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# Type-II Weyl semimetals

## Abstract

Fermions—elementary particles such as electrons—are classified as Dirac, Majorana or Weyl. Majorana and Weyl fermions had not been observed experimentally until the recent discovery of condensed matter systems such as topological superconductors and semimetals, in which they arise as low-energy excitations1,2,3,4,5,6. Here we propose the existence of a previously overlooked type of Weyl fermion that emerges at the boundary between electron and hole pockets in a new phase of matter. This particle was missed by Weyl7 because it breaks the stringent Lorentz symmetry in high-energy physics. Lorentz invariance, however, is not present in condensed matter physics, and by generalizing the Dirac equation, we find the new type of Weyl fermion. In particular, whereas Weyl semimetals—materials hosting Weyl fermions—were previously thought to have standard Weyl points with a point-like Fermi surface (which we refer to as type-I), we discover a type-II Weyl point, which is still a protected crossing, but appears at the contact of electron and hole pockets in type-II Weyl semimetals. We predict that WTe2 is an example of a topological semimetal hosting the new particle as a low-energy excitation around such a type-II Weyl point. The existence of type-II Weyl points in WTe2 means that many of its physical properties are very different to those of standard Weyl semimetals with point-like Fermi surfaces.

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## Acknowledgements

A.A.S., D.G., QS.W. and M.T. acknowledge the support of Microsoft Research, the Swiss National Science Foundation through the National Competence Center in Research MARVEL and the European Research Council through ERC Advanced Grant SIMCOFE. Z.W. and B.A.B. acknowledge the support of ARO MURI W911NF-12-1-0461, ONR-N00014-11-1-0635, NSF CAREER DMR-0952428, NSF MRSEC DMR-0819860, the Packard Foundation and a Keck grant. X.D. is supported by the National Natural Science Foundation of China, the 973 program of China (no. 2011CBA00108 and no. 2013CB921700) and the “Strategic Priority Research Program (B)” of the Chinese Academy of Sciences (no. XDB07020100).

## Author information

Authors

### Contributions

All authors contributed to performing the calculations and the analysis of the results.

### Corresponding author

Correspondence to Alexey A. Soluyanov.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-13, Supplementary Tables 1-4 and Supplementary References. (PDF 2074 kb)

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Soluyanov, A., Gresch, D., Wang, Z. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015). https://doi.org/10.1038/nature15768

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• DOI: https://doi.org/10.1038/nature15768

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