Transport evidence for the three-dimensional Dirac semimetal phase in $\mathrm{ZrT}{\mathrm{e}}_{5}$

Transport evidence for the three-dimensional Dirac semimetal phase in $ZrT e_{5}$

Guolin Zheng, Jianwei Lu, Xiangde Zhu, Wei Ning, Yuyan Han, Hongwei Zhang, Jinglei Zhang, Chuanying Xi, Jiyong Yang, Haifeng Du, Kun Yang, Yuheng Zhang, and Mingliang Tian

Phys. Rev. B 93, 115414 – Published 9 March 2016

Abstract

Topological Dirac semimetal is a newly discovered class of materials which has attracted intense attention. This material can be viewed as a three-dimensional (3D) analog of graphene and has linear energy dispersion in bulk, leading to a range of exotic transport properties. Here we report direct quantum transport evidence of the 3D Dirac semimetal phase of layered material $ZrT e_{5}$ by angular-dependent magnetoresistance measurements under high magnetic fields up to 31 T. We observed very clear negative longitudinal magnetoresistance induced by chiral anomaly under the condition of the magnetic field aligned only along the current direction. Pronounced Shubnikov–de Hass (SdH) quantum oscillations in both longitudinal magnetoresistance and transverse Hall resistance were observed, revealing anisotropic light cyclotron masses and high mobility of the system. In particular, a nontrivial π-Berry phase in the SdH oscillations gives clear evidence for the 3D Dirac semimetal phase. Furthermore, we observed clear Landau level splitting under high magnetic field, suggesting possible splitting of the Dirac point into Weyl points due to broken time-reversal symmetry. Our results indicate that $ZrT e_{5}$ is an ideal platform to study 3D massless Dirac and Weyl fermions in a layered compound.

Received 1 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.115414

Physics Subject Headings (PhySH)

Electronic structure Magnetotransport

Dirac semimetal Single crystal materials

Shubnikov-de Haas effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Guolin Zheng^1,2, Jianwei Lu^1,2, Xiangde Zhu^1,3, Wei Ning^1,3,*, Yuyan Han^1,3, Hongwei Zhang^1,2, Jinglei Zhang^1,3, Chuanying Xi^1,3, Jiyong Yang^1,3, Haifeng Du^1,3, Kun Yang⁴, Yuheng Zhang^1,3,5, and Mingliang Tian^1,3,5,†

¹High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, Anhui, People's Republic of China
²University of Science and Technology of China, Hefei 230026, Anhui, People's Republic of China
³Hefei Science Center, Chinese Academy of Sciences, Hefei 230031, Anhui, People's Republic of China
⁴National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306-4005, USA
⁵Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China

^*ningwei@hmfl.ac.cn
^†tianml@hmfl.ac.cn

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Vol. 93, Iss. 11 — 15 March 2016

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Figure 1
Temperature dependence of the longitudinal resistance $R_{x x}$ for samples S1 (160 nm) and S2 (80 nm); the inset shows the SEM image of a Hall bar device used in the measurement. The out-of-plane direction is the $b$ axis while the current is applied along the $a$ -axis direction (long axis of the ribbon).
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Figure 2
(a,d) are, respectively, the angular dependence of longitudinal magnetoresistance (LMR), $R_{x x}$ ( $B$ )/ $R_{x x}$ (0), of sample S1 (thickness: 160 nm) by tilting the magnetic field $B$ in $a b$ and $b c$ planes measured at 2 K, where a dc current is injected along the $a$ axis (i.e., the lengthwise direction of the ribbon) in (a) and the $c$ axis (i.e., the transverse direction) in (d), respectively. The insets are the blowup of the plot in the low-field range. Negative LMR is found when the magnetic field is aligned parallel to the dc current at $θ = 90^{\circ}$ or $φ = 90^{\circ}$ ). (b,e) are the $R_{x x}$ ( $B$ )/ $R_{x x}$ (0) versus $B$ at several angles near $θ = 90^{\circ}$ or $φ = 90^{\circ}$ , respectively. The negative LMR disappears when the tilted angle $θ$ or $φ$ ) is off the current directions. (c,f) are the $R_{x x}$ ( $B$ )/ $R_{x x}$ (0) versus $B$ with $B$ // $I$ (i.e., along the $a$ and $c$ axis) at different temperatures. The negative LMR is suppressed by increasing temperatures.
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Figure 3
(a) The hall resistance, $R_{x y}$ , versus $B$ aligned along the $b$ axis at different temperatures. It presents a negative slope in $B < 4$ T and then a sign reversal above 4 T. All curves are offset vertically for clarity. (b) The oscillatory component, $Δ R_{x y}$ versus 1/ $B$ under different temperatures; the periodic oscillating behavior with 1/ $B$ indicates the nature of Shubnikov–de Haas (SdH) oscillations due to Landau quantization of the energy levels. The Landau index number $n$ is marked with the peak position defined by integer indices. (c) The amplitudes of the oscillatory component $Δ R_{x y} / Δ R_{x y} (2 K)$ at $n = 2$ peak under different temperatures. The red line is the theoretical fit, generating an effective mass $m^{*} = 0.026 m_{e}$ . (d) The Landau index $n$ versus 1/ $B$ ; the best linear fit generates a nonzero intercept about $- 0.18$ with the $n$ axis.
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Figure 4
(a,d) are, respectively, the $R_{x y}$ versus $B$ tilted within $a − b$ and $b − c$ planes for sample S2. (b,e) are the $d R_{x y} / d B$ as the function of $1 / B_{⊥}$ with $B_{⊥} = B \cos θ$ or $B \cos φ$ , respectively. The arrows indicate the shift for Landau index $n = 3$ peak. All curves are offset vertically for clarity. (c,f) are the angular dependence of the oscillation frequency derived from FFT analysis from (b) and (e). The FFT frequency deviated from $1 / \cos (θ)$ and $1 / \cos (φ)$ relation with $B$ tilted in $a − b$ and $b − c$ planes, respectively.
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Figure 5
(a) The $R_{x x}$ versus $B$ up to 30 T aligned along the $c$ axis at different temperatures. (b) The oscillatory component $Δ R_{x x}$ versus 1/ $B$ at different temperatures. The splitting of the peaks of $n = 1$ and 2 was clearly seen, as marked by the arrows. The splitting is smeared out with the increase of temperature above 15 K due to thermal fluctuation.
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Physical Review B

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Transport evidence for the three-dimensional Dirac semimetal phase in $ZrT e_{5}$

Guolin Zheng, Jianwei Lu, Xiangde Zhu, Wei Ning, Yuyan Han, Hongwei Zhang, Jinglei Zhang, Chuanying Xi, Jiyong Yang, Haifeng Du, Kun Yang, Yuheng Zhang, and Mingliang Tian

Phys. Rev. B 93, 115414 – Published 9 March 2016

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Physical Review B

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Transport evidence for the three-dimensional Dirac semimetal phase in ZrTe5

Guolin Zheng, Jianwei Lu, Xiangde Zhu, Wei Ning, Yuyan Han, Hongwei Zhang, Jinglei Zhang, Chuanying Xi, Jiyong Yang, Haifeng Du, Kun Yang, Yuheng Zhang, and Mingliang Tian

Phys. Rev. B 93, 115414 – Published 9 March 2016

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Transport evidence for the three-dimensional Dirac semimetal phase in $ZrT e_{5}$