Dirac nodal lines in the quasi-one-dimensional ternary telluride ${\mathrm{TaPtTe}}_{5}$

Dirac nodal lines in the quasi-one-dimensional ternary telluride ${TaPtTe}_{5}$

Shaozhu Xiao, Wen-He Jiao, Yu Lin, Qi Jiang, Xiufu Yang, Yunpeng He, Zhicheng Jiang, Yichen Yang, Zhengtai Liu, Mao Ye, Dawei Shen, and Shaolong He

Phys. Rev. B 105, 195145 – Published 27 May 2022

Abstract

A Dirac nodal-line phase as a quantum state of topological materials, usually occur in three-dimensional or, at least, two-dimensional materials with sufficient symmetry operations that could protect the Dirac band crossings. Here, we report a combined theoretical and experimental study on the electronic structure of the quasi-one-dimensional ternary telluride ${TaPtTe}_{5}$ , which is corroborated as being in a robust nodal-line phase with fourfold degeneracy. Our angle-resolved photoemission spectroscopy measurements show that two pairs of linearly dispersive Dirac-like bands exist in a very large energy window, which extend from a binding energy of $\sim 0.75$ eV to across the Fermi level. The crossing points are at the boundary of Brillouin zone and form Dirac-like nodal lines. Using first-principles calculations, we demonstrate the existing of nodal surfaces on the $k_{y} = \pm π$ plane in the absence of spin-orbit coupling (SOC), which are protected by nonsymmorphic symmetry in ${TaPtTe}_{5}$ . When SOC is included, the nodal surfaces are broken into several nodal lines. By theoretical analysis, we conclude that the nodal lines along $Y − T$ and the ones connecting the $R$ points are nontrivial and protected by nonsymmorphic symmetry against SOC.

Received 27 February 2022
Accepted 11 May 2022

DOI:https://doi.org/10.1103/PhysRevB.105.195145

Physics Subject Headings (PhySH)

Electronic structure Symmetry protected topological states

Node-line semimetals Topological materials

Angle-resolved photoemission spectroscopy First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shaozhu Xiao^1,*, Wen-He Jiao ^2,†, Yu Lin^1,3,4, Qi Jiang⁵, Xiufu Yang¹, Yunpeng He¹, Zhicheng Jiang⁵, Yichen Yang⁵, Zhengtai Liu ⁵, Mao Ye⁵, Dawei Shen ⁵, and Shaolong He^1,6,‡

¹Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China
²Department of Applied Physics, Key Laboratory of Quantum Precision Measurement of Zhejiang Province, Zhejiang University of Technology, Hangzhou 310023, China
³Fujian Provincial Collaborative Innovation Center for Advanced High-Field Superconducting Materials and Engineering, Fuzhou 350117, China
⁴College of Physics and Energy, Fujian Normal University, Fuzhou 350117, China
⁵State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Science, Shanghai 200050, China
⁶University of Chinese Academy of Sciences, Beijing 100049, China

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

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Vol. 105, Iss. 19 — 15 May 2022

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Figure 1
Crystal structure and sample characterization of ${TaPtTe}_{5}$ . (a) Conventional unit cell of ${TaPtTe}_{5}$ . For convenience, the $a$ , $c$ , and $b$ axes are specified as $x$ , $y$ , and $z$ axes, respectively. (b) Perspective view of the crystal structure of ${TaPtTe}_{5}$ along the $x$ axis. (c) View of a ${TaPtTe}_{5}$ layer along the $z$ axis. (d) Three-dimensional bulk Brillouin zone (red lines) and the projected (001) surface Brillouin zone (yellow lines) with the high-symmetry points labeled. (e) Low-energy electron diffraction (LEED) pattern of the cleaved (001) surface.
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Figure 2
Electronic structures of ${TaPtTe}_{5}$ measured by ARPES ( $h ν = 28.5$ eV). (a) ARPES Fermi surface of ${TaPtTe}_{5}$ . The yellow lines represent the surface Brillouin zone. The gray dashed lines in (a) indicate the momentum cuts along which the band dispersions in (b) and (e) are taken. (b) A representative Dirac-like band dispersion along the “cut 6” gray line as indicated in (a). (c) Stacking plot of constant-energy contours at different binding energies. (d) Schematic of the measured Dirac-like nodal lines in the surface Brillouin zone. (e) A series of band dispersions along the gray lines as indicated in (a) to reveal the nodal lines.
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Figure 3
Electronic structures of ${TaPtTe}_{5}$ obtained by theoretical calculation without considering the SOC. (a) Bulk Brillouin zone (red lines) and surface Brillouin zone (yellow lines). (b) Calculated bands along selected high-symmetry lines in the absence of SOC. (c) ARPES measured band dispersions (left side) and the corresponding calculated results (right side), with $k_{x} = \sim 0.5 Å^{- 1}$ . (d) ARPES measured (left side) and calculated (right side) Fermi surface. (e) Calculated surface spectra along the lines in surface Brillouin zone as indicated by the gray lines in (a), which include the contributions from both the projections of bulk bands and the surface states. (f) Calculated bulk bands along the lines on the $k_{z} = π$ plane of the bulk Brillouin zone as indicated by the green lines in (a).
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Figure 4
Electronic structures of ${TaPtTe}_{5}$ obtained by theoretical calculation when considering SOC. (a) Calculated bands along selected high-symmetry lines in the presence of SOC. The bands (along $Y − T$ ) indicated by black arrows are Dirac nodal lines protected by symmetry against SOC. (b) ARPES measured band dispersions (left side) and the corresponding calculated result (right side) with $k_{x} = \sim 0.5 Å^{- 1}$ . (c) Calculated surface spectra along the lines in the surface Brillouin zone (cut S3 to S10) as indicated by the gray lines in Fig. 3. (d) Calculated bulk bands along the lines on the $k_{z} = π$ plane of the bulk Brillouin zone as indicated by the green lines in Fig. 3. (e) The contributions of surface states extracted from (c)
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Figure 5
Nodal lines on the $k_{y} = \pm π$ plane. (a) and (b) The upmost two pairs of bands that cross the Fermi level and (c) and (d) the difference between each pair. Six nodal lines on the $k_{y} = \pm π$ plane are shown, four of which as shown by pink lines in (a) and (b) and as indicated by pink arrows in (c) and (d) are protected by nonsymmorphic symmetry.
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Physical Review B

covering condensed matter and materials physics

Dirac nodal lines in the quasi-one-dimensional ternary telluride ${TaPtTe}_{5}$

Shaozhu Xiao, Wen-He Jiao, Yu Lin, Qi Jiang, Xiufu Yang, Yunpeng He, Zhicheng Jiang, Yichen Yang, Zhengtai Liu, Mao Ye, Dawei Shen, and Shaolong He

Phys. Rev. B 105, 195145 – Published 27 May 2022

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Physical Review B

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Dirac nodal lines in the quasi-one-dimensional ternary telluride TaPtTe5

Shaozhu Xiao, Wen-He Jiao, Yu Lin, Qi Jiang, Xiufu Yang, Yunpeng He, Zhicheng Jiang, Yichen Yang, Zhengtai Liu, Mao Ye, Dawei Shen, and Shaolong He

Phys. Rev. B 105, 195145 – Published 27 May 2022

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Dirac nodal lines in the quasi-one-dimensional ternary telluride ${TaPtTe}_{5}$