Ideal type-II Weyl phonons in wurtzite CuI

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Ideal type-II Weyl phonons in wurtzite CuI

Jian Liu, Wenjie Hou, En Wang, Shengjie Zhang, Jia-Tao Sun, and Sheng Meng

Phys. Rev. B 100, 081204(R) – Published 22 August 2019

Abstract

Weyl materials exhibiting topologically nontrivial touching points in band dispersion pave the way to exotic transport phenomena and novel electronic devices. Here, we demonstrate the signature of an ideal type-II Weyl phase in phonon dispersion of solids through first-principles investigations. Type-II phononic Weyl phase is manifested in noncentrosymmetric wurtzite CuI by six pairs of Weyl points (WPs) in the $k_{z} = 0.0$ plane. On the iodine-terminated surface of the crystal, very clean surface arcs are readily detectable. Each pair of WPs connected by open surface arcs is well separated by a large distance of $0.26 Å^{- 1}$ . The opposite chirality of WPs with quantized Berry curvature produces Weyl phonon Hall effect, in analogy to valley Hall effect of electrons. Such ideal type-II Weyl phase is readily observable in experiment, providing a unique platform to study novel thermal transport properties distinct from type-I Weyl phase.

Received 23 March 2019

DOI:https://doi.org/10.1103/PhysRevB.100.081204

Physics Subject Headings (PhySH)

Optical phonons Phonons

Topological materials Weyl semimetal

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jian Liu ^1,2,*, Wenjie Hou^3,4,*, En Wang^1,2, Shengjie Zhang^1,2, Jia-Tao Sun^1,2,6,†, and Sheng Meng^1,2,5,‡

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
³Fert Beijing Institute, BDBC, School of Microelectronics, Beihang University, Beijing 100191, China
⁴Beihang-Goertek Joint Microelectronics Institute, Qingdao Research Institute, Beihang University, Qingdao 266104, China
⁵Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
⁶School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

^*These authors contributed equally to this work.
^†jtsun@iphy.ac.cn
^‡smeng@iphy.ac.cn

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Issue

Vol. 100, Iss. 8 — 15 August 2019

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Images

Figure 1
Schematics of type-II Weyl phase. (a) Two bands cross each other and form two adjacent Weyl points (WPs). (b) Two bands simply touch and form only one WP. (c) Schematics of the ideal type-II Weyl phase. It must meet the requirement in panel (b) that all WPs are related to each other by symmetry. The surface arc connects two WPs (red and blue spheres) with the opposite chirality. The obvious gap far from the Weyl cone minimizes the hybridization between the type-II WPs and the bulk bands.
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Figure 2
Type-II Weyl phase in wurtzite CuI. (a) The atomic structures of bulk CuI. Blue and yellow spheres denote the Cu and I atoms, respectively. (b) The bulk Brillouin zone (BZ) and the projected surface BZ for the (0001) surface. The six pairs of type-II Weyl points (WPs) are schematically shown by blue/red spheres denoting the chirality of the phonon WP. (c) Phonon dispersion of CuI along the high-symmetry momentum path. The phonon WP along the low-symmetry momentum path is shown in the right section of the phonon dispersion. (d) The enlarged crossing phonon dispersion around one phonon WP along the $θ = \frac{5 π}{6}$ direction relative to the $k_{x}$ axis (the direction along two adjacent bottom Cu atoms). (e) Perspective plot of the phonon WP in the $k_{z} = 0.0$ plane.
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Figure 3
Topology of Weyl points. (a) The momentum-dependent frequency gap between the sixth and seventh phonon bands. The chirality of the phonon Weyl point (WP) is denoted by green ( $C = + 1$ for $W P^{+}$ ) and magenta ( $C = - 1$ for $W P^{-}$ ) spheres, respectively. (b) The calculated Berry curvature around a pair of WPs enlarged from the black dashed rectangle in panel (a). The length of each arrow is the magnitude of the in-plane Berry curvature. (c) [(d)] The proposed Weyl phonon Hall effect excited by right-handed (left-handed) circularly polarized light under a temperature gradient. The blue arrows, black arrows, and black wavy lines denote the Hall current, temperature gradient, and light, respectively.
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Figure 4
Surface states and surface arcs. (a) The momentum-resolved surface local density of states for CuI projected onto the top (0001) surface (Cu-terminated surface). (b) The enlarged surface arc of panel (a) denoted by a black dashed rectangle. It is observed that the open surface arc $β$ connects two Weyl points (WPs) with the opposite charges. The length of the surface arc is near 0.26 $1 / Å$ . The green and magenta spheres represent the projected WPs with the chirality of +1 and −1, respectively. The low, medium, and high DOS are indicated by blue, white, and red, respectively. The states $α$ and $β$ are topological trivial and nontrivial, respectively. (c) Surface band structure along the black lines indicated in panel (b). Panels (d)–(f) are the same as panels (a)–(c), respectively, but for the bottom ( $000 \bar{1}$ ) surface (I-terminated surface).
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