Quantized Hall Effect and Shubnikov--de Haas Oscillations in Highly Doped ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$: Evidence for Layered Transport of Bulk Carriers

Quantized Hall Effect and Shubnikov–de Haas Oscillations in Highly Doped ${Bi}_{2} {Se}_{3}$ : Evidence for Layered Transport of Bulk Carriers

Helin Cao, Jifa Tian, Ireneusz Miotkowski, Tian Shen, Jiuning Hu, Shan Qiao, and Yong P. Chen

Phys. Rev. Lett. 108, 216803 – Published 23 May 2012

Abstract

${Bi}_{2} {Se}_{3}$ is an important semiconductor thermoelectric material and a prototype topological insulator. Here we report observation of Shubnikov–de Hass oscillations accompanied by quantized Hall resistances ( $R_{x y}$ ) in highly doped $n$ -type ${Bi}_{2} {Se}_{3}$ with bulk carrier concentrations of few $10^{19} {cm}^{- 3}$ . Measurements under tilted magnetic fields show that the magnetotransport is 2D-like, where only the $c$ -axis component of the magnetic field controls the Landau level formation. The quantized step size in $1 / R_{x y}$ is found to scale with the sample thickness, and average $\sim e^{2} / h$ per quintuple layer. We show that the observed magnetotransport features do not come from the sample surface, but arise from the bulk of the sample acting as many parallel 2D electron systems to give a multilayered quantum Hall effect. In addition to revealing a new electronic property of ${Bi}_{2} {Se}_{3}$ , our finding also has important implications for electronic transport studies of topological insulator materials.

Received 31 July 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.216803

Authors & Affiliations

Helin Cao^1,2, Jifa Tian^1,2, Ireneusz Miotkowski¹, Tian Shen^1,3, Jiuning Hu^2,4, Shan Qiao⁵, and Yong P. Chen^1,2,4,*

¹Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA
²Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
³Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
⁴School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
⁵Department of Physics, Fudan University, Shanghai 200433, People’s Republic of China

^*To whom correspondence should be addressed. yongchen@purdue.edu

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Vol. 108, Iss. 21 — 25 May 2012

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Figure 1
(a) Temperature dependence of resistivity $ρ$ in sample $A$ , displaying a metallic behavior. The inset shows the optical image of the sample (scale bar is $10 μ m$ ). (b) Hall resistance ( $R_{x y}$ ) and four-terminal longitudinal resistance ( $R_{x x}$ ) of sample $A$ as functions of perpendicular magnetic field ( $B$ ) applied along the $c$ axis (perpendicular to sample surface). Data presented were measured at $T = 450 mK$ . The inset shows $B_{F} / B$ at the magnetic field ( $B$ ) positions of the observed minima in $R_{x x} (B)$ , plotted against the assigned LL index $N$ . The solid line is a linear fit with slope $1 \pm 0.002$ and the $N$ axis intercept $0 \pm 0.03$ .Reuse & Permissions
Figure 2
(a) $R_{x x}$ as a function of $B$ measured at various tilt angles ( $θ$ ). The minima (at $B = B_{13}$ ) in $R_{x x}$ corresponding to $N = 13$ are labeled with arrows. The inset shows that $B_{13}$ varies with $θ$ as $B_{13} (θ = 0) / \cos (θ)$ (solid line), indicating a 2D transport behavior from the charge carriers. (b), (c) $R_{x x}$ and $R_{x y}$ plotted as functions of $B_{⊥} = B \cos (θ)$ , respectively. The inset in Fig. 2c shows the schematic of the sample in a tilted magnetic field ( $B$ ).Reuse & Permissions
Figure 3
(a) $Δ R_{x x} (B)$ , extracted from $R_{x x} (B)$ by subtracting a smooth background, at various temperatures ( $T$ ). Arrows label selected LL indices. (b) $T$ dependence of the relative amplitude of SdH oscillation in $Δ R_{x x} (B)$ for the 10th LL. The solid line is a fit to the Lifshitz-Kosevich formula, from which we extract LL energy gap $Δ E$ . The inset shows $Δ E$ as a function of $B$ (magnetic field positions of minima in $R_{x x}$ corresponding to different LLs), and the effective mass ( $m^{*} \sim 0.14 m_{e}$ ) is extracted from the slope of the linear fitting. (c) ln[D] (defined in the text) plotted as a function of $1 / B$ . The Dingle temperature $T_{D} = 25 K$ is calculated from the slope of the linear fit, corresponding to a carrier lifetime $\sim 5 \times 10^{- 14} s$ and an effective mobility of $\sim 620 {cm}^{2} / V s$ .Reuse & Permissions
Figure 4
(a) $1 / R_{x y}$ divided by the number ( $Z = 150$ ) of QLs plotted as a function of $1 / B$ , displaying plateaus separated by $\sim e^{2} / h$ between adjacent LLs. (b) $Z^{'}$ , step size between the plateaus in $1 / R_{x y}$ in units of $e^{2} / h$ , plotted against the measured number ( $Z$ ) of QLs for multiple samples of different thickness. The dotted line labeling $Z^{'} = Z$ is a guide to eyes. These samples were grown at two different sources (Purdue and Fudan Universities) with bulk carrier densities (as determined by the low $B$ Hall effect) ranging from $\sim 3 \times 10^{19}$ to $\sim 6 \times 10^{19} {cm}^{- 3}$ . The observed $1 / R_{x y}$ is interpreted as due to the contribution from many parallel 2D conduction channels [each found to be $\sim 2 nm$ (2QL) in thickness; see text for more details].Reuse & Permissions

Physical Review Letters

Quantized Hall Effect and Shubnikov–de Haas Oscillations in Highly Doped Bi2Se3: Evidence for Layered Transport of Bulk Carriers

Helin Cao, Jifa Tian, Ireneusz Miotkowski, Tian Shen, Jiuning Hu, Shan Qiao, and Yong P. Chen

Phys. Rev. Lett. 108, 216803 – Published 23 May 2012

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Quantized Hall Effect and Shubnikov–de Haas Oscillations in Highly Doped ${Bi}_{2} {Se}_{3}$ : Evidence for Layered Transport of Bulk Carriers