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Supporting Information for Competing Weak Localization and Weak Antilocalization in Ultrathin Topological Insulators Murong Lang,†,ll Liang He,†,ll, * Xufeng Kou,†,ll Pramey Upadhyaya,† Yabin Fan,† Hao Chu,⊥ Ying Jiang,§ Jens H. Bardarson,‡, # Wanjun Jiang,† Eun Sang Choi,£ Yong Wang,§ Nai-Chang Yeh,⊥ Joel Moore, ‡,# and Kang L. Wang †,* †
Department of Electrical Engineering, University of California, Los Angeles, California
Department of Physics, University of California, Berkeley, CA 94720
Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
Center of Electron Microscopy, State Key Laboratory of Silicon Materials, Department of
Materials Science and Engineering, Zhejiang University, Hangzhou, 310027, China ⊥
Department of Physics, California Institute of Technology, Pasadena, CA 91125
National High Magnetic Field Laboratory, Tallahassee, FL 32310
1. MBE Growth of (Bi0.57Sb0.43)2Te3. High-quality single crystalline (Bi0.57Sb0.43)2Te3 thin films were conducted in a PerkinElmer MBE system under an ultra-high vacuum environment; MBE is proven to be a powerful and reliable technique to produce ultrathin TI films with accurate thickness control to a few quintuple layers.1-3 Intrinsic GaAs (111) wafers (ρ > 106 Ω⋅cm) were cleaned by a standard Radio Corporation of America (RCA) procedure before being transferred into the growth chamber. Then GaAs substrates were annealed in the chamber under Se-protective environment at ~580 ˚C to remove the native oxide on the surface. After removing the native oxides, the GaAs substrate has shown clear 2D pattern with a bright specular spot (Figure S1a), indicating the epi-ready surface for subsequent growth. During growth, Bi, Sb and Te cells were kept at 470, 395 and 320°C respectively, while GaAs (111) substrate was set at 200°C (growth temperature). Figure S1b shows a large-scale atomic force microscope (AFM) image of an as-grown (Bi0.57Sb0.43)2Te3 film with a thickness of 9 QL, exhibiting terraces over 500 nm in size. The surface consists of triangle-shaped terraces and steps, indicative of a hexagonal crystal structure inside (0001) planes. In-situ growth dynamics are monitored by reflection high energy electron diffraction (RHEED) measurements. Digital images of the RHEED were captured using a KSA400 system made by K-space Associate, Inc. Growth rate can be estimated as 1 QL/min from the periodic RHEED oscillations which started from the first layer of the growth (Figure S1c).D-spacing of surface lattice change during growth after 1st (Bi0.57Sb0.43)2Te3 layer growth as indicated in Figure S1d. 2 nm Aluminum (Al) was subsequently deposited in-situ at 20 ˚C to protect the epi-layer from unintentional doping induced by ambient environment.4 Al film was later naturally oxidized to form Al2O3 after the sample was taken out of the chamber and exposed in air, which also further serves as a good seeding layer of the high-k dielectric oxide stack grown by the atomic layer deposition (ALD) process.
Figure S1. (Bi0.57Sb0.43)2Te3 compound growth characterization. a, RHEED pattern along
 direction of an as-grown surface of (Bi0.57Sb0.43)2Te3 with a thickness of 9 QLs. b, An AFM image of the TI thin film with terrace size exceeding 500 nm. c, RHEED oscillations of intensity of the specular beam. The oscillation period is found to be 60 s, corresponding to a growth rate of ~ 1 QL/min. d, D-spacing of surface lattice change during growth. The arrow indicates that the surface morphology has converted from GaAs to after 1st (Bi0.57Sb0.43)2Te3 layer growth.
2. Sample Characterization Methods. (1) TEM. High-resolution TEM experiments were performed on a FEI TITAN Cs-corrected high-resolution STEM operating at 200 KV. The HAADF (high angle annular dark field) images were acquired by a Fischione HAADF detector. (2) EDX. EDX was performed with a FEI Tecnai G2 F20 S-Twin TEM. (3) Transport measurements. High magnetic field and low temperature measurements were conducted at National High Magnetic Field Laboratory with the application of DC magnetic field up to ± 18 T. The temperature range is from 0.3 to 60 K. Standard four-probe measurements were carried out with an ac current sourced from a Keithley 6221. Multiple lock-in-amplifiers were used to measure the longitudinal and transverse resistance. (4) STS measurements. The sample with 3
2 nm passivated Al2O3 was first etched in 5% HF solution for 10 seconds and immediatly transferred to the cryogenic probe of a homemade STM sample holder in argon environment. The STM is then pumped down to 810-5 Torr vacuum and then cooled down to 77K. The spectroscopy data was acquired over a 6464 grid on an area of 10 nm10 nm
3. Device Fabrication. The MBE-grown (Bi0.57Sb0.43)2Te3 thin film was first patterned into a micron-scale Hall bar geometry using conventional optical photolithography and a subsequent CHF3 dry-etching of 15 s. Hall bar contacts were defined by photolithography and followed by e-beam evaporation of 10 nm chromium (Cr) and 100 nm gold (Au). A 25 nm-thick Al2O3 dielectric layer was conformally deposited by ALD at 250°C to serve as the high-k gate dielectric. Another step of photolithography was needed to open window, and dry etching was carried out to etch the Al2O3 in the contact area with subsequent dip in 5% diluted HF. Finally, the top-gate electrode and Hall channel contacts were defined and followed by metal deposition of Cr/Au (10 nm/100 nm).
Figure S2. Fabrication processes of TI based FET by photolithography.
4. Maximum Resistance and 2D Carrier Density vs. Thickness The thickness dependent maximum resistant Rmax obtained from Figure 2 in the main text, 4
presents an abrupt change at 4 QL, as indicated in Figure S3. At 4 QL, Rmax reaches ~ 70 kΩ, owing to the surface bandgap opening (~180 meV) at the Dirac point. As film thickness increases, Rmax decreases monotonically as the surface gap vanishing and continuously increased bulk contribution. At the same time, the 2D carrier concentration nH remains low value < 2.51012 cm-2 for thickness below 8 QL, where bulk contribution is greatly suppressed. However, it is noted that the nH suddenly jumps to 7.51012 cm-2 at t 8 QL, above which gate may not effectively modulate the charge carrier density of the entire film any more. Hence, in order to suppress bulk contribution and achieve low density TI sample, film thickness should be kept below ~8 QL. This is consistent with the literature that by solving Poisson equation, the first order estimated maximum depletion width D is ~ 11 nm, beyond which a portion of carriers cannot be fully depleted by gating effect.5 8 6 40
7 t (QL)
nH min(10 cm )
Figure S3. Rmax and nH as functions of thickness. The largest Rmax is obtained at 4 QL and it rapidly decreases as thickness increases. nH remains < 2.51012 cm-2 for 4 to 7 QLs, and suddenly increases to 7.51012 cm-2 at t 8 QL.
5. Quantum interferences competition in 5 QL sample. For completeness, we also verify the WAL/WL quantum interference modes in the 5 QL film at 0.3 K as shown in Figure S4a. The inset of Figure S4b presents the gate voltage dependence of resistance, in which we roughly define the ambipolar region (-12 V < Vg < 4 V) and n-type region (Vg ≥ 4 V). In Figure S4a, in the ambipolar region, the MC curves firstly display WL-like behavior at low field, and then bend over to WAL at higher field, similarly as 5
4 QL case. The WAL characteristics prevail at the unipolar region, possibly because now EF moves into the upper surface state branch. The evolution of both α0 (upper panel) and α1 (lower panel) fitted by Eq. 2 as functions of gate voltage is present in Figure S4b. The WAL contribution |α0| enhances when Vg moves from the ambipolar to the unipolar region, whereas the |α1| representing WL contribution monotonically decreases.
0 10 Vg(V)
0.4 0.3 0.2
-12 V -10 V -6 V 0V 4V 8V 10 V 12 V 15 V
Figure S4. Quantum interference competition in 5 QL (Bi0.57Sb0.43)2Te3 at 0.3 K. a, Evolution of normalized low field MC as a function of gate voltage. In the ambipolar region (-12 V < Vg < 4 V), where EF is close to the surface band gap, the MC curves firstly show WL-like behavior at low magnetic field, and then bend over to WAL at higher field. The WAL characteristics prevail in the unipolar region (Vg 4 V) when EF moves into the upper surface state branch. b, The evolution of α0 (upper panel) and α1 (lower panel) fitted by Eq. 2 as functions of gate voltage. The WAL contribution |α0| enhances when Vg moves from the ambipolar into the unipolar region, whereas WL contribution |α1| decreases. Inset: gate voltage dependence of resistance for the 5 QL sample.
6. Weak antilocalization in 6 ~10 QLs. Figure S5 a-d demonstrate detailed gated voltage dependence of the normalized magnetoconductivity (MC) ∆σ ( B) = σ xx ( B ) − σ xx (0) of 6, 7, 9, 10 QLs films at T = 0.3 K. All samples present clear weak antilocalization signature, in which ∆σ ( B) has a cusp-like 6
maximum at B = 0. The 6 QL sample shows more dramatic gate dependence of ∆σ ( B) than thicker ones owing to its lower carrier density.6 One component Hikami-Larkin-Nagaoka theory (Eq. 1 in the main text) is applied to fit the prefactor α and phase coherent length lφ .
α in Figure S5 e-h show their maxima ( α ~1) as EF is tuned close to the Dirac point, implying the topological properties is clearly revealed at charge neutrality point. As EF moves far away, it corresponds to the case of coherently coupled bulk and surface electron states since more bulk carriers are accumulated, hence α and lφ reduces. Furthermore, as film thickness increases, the gate-dependent α increases from 0.57~1.04 for 6 QL to 1.01~1.19 for 10 QL, suggesting increased channel separation with thickness.
2 -10 -5
-2 V 0V 2V 4V 6V 8V 10 V
f 6 QL 80
-5 V 0V 5V 10 V 15 V
0.6 0.8 B(T)
0.2 0.4 0.6 0.8 1.0 B(T)
5 10 Vg(V)
-5 V -3 V -1 V 1V 3V 5V 7V
Figure S5. Gate voltage dependence of α and lφ in 6, 7, 9, 10 QLs samples at 0.3 K. a-d, The gate voltage dependence of normalized magnetoconductance of 6 QL(a), 7 QL(b), 9 QL(c), 10 QL (b). Inset: The gate voltage dependence of resistance for the corresponding thin film, where the solid circles present the corresponding gate voltages applied. e-h, Fitted phase coherence length lφ (squares) and coefficient α (circles) from one component HLN theory (Eq. (1)) as functions of gate voltage for 6 QL(a), 7 QL(b), 9 QL(c), 10 QL(b).
7. Theoretical calculation of two parameters α0 and α1. 7
-5 V -3 V -1 V 1V 3V
0.0 0.2 0.4 0.6 0.8 1.0 B(T)
0 5 10 Vg(V)
∆σ xx(e /h)
∆σ xx(e /h)
0.0 R(kΩ Ω)
∆σ xx(e /h)
3.2 R(kΩ Ω)
∆σ xx(e /h)
0.0 R(kΩ) Ω)
In the two-component HLN thoery, the two parameters α0 and α1 present the weight of WAL and WL, respectively, and both of which depend on the position of EF respective to the surface Dirac point. According to the Ref. 7-8, α0 and α1 are derived as following forms. Here we obtained these simplified formula by assuming that the magnetic scattering length
lm → ∞ , since magnetic impurity is absent in our samples.
α0 = −
a 4b4 (a 4 + b 4 )(a 2 − b 2 )2 α = 1 (a 4 + b 4 )(a 4 + b 4 − a 2b 2 ) 2(a 4 + b 4 − a 2b 2 ) 2
where a ≡ cos
Θ Θ ∆ / 2 − Bk F2 , b ≡ sin . Here, Θ is defined as cos Θ = , where ∆ is the 2 2 EF − DkF2
surface band gap. B and D are the parameters in the model Hamiltonian in Ref. 7 , in which B represents the 2nd order correction to the gap size at non-zero momentum and D corresponds to the bulk kinetic energy dispersion coefficient, respectively. At the Dirac point, the relation can be simplified as cos Θ ≈
∆/2 . The corresponding Berry phase as shown in Ref. 7 is EF
given by φ = π (1 − cos(Θ)) . As discussed in Ref. 8, the quantum interference behavior (WAL/WL) is mainly controlled by cos Θ . In the limit when EF is far into the upper surface state (conduction) branch or the lower (valence) branch, i.e., cos Θ → 0 , corresponding to α0 = − 1/2, α1 = 0, one has only WAL with negative MC cusp. However, as EF is moved toward the surface gap controlled by applying the gate voltage, cosΘ increases and consequently drive the system first into the unitary regime; and eventually reach the WL regime with positive MC cusp when cos Θ → 1 (α0 = 0, α1 =1/2).
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