Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Type-II Weyl semimetals


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.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Possible types of Weyl semimetals.
Figure 2: Band structure of WTe2.
Figure 3: Fermi surface at kz = 0.
Figure 4: Topological surface states.


  1. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)

    ADS  Article  Google Scholar 

  2. Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2009)

  3. Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015)

    Google Scholar 

  4. Huang, S.-M. et al. An inversion breaking Weyl semimetal state in the TaAs material class. Nature Commun. 6, 7373 (2015)

    CAS  ADS  Article  Google Scholar 

  5. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015)

    CAS  ADS  Article  Google Scholar 

  6. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015)

    Google Scholar 

  7. Weyl, H. Elektron und Gravitation. I. Z. Phys. 56, 330–352 (1929)

    Google Scholar 

  8. Silaev, M. A. & Volovik, G. E. Topological Fermi arcs in superfluid 3He. Phys. Rev. B 86, 214511 (2012)

    ADS  Article  Google Scholar 

  9. Nielsen, H. B. & Ninomiya, M. The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130, 389–396 (1983)

    ADS  MathSciNet  Article  Google Scholar 

  10. Zyuzin, A. A. & Burkov, A. A. Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B 86, 115133 (2012)

    ADS  Article  Google Scholar 

  11. Hosur, P. & Qi, X. Recent developments in transport phenomena in Weyl semimetals. C. R. Phys. 14, 857–870 (2013)

    CAS  ADS  Article  Google Scholar 

  12. Volovik, G. E. Kopnin force and chiral anomaly. JETP Lett. 98, 753–757 (2014)

    CAS  ADS  Article  Google Scholar 

  13. Zhang, C. et al. Observation of the Adler–Bell–Jackiw chiral anomaly in a Weyl semimetal. Preprint at (2015)

  14. Xiong, J. et al. Signature of the chiral anomaly in a Dirac semimetal: a current plume steered by a magnetic field. Preprint at (2015)

  15. Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015)

    Google Scholar 

  16. Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4 . Phys. Rev. Lett. 107, 186806 (2011)

    ADS  Article  Google Scholar 

  17. Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011)

    CAS  ADS  Article  Google Scholar 

  18. Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2 . Nature 514, 205–208 (2014)

    CAS  ADS  Article  Google Scholar 

  19. Nielsen, H. B. & Ninomiya, M. Absence of neutrinos on a lattice: (I). Proof by homotopy theory. Nucl. Phys. B 185, 20–40 (1981)

    ADS  MathSciNet  Article  Google Scholar 

  20. Soluyanov, A. A. & Vanderbilt, D. Computing topological invariants without inversion symmetry. Phys. Rev. B 83, 235401 (2011)

    ADS  Article  Google Scholar 

  21. Yu, R., Qi, X. L., Bernevig, A., Fang, Z. & Dai, X. Equivalent expression of topological invariant for band insulators using the non-Abelian Berry connection. Phys. Rev. B 84, 075119 (2011)

    Google Scholar 

  22. Pletikosić, I., Ali, M. N., Fedorov, A. V., Cava, R. J. & Valla, T. Electronic structure basis for the extraordinary magnetoresistance in WTe2 . Phys. Rev. Lett. 113, 216601 (2014)

    ADS  Article  Google Scholar 

  23. Brown, B. E. The crystal structures of WTe2 and high-temperature MoTe2 . Acta Crystallogr. 20, 268–274 (1966)

    CAS  Article  Google Scholar 

Download references


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 and Affiliations



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)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Soluyanov, A., Gresch, D., Wang, Z. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing