Giant Magnetic Quantum Oscillations in the Thermal Conductivity of TaAs: Indications of Chiral Zero Sound

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Giant Magnetic Quantum Oscillations in the Thermal Conductivity of TaAs: Indications of Chiral Zero Sound

Junsen Xiang, Sile Hu, Zhida Song, Meng Lv, Jiahao Zhang, Lingxiao Zhao, Wei Li, Ziyu Chen, Shuai Zhang, Jian-Tao Wang, Yi-feng Yang, Xi Dai, Frank Steglich, Genfu Chen, and Peijie Sun

Phys. Rev. X 9, 031036 – Published 28 August 2019

Abstract

Charge transport of topological semimetals is the focus of intensive investigations because of their nontrivial band topology. Heat transport of these materials, on the other hand, is largely unexplored and remains elusive. Here, we report on an observation of unprecedented, giant magnetic quantum oscillations of thermal conductivity in the prototypical Weyl semimetal TaAs. The oscillations are antiphase with the quantum oscillating electronic density of states of a Weyl pocket, and their amplitudes amount to 2 orders of magnitude of the estimation based on the Wiedemann-Franz law. Our analyses show that all the conventional heat-transport mechanisms through diffusions of propagating electrons, phonons, and electron-hole bipolar excitations are far inadequate to account for these phenomena. Taking further experimental facts that the parallel field configuration favors much-higher magnetothermal conductivity, we propose that the newly proposed chiral zero sound provides a reasonable explanation to these exotic phenomena. More work focusing on other topological semimetals along the same line is badly called for.

Received 9 February 2019
Revised 16 July 2019

DOI:https://doi.org/10.1103/PhysRevX.9.031036

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electrical conductivity Thermal conductivity

Weyl semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Junsen Xiang^1,2, Sile Hu^1,3, Zhida Song^4,1, Meng Lv^1,3, Jiahao Zhang^1,3, Lingxiao Zhao^1,3, Wei Li², Ziyu Chen², Shuai Zhang¹, Jian-Tao Wang^1,3, Yi-feng Yang^1,3, Xi Dai⁵, Frank Steglich^1,6, Genfu Chen^1,3,7, and Peijie Sun ^1,3,7,*

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Department of Physics, Key Laboratory of Micro-Nano Measurement-Manipulation and Physics, Beihang University, Beijing 100191, China
³University of Chinese Academy of Sciences, Beijing 100049, China
⁴Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
⁵Department of Physics, Hong Kong University of Science of Technology, Clear Water Bay, Kowloon, Hong Kong
⁶Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
⁷Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*Corresponding author. pjsun@iphy.ac.cn

Popular Summary

In solids, heat conduction is mediated by propagating electrons and phonons. A good heat conductor is usually a good electrical conductor, too. However, researchers have yet to figure out if this correspondence between heat and electrical conductance holds for topological semimetals, which are regarded as superior electrical conductors with relativistic electrons. Here, we report on unprecedented giant magnetic quantum oscillations of heat conduction in a type of topological semimetal known as a Weyl semimetal. This behavior cannot be explained by moving electrons or phonons, but instead appears to arise from chiral zero sound, a newly discovered heat transport mechanism seen in Weyl semimetals.

To study the connection between heat and electrical conduction, we take samples of the Weyl semimetal TaAs and measure how heat conduction, in comparison with electrical conduction, responds to magnetic field. Except for the well-known quantum oscillations in the latter, surprisingly, we observe an unprecedented, largely oscillatory heat conduction as a function of magnetic field. The oscillations of heat transport are so large that they go far beyond the expected heat carried by propagating electrons. Furthermore, the observed unique heat transport prefers to flow along the direction of the magnetic field. All these observations match the expected behaviors of chiral zero sound, a new acoustic vibration mode carried by Weyl electrons.

Our results will motivate further studies of unconventional heat conduction in topological materials. Along with the superior electrical transport, this new heat transport mechanism may help to find feasible applications of topological semimetals.

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Vol. 9, Iss. 3 — July - September 2019

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Figure 1
Thermal conductivity measurement configuration and raw experimental data of temperature gradient $d T (B)$ . (a) TaAs sample (TAc) mounted onto a copper cold plate. A chip resistor of $2000 Ω$ is used as a heater and a thin ( $ϕ = 25 μ m$ ) $chromel - {AuFe}_{0.07 %}$ thermocouple for detecting $d T$ . Manganin wires ( $ϕ = 25 μ m$ ) used for simultaneous electrical resistivity measurements are connected to the back side of the sample by spot welding. See Sec. 6 for more details on the thermal transport measurements. (b) Raw experimental values of $d T$ recorded in a continuous field scan between $B = - 9$ and 9 T at $T = 2 K$ , with a fixed heating power. Both the heat current and magnetic field are applied along the $c$ axis.
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Figure 2
Comparison of quantum oscillations in $σ_{∥} (B)$ (a) and $κ_{∥} (B)$ (b) measured at 2 K for sample TAc. In a parallel field configuration, $σ_{∥} (B) = 1 / ρ_{∥} (B)$ due to the absence of Hall conductivity. The SdH oscillations in $σ_{∥} (B)$ reveal three characteristic oscillation frequencies (see FFT analysis shown in the inset), in full agreement with literature data [19, 21, 22]. The MQOs of $κ_{∥} (B)$ (b) measured in the parallel field configuration have one dominating frequency of $F \approx 7 T$ . Also shown in (b) is the calculated $κ_{e, WF} (B)$ from $σ_{∥} (B)$ using the WF law. The oscillation amplitude of $κ_{e, WF} (B)$ is 2 orders of magnitude smaller than that of the measured ones [red points in (b)]. Note the logarithmic vertical axis in (b). The dashed line marks the position of the last extremum, where the measured $κ_{∥} (B)$ exhibits a minimum, whereas $σ_{∥} (B)$ and the calculated $κ_{e, WF} (B)$ assume a maximum, with opposite phases (phase difference $π$ ).
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Figure 3
Evolution of the $κ_{∥} (B)$ MQOs as a function of the temperature. (a) Isothermal $κ_{∥} / T$ curves as a function of $B^{- 1}$ measured at selected temperatures between $T = 1.8$ and 6 K. A characteristic frequency $F \approx 7 T$ can be readily observed from the $T$ -independent oscillation period of approximately $0.14 T^{- 1}$ for all the curves. The corresponding FFT analysis is shown in Fig. S7. For the sake of clarity, the $κ_{∥} / T$ curves are shifted upward by 7 (6 K), 6 (5 K), 5 (4 K), 5.5 (3.5 K), 4.5 (3 K), 3.5 (2.6 K), 2 (2.3 K), and 1 (2 K) units of $W / K^{2} m$ , respectively. (b) Temperature dependence of the normalized FFT amplitude of the characteristic MQOs with $F \approx 7 T$ , compared to the ones observed in magnetization (extracted from Ref. [22]) and electrical conductivity [cf. Fig. 2].
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Figure 4
Ultrasound velocity (left) and the corresponding ultrasound echo amplitude (right) measured as a function of the field at $T = 2 K$ . A transverse sound of 19 MHz is used, with the propagation $(k)$ and polarization $(u)$ along the $c$ and $a$ axes, respectively (see the inset). The detected sound velocity is approximately $2010 m / s$ , as expected for the transverse acoustic phonons of TaAs [32]. These measurements are performed under the condition that the ultrasound propagation and magnetic field are parallel and along the $c$ axis, corresponding to the field configuration for $κ_{∥} (B)$ measurements. The dominating oscillations in both quantities have a frequency of 7 T, almost in phase with $κ_{∥} (B)$ MQOs; see Fig. 2. The quantum oscillations of the sound velocity are of the order of $1 / 10^{4}$ up to 9 T, whereas the corresponding echo amplitude oscillates within 5% of its zero field value. The dashed blue line indicates the decreasing background of the ultrasound echo amplitude as a function of $B$ , which implies a decreasing phonon mean-free path.
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Figure 5
Comparison of $κ (B)$ measured for sample TAc in parallel ( $d T ∥ c$ , $B ∥ c$ ) and perpendicular ( $d T ∥ c$ , $B ∥ a$ ) field configurations. The dashed black lines denote a smooth background $κ_{bg} (B)$ for $κ_{∥} (B)$ and $κ_{⊥} (B)$ . It is clearly seen that $κ_{bg} (B)$ for the parallel field configuration gradually increases, whereas that for the perpendicular field slightly decreases with $B$ . These apparently different trends of $κ_{bg} (B)$ between the two field configurations provide strong support for CZS being involved in the magnetothermal conductivity. Furthermore, a semiquantitative fitting based on the CZS scenario is also shown [solid green $κ_{cal} (B)$ line], which agrees reasonably well with the experimental results. Inset: The trend of the background contribution for the two different field configurations is much better demonstrated at $T = 8 K$ , where the $F \approx 7 T$ oscillations have almost disappeared; cf. Fig. 3. At a much higher temperature $(T = 150 K)$ , the data for $κ_{∥} (B)$ and $κ_{⊥} (B)$ fall on top of each other.
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