Magnetoresistance evidence of a surface state and a field-dependent insulating state in the Kondo insulator ${\mathrm{SmB}}_{6}$

Magnetoresistance evidence of a surface state and a field-dependent insulating state in the Kondo insulator ${SmB}_{6}$

F. Chen, C. Shang, Z. Jin, D. Zhao, Y. P. Wu, Z. J. Xiang, Z. C. Xia, A. F. Wang, X. G. Luo, T. Wu, and X. H. Chen

Phys. Rev. B 91, 205133 – Published 26 May 2015

Abstract

Recently the resistance saturation at low temperature in the Kondo insulator ${SmB}_{6}$ , a long-standing puzzle in condensed matter physics, was proposed to originate from a topological surface state. Here we systematically studied the magnetoresistance of ${SmB}_{6}$ at low temperature up to 55 T. For temperature decreasing below 16 K, the temperature-dependent magnetoresistance exhibits a negative magnetoresistance, while the angular-dependent magnetoresistance shows a fourfold symmetry. Below 5 K, both temperature- and angular-dependent magnetoresistances show a similar crossover behavior in which the negative magnetoresistance is strongly suppressed and a twofold angular-dependent magnetoresistance appears. Furthermore, the angular-dependent magnetoresistance on a different crystal face confirms a two-dimensional surface state as the origin of magnetoresistance crossover below 5 K. Based on a two-channels model consisting of both surface and bulk states, the critical magnetic field $(H_{c})$ of 125 T for field-dependent insulating behavior is extracted from our temperature-dependent resistance under different magnetic fields. Our results have important implications in understanding the novel low-temperature transport behavior in ${SmB}_{6}$ .

Received 18 February 2015
Revised 7 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.205133

Authors & Affiliations

F. Chen^1,2, C. Shang^1,2, Z. Jin³, D. Zhao^1,2, Y. P. Wu^1,2, Z. J. Xiang^1,2, Z. C. Xia³, A. F. Wang^1,2, X. G. Luo^1,2,4, T. Wu^1,2,4,*, and X. H. Chen^1,2,4,†

¹Hefei National Laboratory for Physical Science at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
²Key Laboratory of Strongly-coupled Quantum Matter Physics, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
³Wuhan National High Magnetic Field Center (WHMFC), Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*wutao@ustc.edu.cn
^†chenxh@ustc.edu.cn

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Vol. 91, Iss. 20 — 15 May 2015

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Figure 1
(a) The CsCl-type structure of ${SmB}_{6}$ with a $P m 3 m$ space group. Sm ions and $B_{6}$ octahedron are located at the corner and center of the cubic lattice, respectively. (b) The picture of a ${SmB}_{6}$ single crystal with both (100) and (110) surfaces. (c) Temperature-dependent resistance for an ideal topological insulator. The black dashed line represents an insulating bulk contribution to total resistance due to thermal activation. The red dashed line represents a metallic surface state contribution to total resistance. The green hollow circles are the total resistance containing contributions from both insulating bulk and a metallic surface state.
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Figure 2
Temperature-dependent resistivity of ${SmB}_{6}$ shown in an Arrhenius plot. The red solid line is the fitting result for regions III and IV with formula $1 / ρ = 1 / ρ_{0} e^{- \frac{Δ_{III}}{k_{B} T}} + 1 / ρ_{s}$ , where $ρ_{0} e^{- \frac{Δ_{III}}{k_{B} T}}$ is the dominated insulating contribution in region III and $ρ_{s}$ is the dominated surface state contribution in region IV. The pink solid line is a guiding line to show Arrhenius law for region II. The inset is the temperature-dependent resistivity of ${SmB}_{6}$ shown in a logarithmic plot. A similar division of the temperature region has already been shown in Ref. [24].
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Figure 3
Magnetic-field dependent magnetoresistance of ${SmB}_{6}$ with the $H ⊥ (100)$ surface taken (a) below 5 K and (b) between 5 and 15 K. (c) Temperature-dependent magnetoresistance of ${SmB}_{6}$ under $H ⊥ (100) = 9$ T. The colored circles stand for the value of magnetoresistance taken under $H = 9$ T at different temperatures, and the black dashed line is a guide for the eyes. (d) A temperature-dependent proportion of the bulk state contribution to magnetoresistance from a two-channels model fitting in Fig. 2. The surface state is supposed to have no field effect on resistance and the negative magnetoresistance is only from a bulk state contribution. In this case we have $ɛ = {(ρ / ρ_{0} e^{- \frac{Δ}{k_{B} T}})}^{2}$ .
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Figure 4
( $a_{1}$ ) The electric current with 100 $μ A$ is applied along the [001] direction of the sample with the (100) surface and the magnetic field rotating in the plane perpendicular to the current direction. ( $a_{2}$ )–( $a_{9}$ ) Temperature-dependent AMR patterns of a ${SmB}_{6}$ sample with the (100) surface under 9 T of external magnetic field ( $H$ ). ( $b_{1}$ ) The electric current with $100 μ A$ is applied along the [001] direction of the sample with the (110) surface and the magnetic field rotating in the plane perpendicular to the current direction. ( $b_{2}$ ) and ( $b_{3}$ ) AMR patterns at 2 and 5 K for a ${SmB}_{6}$ single crystal with the (110) surface under $H = 9$ T. $R (0)$ is about 200.3 and 339.7 $Ω$ at 2 K for the (100) and (110) surfaces, respectively. Note that $θ^{'} = θ - \frac{π}{4}$ . The angular coordinate in all graphs is $θ$ .
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Figure 5
Temperature-dependent resistances of ${SmB}_{6}$ shown in the Arrhenius plot under different magnetic fields. The solid lines are the two-channels model fitting results with formula $1 / ρ = 1 / ρ_{0} e^{- \frac{Δ_{III}}{k_{B} T}} + 1 / ρ_{s}$ , where $ρ_{0} e^{- \frac{Δ_{III}}{k_{B} T}}$ is the dominated insulating contribution in region III and $ρ_{s}$ is the dominated surface state contribution in region IV. The inset is the field-dependent energy gap derived from the above two-channels model fittings. The dotted line is the power-law extrapolation which gives a critical field of about 125 T to collapse the energy gap.
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Physical Review B

covering condensed matter and materials physics

Magnetoresistance evidence of a surface state and a field-dependent insulating state in the Kondo insulator ${SmB}_{6}$

F. Chen, C. Shang, Z. Jin, D. Zhao, Y. P. Wu, Z. J. Xiang, Z. C. Xia, A. F. Wang, X. G. Luo, T. Wu, and X. H. Chen

Phys. Rev. B 91, 205133 – Published 26 May 2015

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Physical Review B

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Magnetoresistance evidence of a surface state and a field-dependent insulating state in the Kondo insulator SmB6

F. Chen, C. Shang, Z. Jin, D. Zhao, Y. P. Wu, Z. J. Xiang, Z. C. Xia, A. F. Wang, X. G. Luo, T. Wu, and X. H. Chen

Phys. Rev. B 91, 205133 – Published 26 May 2015

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Magnetoresistance evidence of a surface state and a field-dependent insulating state in the Kondo insulator ${SmB}_{6}$