmental conditions. The bulk carriers the mixed state, R approaches a peak value where the in low-density (BixSb1-x)2Te3 total carrier density is minimized; RH changes sign when nanoplates can be electrically suppressed with back-gate the dominant carrier type (electrons or holes) switches. As 4 120 c b 5 μm 0 3 2x10 R / R (T=117K) R (Ω) 4x10 RH (Ω) 60 3 -80 -40 0 40 2.0 1.6 1.2 80 20 0 40 VG (V) -55 e 600 R (Ω) -65 RH (Ω) -60 560 520 -70 80 100 -80 1.5 120 0 20 40 -40 f 0.96 0.92 0 -20 -30 -40 -70 0.88 0 0 20 40 60 60 100 120 80 100 1.00 0.96 -70 -80 -90 -100 -110 -120 0.92 0.88 120 0 20 40 60 80 100 120 T (K) T (K) VG (V) 80 T (K) 1.00 -75 -120 60 0.84 5 μm 480 2.0 T (K) R / R (T=109K) d -25 -40 -50 -60 -80 1.0 0.8 -60 0.0 2.5 80 10 0 -10 -20 -25 2.4 R / R (T=117K) 3 6x10 R / R (T=109K) a Figure 4. Temperature-dependent field effect in (BixSb1-x)2Te3 nanoplates. a, Dependence of resistance, R, and Hall coefficient, RH, on gate voltage, VG, from a 5 nm-thick (Bi0.50Sb0.50)2Te3 nanoplate (Inset) showing the ambipolar field effect. For Hall effect measurements, the solid circles are extracted from Hall traces between ±6T at specific VG. The curve is obtained by measuring the Hall resistance versus VG at magnetic fields of ±4T. b, c, Temperature dependence of R at different VG from electron conductor to mixed state (b) and hole conductor to mix state(c) respectively. R is normalized to its value at the highest measured temperature. d, Dependence of resistance, R, and Hall coefficient, RH, on gate voltage, VG, from a 9 nm-thick (Bi0.50Sb0.50)2Te3 nanoplate (Inset). e, f, Temperature dependence of R at different VG. R is normalized to the value at the highest measured temperature. expected, there is no zero-conductance region observed (kB is the Boltzmann constant) owing to multiple-channel presumably due to the presence of surface states inside conduction in the presence of surface carriers . In the bulk bandgap although other contributions cannot be addition, excluded (Supplementary Information, Fig S7 and S8). temperature but gradually saturates to a finite value below 22 the resistance does not diverge at low The temperature dependence of R further confirms the 10K consistent with metallic surface conduction in parallel suppression of bulk conduction in the mixed state. with bulk states. Further sweeping VG to negative values Systematic dependence studies were performed on restores the metallic behaviour of the nanoplate as a hole another device exhibiting the ambipolar field effect (Fig. conductor (Fig. 4c). 4a). In nanoplate the purely shows electron-conductive typical metallic region, behaviour the Finally, we observe a thickness dependence of the with transport measurements in FET devices. The suppression decreasing R as the temperature, T, is decreased due to of bulk conduction requires the nanoplate to be much electron-phonon scattering (Fig. 4b). As the nanoplate thinner than the depletion length, D, the length scale approaches the mixed state, R begins to increase with controlled by the gate. An order-of-magnitude estimation continued decreasing T for the entire temperature range found by solving the Poisson equation yields D ~ 11 nm (~2 to 120K) primarily due to the freeze-out of bulk carriers, (Supplementary Information, Fig S7). For a thicker also observed in lightly doped topological insulator Bi2Se3 nanoplate 13 of ~9 nm in thickness, however, the dependence of R on VG (Fig. 4d) shows a much weaker a / T kB ≈ R cannot be simply extracted by the relation E e R0 crystals . Note that the actual activation energy, Ea, tenability than the ultrathin nanoplates, and the entire sample remains n-type as RH does not reverse the sign. In 5 addition, R decreases with T for all VG exhibiting metallic layer nanoplates for the effective manipulation of bulk behaviour until ~20K below which weak carrier freeze-out conductivity. We also note that in the thinnest limit, the top is indicated by a slight rise in R (Fig. 4e-f). Apparently, the and bottom surface states may hybridize by quantum nanoplate is too thick to be effectively depleted by gating, tunnelling and open an energy gap, resulting in either a and large metallic bulk conduction is always present in the conventional insulator or two dimensional quantum spin device and contributes to the charge transport. It is hall system therefore important to fabricate FET devices from few- are beyond the thickness threshold for such a transition. METHODS Perdew-Burke-Ernzerhof type generalized gradient approximation 19,28-30 was used to describe the exchange–correlation potential. SOC Synthesis. Single crystals of BixSb2-xTe3 were obtained by slow was included using scalar-relativistic eigenfunctions as a basis cooling a binary melt of varying Bi/Sb/Te ratios. This mixture was after the initial calculation is converged to self-consistency. A k- sealed in quartz under a partial pressure of argon. The mixture grid of 10×10×1 points was used in the calculations and the was heated to a temperature of 800 ℃ over 14 hrs, held for an energy cutoff set to 300 eV. A 2 × 2 unit cell of Bi and Sb atoms additional 6 hrs, then cooled to 500 ℃ for 100 hrs, and finally the randomly substituted is used to simulate the structure. Lattice parameters of (BixSb1-x)2Te3 are interpolated from experimental furnace was naturally cooled to room temperature. lattice parameters of Bi2Te3 and Sb2Te3 according to the Ultrathin BixSb2-xTe3 nanoplates were grown inside a 12 inch composition. horizontal tube furnace (Lindberg/Blue M) with a 1-inch diameter Nanostructure Characterizations. Characterization was done using quartz tube. A uniform mixture of Bi2Te3 and Sb2Te3 powders optical microscopy (Olympus BX51M, imaged with 100X objective (Alpha Aesar, 99.999%) with specific molar ratio is placed at the under normal white illumination), TEM (FEI Tecnai G2 F20 X-Twin hot center region as precursors for evaporation. Degenerately microscope, acceleration voltage 200kV) equipped with an energy doped silicon substrates with 300nm thermally grown oxide film were placed downstream at certain . The measured thin nanoplates (≥5nm) locations using dispersive X-ray spectrometer, and AFM (Park Systems XE-70). the For TEM and EDX characterizations, (BixSb1-x)2Te3 nanoplates temperature gradient along the tube to control the growth are directly grown on 50nm Si3N4 membranes supported by temperature. The tube was initially pumped down to a base silicon pressure less than 100 mtorr and flushed with ultrapure argon windows. The actual composition of (BixSb1-x)2Te3 nanoplates are calibrated by EDX spectra with Bi2Te3 and Sb2Te3 repeatedly to reduce residual oxygen. During growth, argon flow spectra as references. provided impetus to transport the vapor to the subtrates. The Device Fabrication. Back-gate FET devices were directly typical growth conditions of (BixSb1-x)2Te3 nanoplates are: ~0.5 g fabricated on as-grown substrates with 300nm SiO2 films on power mixture, 10 torr pressure, 15 s.c.c.m. carrier gas flow, silicon. The substrates were first decorated with metal markers 490 ℃ precursor temperature, 10 min duration time. (BixSb1-x)2Te3 based on standard e-beam lithography followed by thermal tended to grow at locations of ~12cm away from the hot centre evaporation of Cr/Au (5nm/60nm). After a suitable nanoplate was region, corresponding to a temperature of ~300 ℃. selected, a second patterning step defined multiple Cr/Au Angular Resolved Photoemission Spectroscopy (5nm/100nm) electrodes by means of the markers. Measurements. Transport Measurements. Low-frequency (~ 200Hz to 1000Hz) ARPES measurements were performed at beamline 10.0.1 of the magnetotransport experiments were carried out in an Oxford Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory. The measurement pressure was kept below 3x10 cryostat with digital lock-in amplifiers (Stanford Research Systems 11 SR830). All transport measurements are measured at the base torr for all time, and data was acquired by Scienta R4000 temperature of 2.0K unless specified otherwise. A Keithley 2400 analyzers at a 10K sample temperature. The total convolved sourcemeter was used to apply gate voltage. The resistance is energy and angle resolutions were 15meV and 0.2°, i.e. measured with standard four-terminal configuration to eliminate 0.012(1/Å) for photoelectrons excited by 48eV photons. The fresh contact resistance. surface for ARPES measurement was obtained by cleaving the sample in situ along its natural cleavage plane. Theoretical calculations. Acknowledgement. Y.C. acknowledges the supported from the The first-principle electronic band Keck Foundation, and King Abdullah University of Science and calculations were performed in 6-quintuple-layer slab geometry Technology (KAUST) Investigator Award (No. KUS-l1-001-12). Y. using the Vienna Ab-initio Simulation Package (VASP). The 6 L. C., Z.K.L., Z.X.S., J.G.A. and I.R.F acknowledge the support from Department of Energy, Office of Basic Energy Science, 13 under contract DE-AC02-76SF00515. K.L. acknowledges the 14 KAUST Postdoctoral Fellowship support No. KUS-F1-033-02. 15 Author contributions. D.K.,Y.L.C. and Y.C. conceived the 16 experiments. Y.L.C. and Z.K.L. carried out ARPES measurements. J.G.A. synthesized and characterize bulk single crystals. Q.F.Z. 17 performed electronic structure calculations. D.K. and J.J.C. carried out synthesis, structural characterization and device fabrication for nanoplates. D.K., K.L., J.J.C., S.S.H. and K.J.K. 18 carried out transport measurements and analyses. All authors contributed to the scientific planning and discussions. 19 Additional information. The authors declare no competing financial interests. Supplementary information accompanies this 20 paper at arxiv.org. Correspondence and requests for materials 21 should be addressed to Y.C, email: yicui@stanford.edu. REFERENCES AND NOTES 1 2 3 4 5 6 7 8 9 10 11 12 22 Moore, J.E., The birth of topological insulators. Nature 464 (7286), 194‐198 (2010). Hasan, M.Z. & Kane, C.L., Colloquium: Topological insulators. Reviews of Modern Physics 82 (4), 3045 (2010). Qi, X.‐L. & Zhang, S.‐C., Topological insulators and superconductors. Preprint available at <http://arxiv.org/abs/1008.2026>. Bernevig, B.A., Hughes, T.L., & Zhang, S.‐C., Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314 (5806), 1757‐1761 (2006). Konig, M. et al., Quantum spin Hall insulator state in HgTe quantum wells. Science 318 (5851), 766‐770 (2007). Fu, L. & Kane, C.L., Topological insulators with inversion symmetry. Physical Review B 76 (4), 045302 (2007). Zhang, H. et al., Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5 (6), 438‐442 (2009). Xia, Y. et al., Observation of a large‐gap topological‐insulator class with a single Dirac cone on the surface. Nature Phys. 5 (6), 398‐402 (2009). Chen, Y.L. et al., Experimental realization of a three‐dimensional topological insulator, Bi2Te3. Science 325 (5937), 178‐181 (2009). Hsieh, D. et al., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 (7259), 1101‐1105 (2009). Chadov, S. et al., Tunable multifunctional topological insulators in ternary Heusler compounds. Nature Mater. 9 (7), 541‐545 (2010). Analytis, J.G. et al., Bulk fermi surface coexistence with Dirac surface state in Bi2Se3 : A comparison of photoemission and 23 24 25 26 27 28 29 30 7 Shubnikov‐de Haas measurements. Physical Review B 81 (20), 205407 (2010). Analytis, J.G. et al., Two‐dimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6 (12), 960‐964 (2010). Kong, D. et al., Rapid surface oxidation as a source of surface degradation factor for Bi2Se3. ACS Nano 5 (6), 4698‐4703 (2011). Novoselov, K.S. et al., Electric field effect in atomically thin carbon films. Science 306 (5696), 666‐669 (2004). Hsieh, D. et al., Observation of time‐reversal‐protected single‐ Dirac‐cone topological‐insulator states in Bi2te3 and Sb2Te3. Physical Review Letters 103 (14), 146401 (2009). Chen, Y.L. et al., Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329 (5992), 659‐ 662 (2010). Alpichshev, Z. et al., STM imaging of electronic waves on the surface of Bi2Te3: Topologically protected surface states and hexagonal warping effects. Physical Review Letters 104 (1), 016401 (2010). Zhang, Y. et al., Crossover of the three‐dimensional topological insulator Bi2Se3 to the two‐dimensional limit. Nature Phys. 6 (8), 584‐588 (2010). Peng, H. et al., Aharonov‐Bohm interference in topological insulator nanoribbons. Nature Mater. 9 (3), 225‐229 (2010). Qu, D.‐X., Hor, Y.S., Xiong, J., Cava, R.J., & Ong, N.P., Quantum oscillations and hall anomaly of surface states in the topological insulator Bi2Te3. Science 329 (5993), 821‐824 (2010). Xiu, F. et al., Manipulating surface states in topological insulator nanoribbons. Nature Nanotech. 6 (4), 216‐221 (2011). Chen, J. et al., Gate‐voltage control of chemical potential and weak antilocalization in Bi2Se3. Physical Review Letters 105 (17), 176602 (2010). Checkelsky, J.G., Hor, Y.S., Cava, R.J., & Ong, N.P., Bulk band gap and surface state conduction observed in voltage‐tuned crystals of the topological insulator Bi2Se3. Physical Review Letters 106 (19), 196801 (2011). Fu, L., Hexagonal warping effects in the surface states of the topological insulator Bi2Te3. Physical Review Letters 103 (26), 266801 (2009). Xu, S.‐Y. et al., Topological phase transition and texture inversion in a tunable topological insulator. Science 332 (6029), 560‐564 (2011). Kong, D. et al., Few‐layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential. Nano Letters 10 (6), 2245‐2250 (2010). Liu, C.‐X. et al., Oscillatory crossover from two‐dimensional to three‐dimensional topological insulators. Physical Review B 81 (4), 041307 (2010). Li, Y.Y. et al., Intrinsic topological insulator Bi2Te3 thin films on Si and their thickness limit. Advanced Materials 22 (36), 4002‐4007 (2010). Cho, S., Butch, N.P., Paglione, J., & Fuhrer, M.S., Insulating behavior in ultrathin bismuth selenide field effect transistors. Nano Letters 11 (5), 1925‐1927 (2011).