Thermal transport properties and some hydrodynamic-like behavior in three-dimensional topological semimetal $\mathrm{Zr}{\mathrm{Te}}_{5}$

Thermal transport properties and some hydrodynamic-like behavior in three-dimensional topological semimetal $Zr {Te}_{5}$

Chang-woo Cho, Peipei Wang, Fangdong Tang, Sungkyun Park, Mingquan He, Rolf Lortz, Genda Gu, Qiang Li, and Liyuan Zhang

Phys. Rev. B 105, 085132 – Published 22 February 2022

Abstract

Hydrodynamic fluidity in condensed-matter physics has been experimentally demonstrated only in a limited number of compounds due to the stringent conditions that must be met. Herein, we performed thermal and electrical transport experiments in three-dimensional topological semimetal $Zr {Te}_{5}$ . By measuring the thermal properties in a wide temperature range, two representative experimental evidences of the hydrodynamics are observed in the temperature window between the ballistic and diffusive regimes: a faster evolution of the thermal conductivity than in the ballistic regime and the nonmonotonic temperature-dependent effective quasiparticle mean-free-path. In addition, magnetothermal conductivity results indicate that charged quasiparticles, as well as phonons, may also play an important role in this hydrodynamic-like flow in $Zr {Te}_{5}$ .

Received 28 June 2021
Revised 29 November 2021
Accepted 26 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.085132

Physics Subject Headings (PhySH)

Electrical conductivity Phonons Quasiparticles & collective excitations Thermal conductivity

Semimetals Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chang-woo Cho ^1,2, Peipei Wang¹, Fangdong Tang¹, Sungkyun Park², Mingquan He³, Rolf Lortz ⁴, Genda Gu⁵, Qiang Li ^5,6, and Liyuan Zhang^1,*

¹Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
²Department of Physics, Pusan National University, Busan 46241, South Korea
³Low Temperature Physics Lab, College of Physics & Center of Quantum Materials and Devices, Chongqing University, Chongqing 401331, China
⁴Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
⁵Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
⁶Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA

^*zhangly@sustech.edu.cn

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Vol. 105, Iss. 8 — 15 February 2022

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Figure 1
(a) Photograph of the thermal conductivity setup used in this study. (b) To minimize thermal leakage during the heat flow (from the resistive heater to the thermal bath), we connected the sample to the heater and thermometers through 100- $μ m$ -thick Ag wires. And, the connections for the electrical measurements are made by 25- $μ m$ -thin Pt/W wires since it is a good electrical conductor but a relatively poor thermal conductor. (c) Schematic diagram of our thermal conductivity experimental setup.
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Figure 2
(a) Thermal conductivity as a function of temperature in a log-log plot in three different $Zr {Te}_{5}$ samples. The squares (sample No. 1), circles (sample No. 2), and triangles (sample No. 3) indicate the total thermal conductivity $κ_{tot}$ , respectively. All the dashed lines are proportional to $T^{3}$ . In sample No. 2 and No. 3, the shaded regions denote the area that exceeds $T^{3}$ dependence. The vertical arrows denote the temperature that is occurring during phonon-drag effect of each sample. (b) Temperature-dependent charge carrier thermal conductivity $κ_{WF}$ , which is calculated according to the Wiedemann-Franz law ( $κ_{WF} = \frac{T}{ρ} L_{0}$ , where the Lorenz number $L_{0} = 2.44 \times 10^{- 8} W Ω K^{- 2}$ ). Compared to $κ_{tot}$ , it is smaller by a factor of hundreds in almost all temperature ranges.
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Figure 3
(a) Longitudinal total thermal conductivity $κ_{x x}$ (closed square) and electronically contributed thermal conductivity $κ_{WF}$ (red solid line) as a function of magnetic fields. The data were taken at $T = 0.81 K$ ( $κ_{x x}$ ) and $T = 0.70 K$ ( $κ_{WF}$ ), respectively. (b) Extracted charged quasiparticles contribution to the thermal conductivity of sample No. 3 (closed circle). Sample No. 2 result is added in the inset of (b). Both samples show the deviation of $Δ κ$ in a hydrodynamic regime as shaded. See main text for details.
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Figure 4
(a) Magnetic field dependence of the thermal Hall resistivity $ω_{x y}$ at various temperatures on sample No. 2. (b) Tangential Hall angle $(tan θ_{H} = \frac{κ_{x y}}{κ_{x x}})$ in a magnetic field range of −0.5 to 0.5 T at different temperatures on sample No. 2. (c) Temperature-dependent slope of $tan θ_{H} / B$ in the zero magnetic-field limit for sample No. 2 and No. 3. In principle, this quantity is proportional to the mean-free-path of the quasiparticles. The vertical arrows denote the local minima. The inset of (c) presents the initial slope of the electronic Hall angle.
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Figure 5
Temperature dependence of Lorenz ratio $(L / L_{0})$ for $Zr {Te}_{5}$ single crystals used this study. Horizontal line (dotted) is a guideline when $L = L_{0}$ .
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Physical Review B

covering condensed matter and materials physics

Thermal transport properties and some hydrodynamic-like behavior in three-dimensional topological semimetal $Zr {Te}_{5}$

Chang-woo Cho, Peipei Wang, Fangdong Tang, Sungkyun Park, Mingquan He, Rolf Lortz, Genda Gu, Qiang Li, and Liyuan Zhang

Phys. Rev. B 105, 085132 – Published 22 February 2022

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Physical Review B

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Thermal transport properties and some hydrodynamic-like behavior in three-dimensional topological semimetal ZrTe5

Chang-woo Cho, Peipei Wang, Fangdong Tang, Sungkyun Park, Mingquan He, Rolf Lortz, Genda Gu, Qiang Li, and Liyuan Zhang

Phys. Rev. B 105, 085132 – Published 22 February 2022

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Thermal transport properties and some hydrodynamic-like behavior in three-dimensional topological semimetal $Zr {Te}_{5}$