Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride ${\mathrm{NbNiTe}}_{5}$

Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride ${NbNiTe}_{5}$

Wen-He Jiao, Shaozhu Xiao, Wei Liu, Yi Liu, Hang-Qiang Qiu, Keqi Xia, Shaolong He, Yuke Li, Guang-Han Cao, and Xiaofeng Xu

Phys. Rev. B 107, 195124 – Published 12 May 2023

Abstract

Topological quantum materials, which feature nontrivial band topology, have been one of the most attractive research topics in condensed-matter physics in recent decades. The low-dimensional topologically nontrivial materials are especially appealing due to the rich implications for topological physics and the potential applications in next-generation spintronic devices. Here, we report the crystal growth, anisotropic magnetotransport, Hall effect, and quantum de Haas–van Alphen (dHvA) oscillations of a quasi-one-dimensional ternary telluride ${NbNiTe}_{5}$ . The pronounced dHvA oscillations under $H ∥ b$ reveal three major oscillation frequencies $F_{α} = 136.41 T, F_{β} = 240.34 T$ , and $F_{γ} = 708.03$ T and the associated light effective masses of charge carriers. From the angular dependence of dHvA oscillations, we have revealed the identified frequencies exhibit anisotropic character, all of which arise from the holelike Fermi surface sheets formed by band 1 ( $F_{α}$ and $F_{β}$ ) and band 2 ( $F_{γ}$ ) by comparing with the Fermi surface calculations. First-principles calculations demonstrate that ${NbNiTe}_{5}$ is a candidate of multiple topological material. In addition to the nonsymmorphic symmetry-protected nodal lines and band inversion (anticrossing) induced topological surface states, a ladder of topological gaps with the coexistence of strong and weak topology and a series of induced topological surface states are also identified.

Received 18 January 2023
Revised 20 April 2023
Accepted 20 April 2023

DOI:https://doi.org/10.1103/PhysRevB.107.195124

Physics Subject Headings (PhySH)

First-principles calculations Magnetic susceptibility Magnetotransport Topological materials

Crystal growth Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wen-He Jiao ^1,*, Shaozhu Xiao^2,†, Wei Liu², Yi Liu¹, Hang-Qiang Qiu³, Keqi Xia⁴, Shaolong He², Yuke Li ⁴, Guang-Han Cao^5,6, and Xiaofeng Xu ^1,‡

¹Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
²Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
³Department of Applied Physics, Zhejiang University of Science and Technology, Hangzhou 310023, China
⁴School of Physics and Hangzhou Key Laboratory of Quantum Matters, Hangzhou Normal University, Hangzhou 311121, China
⁵School of Physics, Interdisciplinary Center for Quantum Information, and State Key Lab of Silicon Materials, Zhejiang University, Hangzhou 310058, China
⁶Collaborative Innovation Centre of Advanced Microstructures, Nanjing 210093, China

^*whjiao@zjut.edu.cn
^†xiaoshaozhu@nimte.ac.cn
^‡xuxiaofeng@zjut.edu.cn

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Vol. 107, Iss. 19 — 15 May 2023

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Figure 1
(a) The crystallographic structure of ${NbNiTe}_{5}$ with an orthorhombic unit cell viewed perspectively along the $a$ axis. (b) Single-crystal x-ray diffraction pattern at room temperature. The right inset enlarges the second reflection in the x-ray diffraction pattern. The left inset is a photograph of the as-grown ${NbNiTe}_{5}$ crystals on a millimeter paper. (c) Temperature dependence of the electrical resistivity $ρ_{a}, ρ_{c}$ , and $ρ_{b}$ with the current applied along three crystallographic directions. The dotted red lines correspond to the fits to the BG equation above 50 K. The insets enlarge the low- $T$ dependence of $ρ_{a}, ρ_{c}$ , and $ρ_{b}$ below 50 K, all of which can be fitted using a power-law dependence $T^{α}$ (the solid orange lines). (d) Temperature dependence of the resistivity anisotropy $ρ_{c} / ρ_{a}$ (left axis) and $ρ_{b} / ρ_{a}$ (right axis).
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Figure 2
Temperature dependence of $ρ_{a}$ (a), $ρ_{c}$ (b), and $ρ_{b}$ (c) with the magnetic fields parallel to the $b$ -axis, $b$ -axis, and $c$ -axis, respectively, up to 9 T below 50 K. The red arrows in (b) denote the temperature $T^{*}$ . The inset shows the field-dependent $T^{*}$ . The MR for $ρ_{a}$ (d), $ρ_{c}$ (e), and $ρ_{b}$ (f) at several selected temperatures below 100 K. The blue dashed lines are the fits (see main text). Kohler's scaling for $ρ_{a}$ (g), $ρ_{c}$ (h), and $ρ_{b}$ (i) at the corresponding temperatures.
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Figure 3
The dHvA oscillations and nontrivial Berry phase of ${NbNiTe}_{5}$ . (a) Isothermal magnetization under the $H ∥ b$ -axis at 1.8 K. (b) The magnetization oscillations after subtracting the polynomial background at selected temperatures below 14 K. (c) The corresponding FFT spectrum. (d) The $T$ -dependent FFT amplitude and the fit to $R_{T}$ to determine the corresponding effective mass. (e) The Lifshitz-Kosevich fit (green line) of the oscillation pattern at 1.8 K. The inset shows the extracted three single-frequency oscillatory components, which are shifted vertically for clarity. (f) Landau's fan diagram for the identified frequencies $F_{α}, F_{β}$ , and $F_{γ}$ . The $n$ -axis intercepts for each of the frequencies are illustrated in the inset.
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Figure 4
Fermi surface morphology of ${NbNiTe}_{5}$ . (a) The magnetization oscillations after subtracting the polynomial background at different angles ( $T = 1.8 K$ ). Data at different field orientations have been shifted for clarity. Angle $θ = 0^{\circ}$ ( $90^{\circ}$ ) corresponds to $H ∥ b$ -axis ( $c$ -axis). The measurement setup is plotted in the inset. (b) The corresponding FFT spectra at different angles. (c) The angular dependence of the oscillation frequencies. The green lines are fits to $F = F_{3 D} + F_{2 D} / \cos θ$ for $F_{α}$ and $F_{β}$ . (d) The calculated and experimental angular dependence of dHvA frequencies. The open symbols are data based on the theoretical calculation, and the calculated data are plotted with the same color as the corresponding experimental data.
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Figure 5
(a)–(e) 3D Fermi surfaces of the bands 1–5 specified in (h) in the presence of SOC. The orbits H1–H6 and E1 in (a), (b), and (e) denote the pockets that contribute to the dHvA oscillations when the external field is applied along the direction from principal axes $b$ to $c$ . H represents the hole pocket, while E denotes the electron pocket. (f) Bulk Brillouin zone with high symmetric points labeled. (g),(h) Calculated band structures of ${NbNiTe}_{5}$ along high symmetric paths (g) without considering SOC and (h) with considering SOC. The black arrows in (h) indicate the topologically nontrivial Dirac nodal lines surviving against SOC.
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Figure 6
Nontrivial surface states in ${NbNiTe}_{5}$ . (a) Bulk Brillouin zone (black lines) and the projected surface Brillouin zones, with the light blue one for the surface perpendicular to $b$ and the light green one for that perpendicular to $c$ . (b) Crystal structure of ${NbNiTe}_{5}$ with three cleaved surfaces indicated by the black arrows. The top surface, parallel to ${NbNiTe}_{5}$ layers, is the most easily obtained surface. The side surfaces that we consider are perpendicular to the $c$ axis, and they can be obtained by cleaving between $Te − Te$ bonds, which both terminate with Te atoms but still have two types. (c) Calculated surface spectrum of both bulk and surface states along $\bar{T} − \bar{Γ} − \bar{T}$ on the top surface. (d) Spin-resolved surface spectrum corresponding to (c). (e),(f) Same as (c),(d) but along $\bar{Γ} − \bar{Y} − \bar{Γ}$ on the side surface $A$ . (g),(h) Same as (e),(f) but on the side surface $B$ . (i) Calculated surface spectrum of only the bulk states along $\bar{T} − \bar{Γ} − \bar{T}$ on the top surface. (j) Same as (i) but on the side surface $A$ or $B$ .
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Physical Review B

covering condensed matter and materials physics

Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride ${NbNiTe}_{5}$

Wen-He Jiao, Shaozhu Xiao, Wei Liu, Yi Liu, Hang-Qiang Qiu, Keqi Xia, Shaolong He, Yuke Li, Guang-Han Cao, and Xiaofeng Xu

Phys. Rev. B 107, 195124 – Published 12 May 2023

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Physical Review B

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Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride NbNiTe5

Wen-He Jiao, Shaozhu Xiao, Wei Liu, Yi Liu, Hang-Qiang Qiu, Keqi Xia, Shaolong He, Yuke Li, Guang-Han Cao, and Xiaofeng Xu

Phys. Rev. B 107, 195124 – Published 12 May 2023

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Anisotropic transport and multiple topology in quasi-one-dimensional ternary telluride ${NbNiTe}_{5}$