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Surface-dominated Conduction in a 6 nm-thick Bi2Se3 Thin Film Liang He, Faxian Xiu, Xinxin Yu, Marcus Teague, Wanjun Jiang, Yabin Fan, Xufeng Kou, Murong Lang, Yong Wang, Guan Huang, Nai-Chang Yeh, and Kang L. Wang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl204234j • Publication Date (Web): 08 Feb 2012 Downloaded from http://pubs.acs.org on February 14, 2012

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Surface-dominated Conduction in a 6 nm-thick Bi2Se3 Thin Film

Liang He1*, Faxian Xiu2, Xinxin Yu1, Marcus Teague4,Wanjun Jiang1, Yabin Fan1, Xufeng Kou1, Murong Lang1, Yong Wang3, Guan Huang1, Nai-Chang Yeh4, Kang L. Wang1*. 1

Device Research Laboratory, Department of Electrical Engineering, University of California, Los

Angeles, California, 90095, USA 2 Department of Electrical and Computer Engineering, Iowa State University, Ames, 50011, USA 3 State Key Laboratory of Silicon Materials and Center for Electron Microscopy, Department of Materials Science and Engineering, Zhejiang University, Hangzhou, 310027, China, 4Department of Physics, California Institute of Technology, Pasadena, California, 91125, USA *To whom correspondence should be addressed. E-mail: heliang@ee.ucla.com, wang@ee.ucla.edu,

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Abstract

We report a direct observation of surface dominated conduction in an intrinsic Bi2Se3 thin film with a thickness of 6 quintuple layers (QLs) grown on lattice-matched CdS (0001) substrates by molecular beam epitaxy (MBE). Shubnikov-de Haas (SdH) oscillations from the topological surface states suggest that the Fermi level falls inside the bulk band gap and is 53 Âą 5 meV above the Dirac point, in agreement with 70 Âą 20 meV obtained from scanning tunneling spectroscopies (STS). Our results demonstrate a great potential of producing genuine topological insulator devices using Dirac Fermions of the surface states, when the film thickness is pushed to nano-meter range.

Keywords: Intrinsic topological insulator, Bi2Se3, transport properties, surface states, Quantum oscillations.

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ToC figure 1.9 K 5K 8K 10 K

20 10 0 -10

0.8 0.7 dI/dV (a.u.)

30

∆ Rxx (Ω Ω)

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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-20 -30 0.15

0.20 -1 1/B (T )

0.25

0.30

0.6 0.5

Dirac point

0.4 0.3 -400 -300 -200 -100 0 E (meV)

100 200

Intrinsic 3D topological insulators of Bi2Se3 have been grown on CdS (0001) substrates by molecular beam epitaxy. Shubnikov-de Haas (SdH) oscillations and scanning tunneling spectroscopies confirm the Fermi level is within the bulk band gap. Our results demonstrate a great potential of producing genuine topological insulator devices using Dirac Fermions of the surface states.

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Three-dimensional (3D) topological insulators (TIs) have attracted great attention from both theoretical and experimental aspects1-6. It is known that they have a semiconductor gap in the bulk with an odd number of Dirac-cone surface states. Soon after theoretical predictions, the surface states of 3D TIs have been demonstrated by angle-resolved photoemission spectroscopy (ARPES)7-10 and scanning tunneling microscopy (STM)9, 11, 12. However, a direct transport measurement of the surface effects is significantly hindered by the dominant bulk carrier conduction. Scientist have tried various approaches to overcome the bulk conduction, such as electrical tuning of the Fermi level into bulk band13, 14, counter doping with Ca or Na15, and synthesizing novel complex materials such as (BiSb)2Se316, and Bi2(SeTe)317, 18. To some extent, these approaches have demonstrated success in enhancing surface conduction. However, the fundamental understanding of surface conduction in high quality samples is crucial for utilization of surface states in microelectronics and spintronics. In this paper, we report highcrystalline quality Bi2Se3 thin films grown on CdS (0001) substrate by molecular beam epitaxy demonstrate surface-dominated conduction. Importantly, the Fermi levels of current thin films fall inside the bulk band gap. As a result, the surface state conduction can be clearly distinguished from other conducting channels. In particular, for a 6 QLs thin film, we show most of conduction come from the surface. Bi2Se3 thin films were grown with an ultra-high vacuum MBE chamber on lattice-matched insulating CdS (0001).19 After growth, standard Hall bar devices were fabricated with a physical mask, as shown schematically in Fig. 1 (a). The longitudinal sheet resistance (Rs) as a function of temperature (T) is displayed in Fig. 1 (b), where four different regimes can be clearly identified, marked as I, II, III and IV from high to low temperatures. In regime I, for thinner films (< 9 QLs), Rs exponentially increases as the temperature decreases. This is most likely associated with the bulk band gap. The activation energy of it can be estimated from the Arrhenius slope of ln(Rs) vs. 1/T .20,

21

The thickness dependent

activation energy is plotted in Fig. 1 (c). The systematic increase of the estimated bulk band gap with the reduced the film thickness is attributed to the quantum confinement of the film along the growth

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direction (perpendicular to the substrate), which is qualitatively agreed with the recent ARPES measurements of Bi2Se3 grown on SiC (0001) by MBE.22 For thicker films, however, Rs does not show the same exponential behavior at high temperatures, which can be ascribed to the overwhelming electrons activated from the bulk impurity band as will be discussed later. In Regime II, the resistance reduces as temperature decreases, resembling a metallic behavior as observed widely in TIs.13, 16,

24

Such a decrease can be explained by alleviated phonon scatterings when

temperature decreases. This can be further confirmed by a power-law increase of mobility ( µ ∝ T −2 ), as will be described in Fig. 2 (e) (dashed line). In Regime III (30 K < T < ~ 80 K), the resistivity exhibits another exponential increase with respect to 1/T. This exponential increase is most likely associated with the frozen-out effect of electrons from the bulk conduction band to a shallow impurity band below it.21, 25 In Regime IV (T < 30 K), the resistivities of all samples approach to constant values. A similar temperature-dependent behavior was reported in our previous work: Bi2Se3 grown on Si (111) substrate.26 And this temperature regime is believed to be dominated by surface conduction. In Region IV where the bulk carriers freeze out, the transport is presumably a combination of surface states and impurity band conduction.17, 18, 21 The sheet conductance is monotonically increases with film thickness as shown in Fig. 1(d). This variation of the conductance with film thickness is attributed to the impurity band. By fitting the conductance of thicker films (20 to 60 QLs), where the impurity band conduction dominates, a linear relationship of G = 8.75 × (t-6.4) can be obtained (solid line in Fig. 1 (d) and (e)), where G is the conductance in the unit of e2/h, and t is the film thickness. This result suggests that below a critical thickness 6.4 QLs, the contribution from the thickness dependent component is close to zero. We have noticed linearly fitted solid line from the thicker samples deviated from the data of thinner films below 10 QLs, as shown in Fig. 1 (e). The difference of ~10 e2/h, as indicated by the double arrows, is considered to be the conduction from the surface states which agrees closely with the Hall data to be described later. As samples getting thinner, the surface states also open a band gap because of

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the hybridization between the top and bottom surfaces;22 therefore the metallic surface states seem to disappear. These samples behave like normal insulators and thus the conductance drops dramatically down to 1.5 e2/h (5 QLs) and 0.1 e2/h (3 QLs). Based on the simplified model, for samples around the critical thickness (~ 6.4 QLs), the surface state conduction is the dominant channel. In other words, for our 6 QL sample, most of the total conduction is provided by surface states. In order to further investigate the multiple channel conduction for thicker films, magnetic field and temperature dependent longitudinal resistance (Rxx) and Hall resistance (Rxy) have been measured. These data reveal the co-existence of three conducting channels: the bulk, the impurity band and the surface states.17 The parallel Hall conductance is given by

G xy ≡

R xy R xy2 + RS2

= G Bulk + GIm purity + G Surface

(1)

where Rxy is the Hall resistance, Rs is the sheet resistance, GBulk, Gimpurity and Gsurface represent the Hall conductance of the bulk, the impurity band, and the surface states, respectively. Additionally, the Hall conductance of each channel is described by a semiclassical expression, G = enµ ×

µB , (1 + µ 2 B 2 )

(2)

where n is the 2D carrier density and µ is the mobility of each channel.16 As an example, we present the analysis results of the Hall conductance for a 10 QL sample at different temperatures as described below. At high temperatures (Regime II in Fig. 1 (b)) where the phonon scattering dominates, the total conductance is then overwhelmed by electrons in the bulk conduction band excited from the impurity band. As a result, the total conductance of Gxy can be simplified by the dominant bulk conducting channel, as given in Fig. 2 (a). At low temperature (Regime IV in Fig. 1(b)), when all electrons are frozen in the impurity band, there is nearly no contribution from bulk, thus the total conduction is a combination of those of the surface and the impurity band, evident in Figure 2 (b). In the intermediate temperature (Regime III in Fig. 1(b)), the total conduction consequently results from all three channels, ACS Paragon Plus Environment

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illustrated in Fig. 2 (c). Following this procedure, we can obtain the temperature dependence of carrier density and mobility for the three channels (1.9 to 300K). Figure 2(d) illustrates the temperature dependence of the two-dimensional carrier density of the three channels. The bulk carrier densities (green triangles) decrease exponentially as carriers are frozen to the impurity band. Since the carriers in the bulk conduction band are electrons, their temperature dependent

(

)

density can be described as a classic Fermi-Dirac distribution of nb = n0 / e Ea / k BT + 1 (solid yellow line in Fig. 2 (d)), where n0 is the bulk carrier density of ~ 4 × 1015 cm-2, and Ea of 20 meV is the energy gap between the impurity band and the bottom of the bulk conduction band. The carrier densities of the impurity band (blue squares) and surface states (red circles) remain approximately a constant of 1.3 × 1013 cm-2 and 4 × 1011 cm-2, respectively. Figure 2 (e) shows the corresponding mobility at different temperatures. The mobility of bulk electrons (green triangles) exhibits a power law µ ∝ T-2 at high temperatures, consistent with the dominant phonon scattering as mentioned before in the Region II of Fig. 1 (b). At low temperatures (T < 20 K), mobilities of both the impurity band and the surface states reach constant values of ~ 380 cm2/V⋅s and ~ 5000 cm2/V⋅s, respectively. Based on the above analysis, we can subsequently estimate the longitudinal conductance Gxx (=neu) of 20 e2/h and 8 e2/h for the impurity band and the surface states, respectively. The numbers are in quantitative agreement with the previous results from the thickness dependent conductance as shown in Fig. 1 (e), in which the estimated conductance of the impurity band and surface states is 22 e2/h and 10 e2/h respectively for 10 QL sample. As we demonstrated above, samples with a film thickness around 6.4 QLs will have the most pronounced surface conduction. Indeed, we have observed characteristic quantum oscillations originated from the surface states for our 6 QLs sample. In Fig. 3 (a), we present the field dependent longitudinal resistance, Rxx, acquired at 1.9K for the 6 QL sample. Strong oscillations of Rxx at various temperatures after subtracting a smooth background can be observed, as shown in Fig. 3 (b). The oscillations become stronger with the increase of magnetic field and decrease of temperature. For a two-dimensional Fermi

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surface, the peak positions depend only on the field B⊥ = B cos(θ ) , normal to sample surface, (θ is the tilt angle between B and c). As show in the inset of Fig. 3 (b), the peak field of Landau level n=3.5 (second peak in Fig. 3(a)) has been plotted at different field angels. It follows 1/cos(θ) perfectly, suggesting the SdH oscillations originated from a 2D Fermi surface. It is well know that in the SdH oscillations, the Landau level index n is related to the cross section area of the Fermi surface (SF) by 2π (n + γ ) = S F

h , eB

(3)

where e is the electron charge, ћ is the Plank’s constant divided by 2π, B is the magnetic flux density, and γ = 1/2 or 0 represent the Berry phase of π or 0. As shown in Fig. 3 (c), the value of 1/B corresponding to the maximum and the minimum in ∆Rxx (arrows in Fig. 3(a) and lines in Fig. 3(b)) is plotted as a function of the Landau-level number. A linear fit yields SF = 1.53 × 1017 m-2, with the Fermi wave vector kF = 0.022 Å-1, and a 2D carrier density of 3.9 × 1011 cm-2, consistent with our previous results of 4 × 1011 cm-2 for the surface states in Fig. 2 (d). The n-axis intercept, γ ~ 0.35 ± 0.08 slightly deviates from exactly π Berry phase, as has also been reported on other SdH studies of TIs.17, 18, 24, 27 Following the Lifshitz-Kosevich (LK) theory,28 the temperature dependence of the SdH amplitude is described

by

∆σ xx (T ) / ∆σ xx (0) = λ (T ) / sinh(λ (T ))

.

The

thermal

factor

is

given

by

λ (T ) = 2π 2 k BTmcyc /( heB ) , where mcyc is cyclotron mass and ћ is the reduced Planck constant. As shown in Fig. 3 (d), the best fit gives the cyclotron mass mcyc = 0.07 me, where me is the free electron mass. Assuming

that

the

electrons

are

Dirac

type,

the

Fermi

velocity

can

be

calculated

as ν F = hk F / mcyc = 3.6 × 105 m / s , and E F = mcycν F2 = 53meV . The estimated Fermi level of 53 meV above the Dirac point is surprisingly low, suggesting the surface carriers are electrons and the EF is within the bulk band gap. To acquire the lifetime of the surface states ( τ ), the Dingle factor e − D has been examined, where D = 2π 2 E F / (τ eBVF2 ) 13, 16. Note that ∆R / R is proportional to [λ (T ) / sinh(λ (T ))]e − D , and the lifetime

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can

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be

inferred

from

the

slope

in

the

logarithmic

plot

of

log[( ∆R / R0 ) B sinh(λ (T ))] ~ [2π 2 E F / (τ eVF2 )] × (1 / B ) (Fig. 3 (e)). By applying the extracted cyclotron

mass, the scattering time τ = 1.3 × 10-12 s can be estimated. Thus the mean-free path of the surface electrons is l = ν F τ = 4.6 × 10 −7 m , and the surface mobility is µ =

eτ = 13,200cm 2 / V ⋅ s . We have mcyc

noticed that the estimated mobility is higher than the results from our previous fitting from Hall data of surface carrier mobility, 5000 cm2/Vs. In other systems,17,

28, 29

the similar discrepancy was also

observed, and the reason maybe lies in the difference between relaxation time and scattering time.30 To investigate the surface states as well as the position of surface Fermi level, we performed ARPES measurements on our samples. Figure 4(a) presents a standard ARPES spectroscopy cut along Γ - K direction of a 60 QL sample, the zero point of the energy scale has been shifted to the Dirac point. We have noticed that the Fermi level of the ARPES data is inside the bulk conduction band. This may be due to the n-type doping over long time between sample growth and ARPES measurement, as previously show

18, 31

. Another possible reason is due to optical doping induced charge accumulation

during ARPES measurement.31 By finding the maximum of the surface state in the K direction for different energies, we can attain the Fermi area and the surface carrier density (ns) as a function of energy. In Figure 4 (b), the horizontal axis has been scaled to fit our experiment data (red circle). The green square is adopted from Ref.

24

and the purple triangles are the results from our other samples of

Bi2Se3 grown on Si (111).32 The consistence between transport results and ARPES supports our estimation of the Fermi level position. Scanning tunneling spectroscopy (dI/dV) was also performed on the 6 QL sample to measure the density of states (DOS). As expected, the minimum of the conduction corresponding to the Dirac point is ~ 70 ± 20 meV below the Fermi level (Fig. 4(c)), in reasonable agreement with our estimation from the SdH oscillations. The STS data further confirms that our Fermi level is inside the bulk band gap and very close to the Dirac point.

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To conclude, we have observed surface dominated conduction from a 6 QL Bi2Se3 thin film grown by MBE. We demonstrated that the intrinsic Bi2Se3 thin film has a Fermi level positioned within bulk band gap. Our results shed the light on the possibility of producing genuine topological insulator states on lattice-matched CdS substrate, and pave a pathway towards the practical device application of topological insulators.

Acknowledgements This work was in part supported by the Focus Center Research Program - Center on Functional Engineered Nano Architectonics (FENA) and DARPA. Y. W. acknowledges the support from the National Science Foundation of China (No. 11174244).

Reference 1. Fu, L.; Kane, C. L.; Mele, E. J. Physical Review Letters 2007, 98, (10), 106803-106803. 2. Fu, L.; Kane, C. L. Physical Review B 2007, 76, (4), 045302. 3. Moore, J. E.; Balents, L. Physical Review B 2007, 75, 121306(R). 4. Zhang, H.; Liu, C.-X.; Qi, X.-L.; Dai, X.; Fang, Z.; Zhang, S.-C. Nature Physics 2009, 5, (6), 438-442. 5. Moore, J. Nature Physics 2009, 5, (6), 378-380. 6. Franz, M. Nature Materials 2010, 9, (7), 536-537. 7. Hsieh, D.; Qian, D.; Wray, L.; Xia, Y.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. Nature 2008, 452, (7190), 970-974. 8. Chen, Y. L.; Analytis, J. G.; Chu, J.-H.; Liu, Z. K.; Mo, S.-K.; Qi, X. L.; Zhang, H. J.; Lu, D. H.; Dai, X.; Fang, Z.; Zhang, S. C.; Fisher, I. R.; Hussain, Z.; Shen, Z.-X. Science 2009, 325, (5937), 178181. 9. Hor, Y. S.; Richardella, A.; Roushan, P.; Xia, Y.; Checkelsky, J. G.; Yazdani, A.; Hasan, M. Z.; Ong, N. P.; Cava, R. J. Physical Review B 2009, 79, (19), 195208. 10. Hsieh, D.; Xia, Y.; Qian, D.; Wray, L.; Meier, F.; Dil, J. H.; Osterwalder, J.; Patthey, L.; Fedorov, A. V.; Lin, H.; Bansil, A.; Grauer, D.; Hor, Y. S.; Cava, R. J.; Hasan, M. Z. Physical Review Letters 2009, 103, (14), 146401. 11. Roushan, P.; Seo, J.; Parker, C. V.; Hor, Y. S.; Hsieh, D.; Qian, D.; Richardella, A.; Hasan, M. Z.; Cava, R. J.; Yazdani, A. Nature 2009, 460, (7259), 1106-1109. 12. Alpichshev, Z.; Analytis, J. G.; Chu, J. H.; Fisher, I. R.; Chen, Y. L.; Shen, Z. X.; Fang, A.; Kapitulnik, A. Physical Review Letters 2010, 104, (1), 016401. 13. Xiu, F.; He, L.; Wang, Y.; Cheng, L.; Chang, L.-T.; Lang, M.; Huang, G.; Kou, X.; Zhou, Y.; Jiang, X.; Chen, Z.; Zou, J.; Shailos, A.; Wang, K. L. Nature Nanotechnology 2011, 6, (4), 216-221. 14. Steinberg, H.; Laloe, J. B.; Fatemi, V.; Moodera, J. S.; Jarillo-Herrero, P. Arxiv.org 1104.1404 2011, (1104.1404). 15. Wang, Z.; Lin, T.; Wei, P.; Liu, X.; Dumas, R.; Liu, K.; Shi, J. Applied Physics Letters 2010, 97, ACS Paragon Plus Environment

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(4), 042112-3. 16. Qu, D.-X.; Hor, Y. S.; Xiong, J.; Cava, R. J.; Ong, N. P. Science 2010, 329, (5993), 821-824. 17. Ren, Z.; Taskin, A. A.; Sasaki, S.; Segawa, K.; Ando, Y. Physical Review B 2010, 82, (24), 241306. 18. Taskin, A. A.; Ren, Z.; Sasaki, S.; Segawa, K.; Ando, Y. Physical Review Letters 2011, 107, (1), 016801. 19. Kou, X. F.; He, L.; Xiu, F. X.; Lang, M. R.; Liao, Z. M.; Wang, Y.; Fedorov, A. V.; Yu, X. X.; Tang, J. S.; Huang, G.; Jiang, X. W.; Zhu, J. F.; Zou, J.; Wang, K. L. Applied Physics Letters 2011, 98, 242102. 20. Grove, A. S., Physics and Technology of Semiconductor Devices. Wiley: 1967. 21. Köhler, H.; Fabbicius, A. physica status solidi (b) 1975, 71, (2), 487-496. 22. Zhang, Y.; He, K.; Chang, C.-Z.; Song, C.-L.; Wang, L.-L.; Chen, X.; Jia, J.-F.; Fang, Z.; Dai, X.; Shan, W.-Y.; Shen, S.-Q.; Niu, Q.; Qi, X.-L.; Zhang, S.-C.; Ma, X.-C.; Xue, Q.-K. Nature Physics 2010, 6, (8), 584-588. 23. Kong, D.; Chen, Y.; Cha, J. J.; Zhang, Q.; Analytis, J. g.; Lai, K.; Liu, Z.; Hong, S. S.; Koski, K. J.; Mo, S.-K.; Hussain, Z.; Fisher, I. R.; Shen, Z.-X.; Cui, Y. Nature Nano 2011, 6, (11), 705-709. 24. Analytis, J. G.; McDonald, R. D.; Riggs, S. C.; Chu, J.-H.; Boebinger, G. S.; Fisher, I. R. Nature Physics 2010, 6, (12), 960-964. 25. Kulbachinskii, V. A.; Miura, N.; Nakagawa, H.; Arimoto, H.; Ikaida, T.; Lostak, P.; Drasar, C. Physical Review B 1999, 59, (24), 15733. 26. He, L.; Xiu, F.; Wang, Y.; Fedorov, A. V.; Huang, G.; Kou, X.; Lang, M.; Beyermann, W. P.; Zou, J.; Wang, K. L. Journal of Applied Physics 2011, 109, 103702. 27. Brüne, C.; Liu, C. X.; Novik, E. G.; Hankiewicz, E. M.; Buhmann, H.; Chen, Y. L.; Qi, X. L.; Shen, Z. X.; Zhang, S. C.; Molenkamp, L. W. Physical Review Letters 2011, 106, (12), 126803. 28. Shoenberg, D., Magnetic Oscillations in Metals. Cambridge University Press, Cambridge: 1984. 29. Eto, K.; Ren, Z.; Taskin, A. A.; Segawa, K.; Ando, Y. Physical Review B 2010, 81, (19), 195309. 30. Das Sarma, S.; Stern, F. Physical Review B (Condensed Matter and Materials Physics) 1985, 32, (12), 8442. 31. Li, Y.-Y.; Wang, G.; Zhu, X.-G.; Liu, M.-H.; Ye, C.; Chen, X.; Wang, Y.-Y.; He, K.; Wang, L.L.; Ma, X.-C.; Zhang, H.-J.; Dai, X.; Fang, Z.; Xie, X.-C.; Liu, Y.; Qi, X.-L.; Jia, J.-F.; Zhang, S.-C.; Xue, Q.-K. Advanced Materials 2010, 22, (36), 4002-4007. 32. Lang, M.; He, l.; Xiu, F.; Yu, X.; Tang, J.; Wang, Y.; Kou, X.; Jiang, W.; Chang, L.-T.; Fan, Y.; Jiang, X.; Wang, K. L. Acs Nano, 2012, in-print.

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Figure captions Figure 1. (color online). (a) Schematic diagram of a typical Hall bar sample. The channel size is 8mm × 1mm. A constant current geometry was used for transport measurement. (b) Temperature dependent sheet resistance Rs (Rxx) of films ranging from 5 to 60 QLs. (c) Estimated bulk band gap vs. film thickness. (d) Total conductance vs. film thickness at 5 K. The solid line presents a linear fit for the four thicker films (20 to 60 QLs), exhibiting a thickness dependence of impurity band conduction and enabling the determination of a critical thickness of 6.4 QL (intercepting the abscissa), below which surface states is the only conducting channel at low temperature. (e) Expanded plot for the thin film range of (d), dotted square. The solid line is the same solid line in (d). The dashed line is the fitted data for thin layer samples. The difference representing the surface conduction fit to 6.4 QL sample is ~ 10 e2/h.

Figure 2 (color online). Hall conductance of a 10 QL sample, from which transport properties of three channels: the bulk, the impurity band and the surface states at various temperatures have been extracted. Magnet field dependent Gxy at various temperatures of (a) 220 K, (b) 20 K and (c) 40 K. Open circles are experimental data and solid lines are fitted results (d) 2D carrier density vs. temperature. Solid yellow line represents the Fermi-Dirac distribution of the bulk carrier density equivalent to 2D. (e) Mobility vs. temperature for the three channels. Dashed line represents the power low dependence of µ

∝ T -2, which suggests the mechanism of phonon scattering in these temperatures.

Figure 3 (color online). Shubnikov-de Haas oscillations of the surface states of a 6 QL sample. (a) Longitudinal resistance Rxx vs. magnetic field at T = 1.9 K. Solid arrows indicate the integer Landau levels from the valley values; open arrows give the peak values. (b) ∆Rxx vs. 1/B at different temperatures. The insert shows the field position of the n= 3.5 LL peak varies with θ as 1/cosθ (solid

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black line), suggesting a 2D Fermi surface. (c) Landau level index plot: 1/B vs. n. The open (close) circles are the Landau level of the maxima (minima) of ∆Rxx. (d) Normalized conductivity amplitude

∆σxx(T)/∆σxx(0) vs. temperature ( 7.6 T). The effective mass deduced is ~ 0.07 me. (e) Dingle plot of ln[(∆R/R0)Bsinh(λ)] vs. 1/B, used to determine τ and l . Figure 4 (color online) (a) A standard APRES image of a 60 QL sample showing the surface states and the Dirac point. (b) Surface density of states (ns) vs. Energy. The data are extracted from ARPES measurement, and horizontal axis has been scaled to fit the transport measurements. The red circle indicates our experiment result in this paper. The green square is adopted from Ref.

24

. The purple

triangles are the data from our other samples of Bi2Se3 grown on Si (111).32 (c) Scanning tunneling spectroscopy of a 6 QL sample. Spatially averaged density of states (dI/dV) measurements show the Dirac point is about ~ 70 ± 20 meV below the Fermi surface.

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Figure 1 I

(b)

(a)

Vxy

10 10

Rs (Ω Ω/ )

B

Vxx

10 10 10

CdS

10

IV III

II

4

9 QL

2

10 QL

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Gs (e /h)

300 2

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8

10

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200 T (K) (e) 40

T=5K

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20 QL 60 QL

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400

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30 2

This paper [21] Zhang etc. [24]

I

5 QL 6 QL 8 QL

3

(d) 400

0.8

0.0

5

Gs (e /h)

(c) 1.0

Eg (eV)

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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20 10

10 20 30 40 50 60 t (QL)

0

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4

6 8 t (QL)

10 12

Fig. 1

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Figure 2 (b)

60

Exp Fitted

200 100

20

Gxy (µ µS)

Gxy (mS)

40 0

-20

Exp Fitted Surface Impurity Band

0

-100

T = 220 K

-40

T = 20 K

10 0 T = 40 K

-200 -20 -8

-4

0 4 B (T)

8

-8

-4

0 4 B (T)

8

-8

-4

8

2

Surface States Impurity Band Bulk

µ (cm /Vs)

14

4

10

4

2

10

13

10

12

10

Surface States Impurity Band Bulk

2 3

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µ ∝ T -2.0

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10

0 4 B (T)

(e)

15

10 -2

Exp Fitted Bulk Surface Impurity Band

-10

-60

(d)

(c) 20 Gxy (mS)

(a)

n2D (cm )

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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6 8

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6 8

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10 T (K)

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Figure 3 (a) 20.70

(b) 20 3

2.5

4

20.60 4.5

T = 1.9 K

20.55

0 -20

10 n=3.5 H (T)

3.5

∆ Rxx (Ω Ω)

Rxx (kΩ Ω)

20.65

1.9 K 5K 8K 10 K

-40 3

4

5

6

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8

9

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(d) ∆σ xx (T) /σ σ xx (0)

-1

(e)

1.0

0.25 0.20 0.15 0.10 0.05

Ln [∆ ∆ R/R0Bsinh(λ λ )]

(c)

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0.00 0

1

2 n

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5

0

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6

8 10

8 6 0

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1/B (T )

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0.20 -1 1/B (T ) -4.0

20 40 Angle θ (deg)

0.25

-4.5

60

0.30

10 K

-5.0

8K

-5.5

5K

-6.0 1.9 K

-6.5 0.12

T (K)

0.20 -1 1/B (T )

Fig. 3

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Figure 4

(b)

300

E - ED (meV)

200 150 100 50 0 -50

(c) 0.8

150

250

-0.8

0.0 K//(Ă&#x2026;-1)

0.8

0.7

100 50

This paper Analytis etc. [24] [21] Lang etc. [28] [32]

0 -50 -100

0

1 2 12 3 -2 4 ns (10 cm )

dI/dV (a.u.)

(a)

E-ED (meV)

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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0.6 0.5

Dirac point

0.4 0.3 -400 -300 -200 -100 0 E (meV)

100 200

Fig. 4

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I

(a)

10

5

IV III

(b)

Vxy

10 Rs ( / )

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Vxx

10 10 10

CdS

II

4

6 QL 8 QL

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9 QL

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10 QL

1

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100

(d) 400 Gs (e /h)

300 2

06 0.6 0.4

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200 100

02 0.2 0.0 6 t (QL)

8

10

300

400

T= 5 K

30 20 10

0 4

200 T (K) 40 ( ) (e)

2

This paper [22] Zhang etc. [20]

2

20 QL

0

Gs (e /h)

10 ( ) 1.0 (c) 0.8

I

5 QL

60 QL

10

Eg (eV V)

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

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0 10 20 30 40 50 60 t (QL)

2

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Fig. 1 ACS Paragon Plus Environment


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(b) Exp Fitted

40

200

20

100

0

-20

Exp Fitted Surface Impurity Band

0

-100

T = 220 K

-40

T = 20 K

10 0 T = 40 K

-200 -20 -8

-4

0 4 B (T)

8

-8

-4

0 4 B (T)

8

-8

-4

8

2

µ (cm /Vs)

Surface States Impurity Band Bulk

14

10

4 4

2

10

13

10

12

10

Surface States Impurity Band Bulk

2

10

3

µ ∝ T -2.0

4 11

10

0 4 B (T)

(e)

15

10 -2

Exp Fitted Bulk Surface Impurity Band

-10

-60

(d)

(c) 20 Gxy (mS)

60

Gxy (µ µS)

Gxy (mS)

(a)

n2D (cm )

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

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2 2

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6 8

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10 T (K)

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6 8

2

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100 ACS Paragon Plus Environment

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6 8

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10 T (K)

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(a) 20.70

(b) 20 3

2.5

4

20 60 20.60 4.5

T = 1.9 K

20.55

0 -20

10 n=3.5 H (T)

3.5

Rxxx ()

Rxxx (k)

20.65

1.9 K 5K 8K 10 K

-40 3

4

5

6

7

8

9

0.15

B (T)

0.30

(d) xx (T) / xx (0)

0.25 --1

( ) (e)

1.0

0.20 0.15 0.10 0 05 0.05

Ln n [R/R0Bsiinh()]

( ) (c)

0.9 0.8 0.7

0.00 0

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2 n

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8 10

T (K)

8 6 0

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0.20 -1 1/B (T ) -4.0 4.0

20 40 Angle  (deg)

0.25

-4.5

60

0.30

10 K

-5 0 -5.0

8K

-5.5

5K

-6 0 -6.0 1.9 K

-6.5 0.12

0.20 -1 1/B (T )

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(b)

300

08 (c) 0.8

150 E - ED (meV)

250 200 150 100 50

100 50

-50

-50 50

-100

0.0 K//(Ă&#x2026;-1)

0.8

This paper Analytis etc. [21] Lang etc. [28]

0

0 -0.8

0.7

0

dI/dV (a.u.)

(a)

E-ED (m meV)

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

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1 2 12 3 -2 4 ns (10 cm )

0.6 0.5

Dirac point

0.4 0.3 -400 -300 -200 -100 0 E (meV)

100 200

Fig. 4

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Surface-dominated Conduction in a 6 nm-thick Bi2Se3 Thin Film IMP  

Liang He, Faxian Xiu, Xinxin Yu, Marcus Teague, Wanjun Jiang, Yabin Fan, Xufeng Kou, Murong Lang, Yong Wang, Guan Huang, Nai-Chang Yeh, and...

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