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Fig. 102: Calculated (001) projection of the Fermi surface (blue: electron pockets; red: hole pockets) and the projection of nesting vectors between Weyl points (Wi) of opposite chirality (+,-). Vectors qi (i = 1, 6) are integer multiples of the CDW modulation unit vectors derived by XRD.

semimetals in particular carry integer-valued topological (chiral) charges, reflecting that the nodal points are sources and sinks of Berry curvature.

This work provides evidence for a link between non- interacting and correlated Weyl-semimetal states in (TaSe4)2I through X-ray diffraction (XRD) combined with first-principles calculations. It is demonstrated that quasi- 1D (TaSe4)2I crystals are in fact Weyl semimetals whose Weyl points (WPs) become coupled and gapped by the onset of a CDW. Thus, (TaSe4)2I is the first known material to host a correlation-driven Weyl semimetal insulator phase transition.

XRD experiments were carried out at beamline BM25 to investigate the CDW instability of (TaSe4)2I in order to establish a link between the CDW-modulated structure and the nesting vectors connecting the WPs. First- principles calculations reveal that the Fermi surface is derived from 48 Weyl points (FSWPs) and that all 48 WPs are located within a range of 15 meV of the Fermi energy.

Figure 101 shows a reciprocal space mapping in the vicinity of the main G=(420) (Figure 101a) and the G=(620) (Figure 101b) main reflections. Satellites next to the main reflections are indexed by the coordinates (m,n,o). From the in-plane (Figure 101a) and out-of- plane (Figure 101b) distances between the satellites and between the satellites and the main reflections, the CDW modulation vectors q=[m h(2p/a), n h(2p/a), o δ(2p/c)] were derived, where m+n+o ∈ 2 Z and h = 0.027 ± 0.001, δ = 0.012 ± 0.001. These CDW modulation vectors are linked to the nesting vectors connecting the WPs, which are shown in Figure 102. For instance, q1, q2 and q4 are given by the integer-valued multiples of the modulation

vectors (m,n,o)=(15,-17,6), (17,17,8) and (16,0,0), respectively.

It can be concluded that FSWP nesting is not the origin of the CDW, because the CDW modulation vectors are considerably shorter than the FSWP nesting vectors between WPs of opposite chiral charge. However, because the FSWP nesting vectors can be expressed as integer linear combinations of the CDW basis vectors, these findings nevertheless suggest that the CDW in (TaSe4)2I still backfolds and couples the FSWPs.

PRINCIPAL PUBLICATION AND AUTHORS

A charge-density-wave topological semimetal, W. Shi (a,b), B.J. Wieder (c), H.L. Meyerheim (d), Y. Sun (a), Y. Zhang (a,e), Y. Li (f), L. Shen (g), Y. Qi (b), L. Yang (g), J. Jena (d), P. Werner (d), K. Koepernik (e), S. Parkin (d), Y. Chen (b,f,g), C. Felser (a), B.A. Bernevig (c), Z. Wang (h,i), Nat. Phys. 17, 381-387 (2021); https:/doi.org/10.1038/s41567-020-01104-z (a) Max Planck Institute for Chemical Physics of Solids, Dresden (Germany) (b) School of Physical Science and Technology, ShanghaiTech University (China) (c) Department of Physics, Princeton University (USA) (d) Max Planck Institute of Microstructure Physics, Halle (Germany) (e) Leibniz Institute for Solid State and Materials Research, Dresden (Germany) (f) Department of Physics, University of Oxford (UK) (g) State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics and Collaborative Innovation Center of Quantum Matter, Tsinghua University, Beijing (China) (h) Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing (China) (i) University of Chinese Academy of Sciences, Beijing (China)

REFERENCES

[1] R. Cava et al., Phys. Rev. B 33, 2439-2443 (1986). [2] G. Chang et al., Nat. Mater. 17, 978-985 (2018). [3] J. Gooth et al., Nature 575, 315-319 (2019).