Eightfold fermionic excitation in a charge density wave compound

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Eightfold fermionic excitation in a charge density wave compound

Xi Zhang, Qiangqiang Gu, Haigen Sun, Tianchuang Luo, Yanzhao Liu, Yueyuan Chen, Zhibin Shao, Zongyuan Zhang, Shaojian Li, Yuanwei Sun, Yuehui Li, Xiaokang Li, Shangjie Xue, Jun Ge, Ying Xing, R. Comin, Zengwei Zhu, Peng Gao, Binghai Yan, Ji Feng, Minghu Pan, and Jian Wang

Phys. Rev. B 102, 035125 – Published 14 July 2020

Abstract

Unconventional quasiparticle excitations in condensed matter systems have become one of the most important research frontiers. Beyond twofold and fourfold degenerate Weyl and Dirac fermions, threefold, sixfold, and eightfold symmetry protected degeneracies have been predicted. However they remain challenging to realize in solid state materials. Here the charge density wave compound $TaT e_{4}$ is proposed to hold eightfold fermionic excitation and Dirac point in energy bands. High quality $TaT e_{4}$ single crystals are prepared, where the charge density wave is revealed by directly imaging the atomic structure and a pseudogap of about 45 meV on the surface. Shubnikov-de Haas oscillations of $TaT e_{4}$ are consistent with band structure calculation. Scanning tunneling microscopy/spectroscopy reveals atomic step edge states on the surface of $TaT e_{4}$ . This work uncovers that the charge density wave is able to induce new topological phases and sheds new light on the novel excitations in condensed matter materials.

Received 12 September 2019
Accepted 24 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.035125

Physics Subject Headings (PhySH)

Charge density waves Dirac fermions Electronic structure First-principles calculations Magnetotransport Shubnikov-de Haas effect Topological materials

Single crystal materials

Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xi Zhang¹, Qiangqiang Gu¹, Haigen Sun², Tianchuang Luo ¹, Yanzhao Liu¹, Yueyuan Chen¹, Zhibin Shao³, Zongyuan Zhang², Shaojian Li², Yuanwei Sun^1,4, Yuehui Li^1,4, Xiaokang Li^2,5, Shangjie Xue^1,6, Jun Ge¹, Ying Xing⁷, R. Comin⁶, Zengwei Zhu^2,5, Peng Gao^1,4,8, Binghai Yan⁹, Ji Feng^1,10,*, Minghu Pan ^2,3,†, and Jian Wang ^1,8,10,‡

¹International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
²School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
³School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China
⁴Electron Microscopy Laboratory, School of Physics, Peking University, Beijing 100871, China
⁵Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
⁶Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁷Department of Materials Science and Engineering, School of New Energy and Materials, China University of Petroleum, Beijing 102249, China
⁸Beijing Academy of Quantum Information Sciences, Beijing 100193, China
⁹Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
¹⁰CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

^*Corresponding author: jfeng11@pku.edu.cn
^†Corresponding author: minghupan@hust.edu.cn
^‡Corresponding author: jianwangphysics@pku.edu.cn

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Vol. 102, Iss. 3 — 15 July 2020

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Images

Figure 1
Band structures of $TaT e_{4}$ with and without CDW. (a) Lower left panel and right panel show unit cell of non-CDW phase and CDW phase $TaT e_{4}$ , where green polyhedrons indicate $T a_{3}$ clusters. Upper left panel is the 3D bulk Brillouin zone of non-CDW/CDW phase $TaT e_{4}$ with high-symmetry points indicated. (b) Band structure along high-symmetry lines in the non-CDW Brillouin zone of $TaT e_{4}$ without CDW. Red dashed rectangles indicate DPs. (c) Band structure along high-symmetry lines in the CDW Brillouin zone of the CDW phase $TaT e_{4}$ . Red dashed rectangles indicate DP and DDP. (d) Magnified dispersion around DDP in (c) and 3D linear dispersion around DDP. $x$ , $y$ , and $z$ , respectively, correspond to the direction of $a$ , $b$ , and $c$ axes.
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Figure 2
Crystal structure, CDW, and ρ-T property of $TaT e_{4}$ . (a) HAADF STEM image of $TaT e_{4}$ $a c$ plane at room temperature with schematic structure. Scale bar represents 1 nm. (b) Sample resistivity as a function of temperature. Upper inset shows an optical image of one of our measured samples. Scale bar represents 200 μm. Lower inset is a schematic plot of magnetotransport measurement setup. (c) STM image of a cleaved $a c$ surface with CDW modulation ( $V_{b} = - 250 mV$ , $I_{t} = 250 pA$ , image size is $10 \times 10 n m^{2}$ ). Blue and black rectangles represent surface unit cell with and without CDW, respectively. (d) STS in a region with CDW modulation. Cyan curves are numerous $d I / d V$ spectra measured at different locations on the bare surface areas (away from the defects) and the black curve is the averaged spectrum. A CDW gap of around 45 meV is clearly identified around Fermi level. Set point: $V_{b} = 150 mV$ , $I_{t} = 200 pA$ , the bias modulation for the lock-in technique is 9 mV.
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Figure 3
Magnetoresistance and SdH oscillations in $TaT e_{4}$ . (a) and (b) MR and SdH oscillations in $TaT e_{4}$ measured at $θ = 0^{\circ}$ . (a) MR as a function of magnetic field applied along $a$ axis at various temperatures. (b) Oscillation components in (a) after subtracting a smooth background. Inset shows the FFT of oscillation at 2 K. (c) and (d) Results for $θ = 45^{\circ}$ .
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Figure 4
Angular-dependent SdH oscillation and CDW phase Fermi surface of $TaT e_{4}$ . (a) FFT of an oscillation component obtained by subtracting an eighth-order polynomial background at various θ. Dashed lines are guides to the eye. (b) Extracted high frequency peak positions in (a) as a function of θ. Colors of data indicate contributions from different but equivalent pockets. Violet points are numerical results from calculated FS in (g). (c) Extracted low frequency peak positions in (a) and frequencies extracted from Landau level fan diagrams as a function of θ. Violet points are numerical results from calculated FS in (d) and red lines are 2D-FS fitting to data. (d)–(g) The FS of bands 1–4 which crosses the Fermi level of the CDW phase $TaT e_{4}$ in the first Brillouin zone.
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Figure 5
States residing on step edges observed by STM. (a) STM image of an edge existing in a region with weak CDW modulation ( $V_{b} = - 70 mV$ , $I_{t} = 200 pA$ , image size is $40 \times 40 n m^{2}$ ). (b) STM image of an edge existing in a region with clear CDW modulation ( $V_{b} = 12 mV$ , $I_{t} = 200 pA$ , image size is $40 \times 40 n m^{2}$ ). (c) Tunneling spectra at different locations along the line in (a). Spectra near the edge are shown in red. (d) Tunneling spectra at different locations along the line in (b). Spectra near the edge are shown in thick curves. Red arrows mark the appearance of edge states. All spectra were taken with the set point: $V_{b} = 150 mV$ , $I_{t} = 200 pA$ . The magnitude of the bias modulation for the lock-in technique is 9 mV.
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