Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator $\mathrm{Sn}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{1.1}\mathrm{S}{\mathrm{b}}_{0.9}\mathrm{T}{\mathrm{e}}_{2}\mathrm{S}$ devices

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Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator $Sn − B i_{1.1} S b_{0.9} T e_{2} S$ devices

Faji Xie, Shuai Zhang, Qianqian Liu, Chuanying Xi, Ting-Ting Kang, Rui Wang, Boyuan Wei, Xing-Chen Pan, Minhao Zhang, Fucong Fei, Xuefeng Wang, Li Pi, Geliang L. Yu, Baigeng Wang, and Fengqi Song

Phys. Rev. B 99, 081113(R) – Published 13 February 2019

Abstract

The scaling physics of quantum Hall transport in optimized topological insulators with a plateau precision of $\sim 1 / 1000 e^{2} / h$ is considered. Two exponential scaling regimes are observed in temperature-dependent transport dissipation, one of which accords with thermal-activation behavior with a gap of 2.8 meV (>20 K), the other being attributed to variable-range hopping (1–20 K). Magnetic-field-driven plateau-to-plateau transition gives scaling relations of ${(d R_{x y} / d B)}^{max} \propto T^{- κ}$ and $Δ B^{- 1} \propto T^{- κ}$ with a consistent exponent of κ ∼ 0.2, which is half the universal value for a conventional two-dimensional electron gas. This is evidence of percolation assisted by quantum tunneling and reveals the dominance of electron-electron interaction of the topological surface states.

Received 6 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.081113

Physics Subject Headings (PhySH)

Continuous phase transition Quantum Hall effect

Topological insulators

Scaling methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Faji Xie^1,*, Shuai Zhang^1,*, Qianqian Liu¹, Chuanying Xi², Ting-Ting Kang³, Rui Wang¹, Boyuan Wei¹, Xing-Chen Pan¹, Minhao Zhang¹, Fucong Fei¹, Xuefeng Wang⁴, Li Pi², Geliang L. Yu¹, Baigeng Wang^1,†, and Fengqi Song^1,‡

¹National Laboratory of Solid State Microstructures, College of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
²High Magnetic Field Laboratory, Chinese Academy of Sciences and Collaborative Innovation Center of Advanced Microstructures, Hefei 230031, China
³State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
⁴National Laboratory of Solid State Microstructures, School of Electronic Science and Engineering and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*These authors contributed equally to this work.
^†Corresponding author: bgwang@nju.edu.cn
^‡Corresponding author: songfengqi@nju.edu.cn

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Vol. 99, Iss. 8 — 15 February 2019

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Figure 1
Quantum Hall transport with low dissipation in optimized topological insulators. (a) Optical photograph of Sn-BSTS single crystals. The white scale bar is 5 mm. (b) The angle-resolved photoemission spectroscopy spectra of Sn-BSTS, which show a Dirac cone. (c) The typical temperature-dependent sheet resistances in six devices with different thicknesses. (d) Magnetic field dependence of $R_{x x}$ and $R_{x y}$ of sample A measured at $V_{g} = 0 V$ and $T = 6 K$ . The inset shows an enlarged view of the plateau. They exhibit quantum Hall (QH) states with low dissipation. (e) The magnetic-field-dependent $R_{x x}$ (red line) and $R_{x y}$ (blue line) at 1 K and $V_{g} = 30 V$ in sample B. The inset shows an atomic force microscopy picture of the device, whose thickness is 62 nm. (f) Back-gate voltage-dependent $R_{54 / 12}$ and $R_{12 / 12}$ in nonlocal measurements at 2 K and −12 T, which also exhibits QH edge states. The inset shows the measurement configuration.
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Figure 2
Transition from thermal activation to variable-range hopping of the temperature-dependent scaling of the QH dissipation (sample B). (a) Back-gate voltage-dependent $σ_{x y}$ at 12 T for different temperatures. (b) $σ_{x x}$ at 12 T for different temperatures. (c) Minima of $σ_{x x}$ (in logarithmic scale) as a function of 1/ $T$ at $ν = 1$ plateau. The red dashed line indicates a linear fit at high temperature with the thermal-activation formula. (d) The variable-range hopping (VRH) fitting by Eq. (2). The axes are rescaled to show a straight line. The critical temperature between thermal activation and VRH is about 20 K. (e) The renormalization-group flow diagram in $(σ_{x y}, σ_{x x})$ space. (f) $Δ σ_{x y}$ ( $T$ ) vs minima of $σ_{x x}$ ( $T$ ). Red and blue dashed lines indicate the linear fitting of different temperature regimes.
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Figure 3
The magnetic-field-driven QH plateau-plateau transitions and anomalous scaling constant. (a) Magnetic-field-dependent $R_{x y}$ measured at zero gate voltage. (b) The $R_{x x}$ at zero gate voltage. (c) The back-gate tuned $R_{54 / 12}$ at 12 T for different temperatures. (d) Blue: temperature dependence of the maxima of $d R_{xy} / d B$ . The slope of the straight line gives ${(d R_{x y} / d B)}^{\max} \propto T^{- κ}$ with $κ = 0.21 \pm 0.02$ . Green: the half width of the longitudinal resistance peaks gives $Δ B^{- 1} \propto T^{- κ}$ with $κ = 0.20 \pm 0.01$ . Purple: the half width of nonlocal resistance peaks gives $Δ V_{g}^{- 1} \propto T^{- κ}$ with $κ = 0.20 \pm 0.015$ . Red dashed lines show linear fits.
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Figure 4
The temperature-dependent weak antilocalization and its scaling physics. (a) The magnetoconductivity at different temperatures, which displays a weak antilocalization effect. (b) The coherence length $l_{ϕ}$ of TSS extracted from the Hikami-Larkin-Nagaoka fitting at different temperatures; the red dashed line indicates the fitting of $l_{ϕ} \propto T^{- p / 2}$ with $p \approx 1.1$ .
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Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator $Sn − B i_{1.1} S b_{0.9} T e_{2} S$ devices

Faji Xie, Shuai Zhang, Qianqian Liu, Chuanying Xi, Ting-Ting Kang, Rui Wang, Boyuan Wei, Xing-Chen Pan, Minhao Zhang, Fucong Fei, Xuefeng Wang, Li Pi, Geliang L. Yu, Baigeng Wang, and Fengqi Song

Phys. Rev. B 99, 081113(R) – Published 13 February 2019

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Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator Sn−Bi1.1Sb0.9Te2S devices

Faji Xie, Shuai Zhang, Qianqian Liu, Chuanying Xi, Ting-Ting Kang, Rui Wang, Boyuan Wei, Xing-Chen Pan, Minhao Zhang, Fucong Fei, Xuefeng Wang, Li Pi, Geliang L. Yu, Baigeng Wang, and Fengqi Song

Phys. Rev. B 99, 081113(R) – Published 13 February 2019

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Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator $Sn − B i_{1.1} S b_{0.9} T e_{2} S$ devices