Observation of Weyl Nodes in Robust Type-II Weyl Semimetal ${\mathrm{WP}}_{2}$

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Observation of Weyl Nodes in Robust Type-II Weyl Semimetal ${WP}_{2}$

M.-Y. Yao, N. Xu, Q. S. Wu, G. Autès, N. Kumar, V. N. Strocov, N. C. Plumb, M. Radovic, O. V. Yazyev, C. Felser, J. Mesot, and M. Shi

Phys. Rev. Lett. 122, 176402 – Published 3 May 2019

Abstract

Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from $(W, Mo) {Te}_{2}$ and $(W, Mo) P_{2}$ families of materials, a large number of experiments have been dedicated to unveiling the possible manifestation of type-II WSMs, e.g., surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved photoemission spectroscopy supported by the first-principles calculations, we probe the tilted Weyl cone bands in the bulk electronic structure of ${WP}_{2}$ directly, which are at the origin of Fermi arcs at the surfaces and transport properties related to the chiral anomaly in type-II WSMs. Our results ascertain that, due to the spin-orbit coupling, the Weyl nodes originate from the splitting of fourfold degenerate band-crossing points with Chern numbers $C = \pm 2$ induced by the crystal symmetries of ${WP}_{2}$ , which is unique among all the discovered WSMs. Our finding also provides a guiding line to observe the chiral anomaly that could manifest in novel transport properties.

Received 6 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.176402

Physics Subject Headings (PhySH)

Electronic structure

Topological materials Weyl semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M.-Y. Yao^1,*, N. Xu^1,2,3,†, Q. S. Wu^2,4, G. Autès^2,4, N. Kumar⁵, V. N. Strocov¹, N. C. Plumb¹, M. Radovic¹, O. V. Yazyev^2,4, C. Felser⁵, J. Mesot^1,2,6, and M. Shi^1,‡

¹Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland
²Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
³Institute of Advanced Studies, Wuhan University, Wuhan 430072, China
⁴National Centre for Computational Design and Discovery of Novel Materials MARVEL, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
⁵Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
⁶Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland

^*mengyu.yao@psi.ch
^†nxu@whu.edu.cn
^‡ming.shi@psi.ch

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Vol. 122, Iss. 17 — 3 May 2019

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Figure 1
(a) Crystal structure of ${WP}_{2}$ . (b) Bulk and surface BZ of ${WP}_{2}$ with high-symmetry points labeled. The green plane represents the $Γ − X − Y$ plane. The yellow plane represents the (0 1 $- 1$ ) cleavage plane. In the momentum coordinate, $k_{x} − k_{y}$ is set up within the (0 1 $- 1$ ) plane. $W 1$ ( $W 1 ’$ ) and $W 2$ ( $W 2 ’$ ) Weyl nodes are indicated by yellow and red open (closed) circles, respectively. The chirality of the Weyl nodes is indicated with $+$ and $-$ signs. The blue plane represents the 2D surface BZ. The orange and green lines schematically illustrate the possible Fermi arc dispersion connecting the Weyl nodes with opposite chirality. (c) Schematic band dispersions of type-II Weyl nodes in the $k_{x} − k_{y}$ plane of the momentum space. The region in momentum space is schematically indicated by red dashed lines in (b). (d) ${WP}_{2}$ core-level spectrum, obtained with $h ν = 650 eV$ .
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Figure 2
(a) FSs of bulk bands from first-principles calculations. (b) BZ of ${WP}_{2}$ with the high-symmetry points indicated. The yellow plane represents the (0 1 $- 1$ ) plane. (c),(d) Constant energy maps at $E_{F}$ measured experimentally with $h ν = 415 eV$ photons and obtained from first-principles calculations, respectively. (e) The ARPES intensity plots with calculated bands overlaid on top (red lines). The data were acquired with $h ν = 415 eV$ along cut 1. The calculated bands are rigidly shifted to match the ARPES data. (f) Same as (e) but along cut 2. (g) The FS map taken along $k_{z}$ , obtained with $h ν$ ranging from 340 to 390 eV.
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Figure 3
(a) Locations of the predicted Weyl nodes in 3D BZ. The yellow plane represents the plane in $k$ space that crosses the Weyl nodes. (b) Series constant energy maps obtained with $h ν = 360 eV$ . The responding region is indicated in the 360 eV spectrum of Fig. 2. (i)–(v) $E_{B} = E_{F}$ , $- 0.28$ , $- 0.34$ , $- 0.41$ , and $- 0.6 eV$ , respectively. The red and white dashed lines are a guide to the eye, showing the profiles of the electron and hole pockets, respectively. (c),(d) The ARPES spectra, obtained with $h ν = 360 eV$ , and the corresponding calculated band structures along the $k_{x}$ and $k_{y}$ directions across the $W 1$ Weyl nodes, as marked by the dashed lines in (a). (e),(f) The same ARPES spectra and calculated bands for the $W 2$ Weyl point. (g) (Upper) Four fourfold degenerate points ( $C = \pm 2$ ) located in the $Γ − X − Y$ plane in the ${WP}_{2}$ bulk BZ. (Lower) When SOC is taken into account, the fourfold degenerate points ( $C = \pm 2$ ) split into two twofold Weyl nodes with the same chirality ( $C = + 1$ or $- 1$ ). Yellow and red color in the upper panel represent the Weyl nodes located at different binding energies.
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Physical Review Letters

Observation of Weyl Nodes in Robust Type-II Weyl Semimetal WP2

M.-Y. Yao, N. Xu, Q. S. Wu, G. Autès, N. Kumar, V. N. Strocov, N. C. Plumb, M. Radovic, O. V. Yazyev, C. Felser, J. Mesot, and M. Shi

Phys. Rev. Lett. 122, 176402 – Published 3 May 2019

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Observation of Weyl Nodes in Robust Type-II Weyl Semimetal ${WP}_{2}$