Observation of a van Hove singularity of a surface Fermi arc with prominent coupling to phonons in a Weyl semimetal

Zhenyu Wang, Cheng-Yi Huang, Chia-Hsiu Hsu, Hiromasa Namiki, Tay-Rong Chang, Feng-Chuan Chuang, Hsin Lin, Takao Sasagawa, Vidya Madhavan, and Yoshinori Okada

Phys. Rev. B 105, 075110 – Published 4 February 2022

Abstract

A van der Waals coupled Weyl semimetal ${NbIrTe}_{4}$ is investigated by combining scanning tunneling microscopy/spectroscopy and first-principles calculations. We observe a sharp peak in the tunneling conductance near the Fermi energy ( $E_{F}$ ). Comparison with calculations indicates that the peak originates from a van Hove singularity (vHs) associated with a Lifshitz transition of the surface Fermi-arc state. Interestingly, our tunneling spectroscopy also shows signatures of strong electron-boson coupling. This is potentially due to an anomalously enhanced charge susceptibility coming from the near- $E_{F}$ vHs formation.

Received 6 May 2021
Revised 11 September 2021
Accepted 7 January 2022

DOI:https://doi.org/10.1103/PhysRevB.105.075110

Physics Subject Headings (PhySH)

Edge states Phonons

Weyl semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhenyu Wang^1,2,*, Cheng-Yi Huang^3,*, Chia-Hsiu Hsu ^4,5,9,*, Hiromasa Namiki ⁶, Tay-Rong Chang^7,8,9, Feng-Chuan Chuang ^5,9, Hsin Lin ^3,9, Takao Sasagawa⁶, Vidya Madhavan^2,†, and Yoshinori Okada ^4,‡

¹Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
²Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
³Institute of Physics, Academia Sinica, Taipei, Taiwan
⁴Quantum Materials Science Unit, Okinawa Institute of Science and Technology (OIST), Okinawa 904-0495, Japan
⁵Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
⁶Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuda, Midori-ku, Yokohama, Kanagawa 226-8503, Japan
⁷Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
⁸Center for Quantum Frontiers of Research and Technology (QFort), Tainan 701, Taiwan
⁹Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan

^*These authors contributed equally to this work.
^†vm1@illinois.edu
^‡yoshinori.okada@oist.jp

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Vol. 105, Iss. 7 — 15 February 2022

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Images

Figure 1
Characteristics of the Weyl semimetal ${NbIrTe}_{4}$ . (a), (b) Schematic of the crystal structure of ${NbIrTe}_{4}$ with side and top views, respectively. (c) STM topographic image with atomic resolution ( $I_{t} = 100 pA$ and $V_{B} = 100 mV$ ). The scale of arrows corresponds to that in (b). (d), (e) Conductance (dI/dV) maps at $e V_{B} = 110$ and 10 meV, respectively. The insets show the raw FT of the dI/dV images, where Bragg peaks are highlighted by circles. (f), (g) The rotated and twofold symmetrized FT images of that in the inset of (d), (e). Here, the horizontal and vertical axes are set along the crystal axes $a$ and $b$ , respectively. (h) Intensity plot of the line cut in the FTs along the $q_{x}$ direction at $q_{y} = 0$ , together with scattering vectors $q_{1} \sim q_{3}$ in (f) and (g). (i) The spatially averaged dI/dV spectrum, which is taken simultaneously with QPI imaging. Theoretical three energies for WP, to be compared with experiment, are indicated by horizontal lines (see main body for details). The FT images in (d)–(g) and (h), (i) are from different measurement settings. (d)–(g) were set for aiming to get high-quality $q$ with better resolution and signal to noise ratio, whereas (h) and (i) were to collect overall dispersion for wider energy region. Note that data were taken from the same area.
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Figure 2
The DFT calculation for electronic state of NbIrTe4. (a) BZ of the system. (b) The calculated WPs with their momentum, energy, and chirality. (c), (d) Total spectral weight on the surface plotted at 134 meV, the energy of WP2, and at −50 meV near the energy of the vHS. The total surface spectral weight contains TSS and NSS contributions. The Weyl points WP1 (green), WP2 (red), and WP3 (blue) are indicated in the momentum space. (e) Zoomed-in image of the pink rectangle in (c), and (f) dispersion along the pink line in (d). The dashed lines in (e) and (f) indicate the trace along which the NSSs sink into the bulk state through Weyl points. (g) Energy dispersion along the $k_{x}$ direction at $k_{y} = π / b$ [see horizontal line in (c)] for total spectral weight and (h) its atomic character dependence. The dashed circle indicates the energy where NSS2 and NSS3 merge (see main body for details). Note that the band merging indicated by dashed circle (∼+100 meV) is different from van Hove singularity at $E_{v Hs}$ [see right axis of (h)].
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Figure 3
Electronic structure calculation near the energy for van Hove singularity $E_{vhs}$ . (a)–(e) Energy evolution of spectral weight for the area indicated by the dashed rectangle in Fig. 2. (f) Three-dimensional display of NSS dispersion (upper part) and $1 / | \nabla_{k} E |$ (lower part), near the critical momentum as in (c). (g) The energy dispersion along the horizontal arrow in (a). The vHs formations associated with a Lifshitz transition are indicated by an arrow and dashed circle in (c), (f), and (g). (h) Calculated DOS for NSS, which is obtained by integrating the spectral weight over all the momenta in the first BZ.
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Figure 4
The comparison between theory and experiments. (a), (b) The experimental energy evolution of QPI pattern and the theoretical JDOS of the total spectral weight along $q_{x}$ direction at $q_{y} = 0$ . Here, vertical axis in (b) is plotted energy relative to vHs. (c) Calculated spectral weight in kx-ky space at $E - E_{v Hs} = 10 meV$ . Here, the rectangle is the momentum area focused in Fig. 3 to represent vHs and associated Lifshitz transition. (d) Comparison between the experimental QPI (upper) and theoretical JDOS sorely from NSS (lower) at $e V_{B} = 10 meV$ and $E - E_{v hs} = 10 meV$ , respectively.
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Figure 5
Enhanced electron-mode coupling. (a) Topographic image ( $I_{t} = 100 pA$ and $V_{B} = 100 mV$ ). (b), (c) Spatial average of dI/dV and $d^{2} I / d V^{2}$ spectra. The spectra are averaged from 2116 curves (46 × 46 pixels) from the area shown in (a). (d) Topographic height variations along A-B in (a). (e), (f) Spatial evolution of dI/dV and $d^{2} I / d V^{2}$ spectra taken along A-B shown in (a).
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