Dirac nodal lines and nodal loops in the topological kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$

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Dirac nodal lines and nodal loops in the topological kagome superconductor ${CsV}_{3} {Sb}_{5}$

Zhanyang Hao, Yongqing Cai, Yixuan Liu, Yuan Wang, Xuelei Sui, Xiao-Ming Ma, Zecheng Shen, Zhicheng Jiang, Yichen Yang, Wanling Liu, Qi Jiang, Zhengtai Liu, Mao Ye, Dawei Shen, Yi Liu, Shengtao Cui, Jiabin Chen, Le Wang, Cai Liu, Junhao Lin, Jianfeng Wang, Bing Huang, Jia-Wei Mei, and Chaoyu Chen

Phys. Rev. B 106, L081101 – Published 2 August 2022

Abstract

The intertwining of charge order, superconductivity, and band topology has promoted the $A V_{3} {Sb}_{5}$ ( $A = K$ , Rb, Cs) family of materials to the center of attention in condensed matter physics. Underlying those mysterious macroscopic properties such as giant anomalous Hall conductivity (AHC) and chiral charge density wave is their nontrivial band topology. While there have been numerous experimental and theoretical works investigating the nontrivial band structure and especially the van Hove singularities, the exact topological phase of this family remains to be clarified. In this work, we identify ${CsV}_{3} {Sb}_{5}$ as a Dirac nodal line semimetal based on the observation of multiple Dirac nodal lines and loops close to the Fermi level. Combining photoemission spectroscopy and density functional theory, we identify two groups of Dirac nodal lines along the $k_{z}$ direction and one group of Dirac nodal loops in the $A - H - L$ plane. These nodal loops are located at the Fermi level within the instrumental resolution limit. Importantly, our first-principles analyses indicate that these nodal loops may be a crucial source of the mysterious giant AHC observed. Our results not only provide a clear picture to categorize the band structure topology of this family of materials, but also suggest the dominant role of topological nodal loops in shaping their transport behavior.

Received 2 November 2021
Revised 11 April 2022
Accepted 18 July 2022

DOI:https://doi.org/10.1103/PhysRevB.106.L081101

Physics Subject Headings (PhySH)

Topological materials Topological phases of matter Topological superconductors

Node-line semimetals

Angle-resolved photoemission spectroscopy Density functional calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhanyang Hao ^1,2,*, Yongqing Cai^1,2,*, Yixuan Liu^1,2,*, Yuan Wang^1,2,*, Xuelei Sui³, Xiao-Ming Ma ^1,2, Zecheng Shen ^1,2, Zhicheng Jiang⁴, Yichen Yang⁴, Wanling Liu⁴, Qi Jiang⁴, Zhengtai Liu⁴, Mao Ye⁴, Dawei Shen⁴, Yi Liu⁵, Shengtao Cui⁵, Jiabin Chen³, Le Wang^1,2, Cai Liu^1,2, Junhao Lin¹, Jianfeng Wang^6,3,†, Bing Huang³, Jia-Wei Mei ^1,2,7,†, and Chaoyu Chen ^1,2,†

¹Shenzhen Institute for Quantum Science and Engineering, and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
²International Quantum Academy, Shenzhen 518048, China
³Beijing Computational Science Research Center, Beijing 100193, China
⁴State Key Laboratory of Functional Materials for Informatics and Center for Excellence in Superconducting Electronics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
⁵National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230029, China
⁶School of Physics, Beihang University, Beijing 100191, China
⁷Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen 518055, China

^*These authors contributed equally to this work
^†Corresponding authors: wangjf06@buaa.edu.cn, meijw@sustech.edu.cn, chency@sustech.edu.cn

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Vol. 106, Iss. 8 — 15 August 2022

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Figure 1
Characterization of single-crystalline ${CsV}_{3} {Sb}_{5}$ . (a) Crystal structure of ${CsV}_{3} {Sb}_{5}$ . Left inset: 3D BZ. (b) Single-crystal XRD pattern of the ( $00 l$ ) plane. Inset: optical image. (c), (d), and (e) Temperature-dependent resistivity ratio, heat capacity, and magnetic susceptibility measurements of ${CsV}_{3} {Sb}_{5}$ single crystal.
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Figure 2
General electronic structure with multiple Dirac nodal lines and loops. (a) Fermi surface in 2D BZ. The ARPES data here is measured with 83 eV photons. (b) Photon energy-dependent spectra. (c) Spectra taken along momentum cuts $A_{6} - H_{6} - L_{6}$ . Black arrows indicate four Dirac nodes. The ARPES data here is measured with 70 $eV$ photons. (d) Spectra along the $\bar{Γ} - \bar{K} - \bar{M}$ path from the projection of DFT. (e) DFT calculated electronic structure. (f) Visualization of Dirac nodal lines and loops formed by nodes N1, N2, N3, and N4. The different colors represent their energy relative to $E_{F}$ . Note that the calculated $E_{F}$ is slightly shifted upward to match the experiment.
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Figure 3
Visualizations of N1 and N2 Dirac nodal lines. (a) Constant energy contours (CECs) in $k_{x} - k_{y}$ plane at $\sim - 0.3 eV$ , which shows the N1 Dirac nodal point (black arrow). (b) CECs in the $k_{x} - k_{y}$ plane at a series of binding energies. Black dashed lines indicate the N1 Dirac cone dispersion. (c) Spectra taken along $M / L - K / H - Γ / A$ cuts at a series of $k_{z}$ planes with black arrows highlighting the positions of N1 and N2. (d) CEC in $k_{x} - k_{y}$ plane at $\sim - 0.15 eV$ , which shows the N2 Dirac nodal point (black arrow). (e) Spectra from a series of momentum cuts whose positions are indicated by black dashed lines in (d). White dashed lines highlight the gap opening of the Dirac cone when moving away from N2. (f) Direct visualizations of N1, N2 Dirac nodal lines. The ARPES spectra shown in (a), (b), (d), (e) are measured with 83 $eV$ photons.
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Figure 4
Visualizations of N3/N4 Dirac nodal loops and their calculated AHC and Berry curvatures. (a) CEC in $k_{x} - k_{y}$ plane at $E_{F}$ . (b) CEC zoom in. Numbered white dots indicate the nodes determined from spectra analysis in (c). (c) Spectra taken from a series of momentum cuts whose positions are indicated by black dashed lines in (b). Numbered white dotted lines indicate the dispersion evolution of N3/N4. The corresponding DFT calculated dispersion are plotted by the red dashed lines. The ARPES data here is measured with 83 eV photons. (d) Simulated Fermi surface by DFT. (e) Calculated AHC as a function of binding energy. (f) Calculated Berry curvature distributions in $A - H - L$ plane at energies of $- 0.3, - 0.1,$ and $0 eV$ , respectively.
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Physical Review B

covering condensed matter and materials physics

Dirac nodal lines and nodal loops in the topological kagome superconductor ${CsV}_{3} {Sb}_{5}$

Zhanyang Hao, Yongqing Cai, Yixuan Liu, Yuan Wang, Xuelei Sui, Xiao-Ming Ma, Zecheng Shen, Zhicheng Jiang, Yichen Yang, Wanling Liu, Qi Jiang, Zhengtai Liu, Mao Ye, Dawei Shen, Yi Liu, Shengtao Cui, Jiabin Chen, Le Wang, Cai Liu, Junhao Lin, Jianfeng Wang, Bing Huang, Jia-Wei Mei, and Chaoyu Chen

Phys. Rev. B 106, L081101 – Published 2 August 2022

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Physical Review B

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Dirac nodal lines and nodal loops in the topological kagome superconductor CsV3Sb5

Zhanyang Hao, Yongqing Cai, Yixuan Liu, Yuan Wang, Xuelei Sui, Xiao-Ming Ma, Zecheng Shen, Zhicheng Jiang, Yichen Yang, Wanling Liu, Qi Jiang, Zhengtai Liu, Mao Ye, Dawei Shen, Yi Liu, Shengtao Cui, Jiabin Chen, Le Wang, Cai Liu, Junhao Lin, Jianfeng Wang, Bing Huang, Jia-Wei Mei, and Chaoyu Chen

Phys. Rev. B 106, L081101 – Published 2 August 2022

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Dirac nodal lines and nodal loops in the topological kagome superconductor ${CsV}_{3} {Sb}_{5}$