Abstract

Weyl nodes are topological objects in three-dimensional metals. Whereas the energy of the lowest Landau band of a conventional Fermi pocket increases with magnetic field due to the zero-point energy (1/2ω), the lowest Landau band of Weyl cones stays at zero energy unless a strong magnetic field couples Weyl fermions of opposite chirality. In the Weyl semimetal TaP, which possesses two types of Weyl nodes (four pairs of W1 and eight pairs of W2 nodes), we observed such a magnetic coupling between the electron pockets arising from the W1 Weyl fermions. As a result, their lowest Landau bands move above the chemical potential, leading to a sharp sign reversal in the Hall resistivity at a specific magnetic field corresponding to the separation in momentum space of the W1 Weyl nodes, . By contrast, annihilation is not observed for the hole pocket because the separation of the W2 Weyl nodes is much larger. These findings reveal the nontrivial topology of Weyl fermions in high-field transport measurements and demonstrate the observation of Weyl node annihilation, which is a unique topological phenomenon associated with Weyl fermions.

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Acknowledgements

We thank R. R. Du, F. Wang, Q. Ma and H. Yao for valuable discussions on the physics and comments on our draft. J.W. acknowledges technical support from Y. Kohama at ISSP, the University of Tokyo. C.-L.Z. thanks Q. Guo for his assistance in high-field measurements. S.J. is supported by National Basic Research Program of China (Grant Nos. 2014CB239302 and 2013CB921901) and by the Opening Project of Wuhan National High Magnetic Field Center (Grant No.PHMFF2015395), Huazhong University of Science and Technology. H.L. acknowledges the Singapore National Research Foundation for support under NRF Award No. NRF-NRFF2013-03. S.-M.H. is supported by the Ministry of Science and Technology in Taiwan under Grant No. MOST105-2112-M-110-014-MY3. C.M.W. is supported by National Natural Science Foundation of China under Grant No. 11474005. H.-Z.L. is supported by Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2016ZT06D348), the National Key R&D Program (Grant No. 2016YFA0301700), and National Natural Science Foundation of China (Grant No. 11574127). The work at Princeton is supported by the National Science Foundation, Division of Materials Research, under Grants No. NSF-DMR-1507585 and No. NSF-DMR-1006492 and by the Gordon and Betty Moore Foundation through Grant GBMF4547 (Hasan). The National Magnet Laboratory is supported by the National Science Foundation Cooperative Agreement no. DMR-1157490, the State of Florida, and the US Department of Energy. Work at Los Alamos National Laboratory is performed under the auspices of the DOE and was supported by the DOE/Office of Science Project Complex Electronic Materials.

Author information

Affiliations

  1. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China

    • Cheng-Long Zhang
    • , Cheng Guo
    • , Hong Lu
    • , Yiyang Feng
    • , Haiwen Liu
    • , Chi Zhang
    • , Xin-Cheng Xie
    •  & Shuang Jia
  2. Laboratory for Topological Quantum Matter and Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    • Su-Yang Xu
    •  & M. Zahid Hasan
  3. Institute for Quantum Science and Engineering and Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China

    • C. M. Wang
    • , Z. Z. Du
    •  & Hai-Zhou Lu
  4. School of Physics and Electrical Engineering, Anyang Normal University, Anyang 455000, China

    • C. M. Wang
  5. Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China

    • Ziquan Lin
    • , Liang Li
    •  & Junfeng Wang
  6. School of Physics, Southeast University, Nanjing 211189, China

    • Z. Z. Du
  7. Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore

    • Chi-Cheng Lee
    • , Shin-Ming Huang
    • , Guoqing Chang
    • , Chuang-Han Hsu
    •  & Hsin Lin
  8. Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore

    • Chi-Cheng Lee
    • , Shin-Ming Huang
    • , Guoqing Chang
    • , Chuang-Han Hsu
    •  & Hsin Lin
  9. Department of Physics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

    • Shin-Ming Huang
  10. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

    • Chi Zhang
    • , Xin-Cheng Xie
    •  & Shuang Jia
  11. Anhui Province Key Laboratory of Condensed Matter Physics at Extreme Conditions, High Magnetic Field Laboratory of the Chinese Academy of Sciences, Hefei 230031, Anhui, China

    • Jinglei Zhang
  12. Department of Physics, University of Zurich, Winterthurerstrass 190, CH-8052 Zurich, Switzerland

    • Titus Neupert

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Contributions

C.-L.Z. and S.J. designed the experiment. C.-L.Z. performed all electrical transport experiments with help from Z.L., C.G., H.Lu, Y.F., L.L., C.Z., J.Z., J.W. and S.J.; S.-Y.X. conducted ARPES experiments with assistance from M.Z.H.; C.-L.Z., C.G., H.Lu and Y.F. grew the single-crystal samples; C.-C.L., G.C., S.-M.H., C.-H.H. and H.Lin performed first-principles band structure calculations; C.M.W., Z.Z.D. and H.-Z.L. did all theoretical simulations and part of theoretical analyses; Z.Z.D. and H.-Z.L. proposed the two-band model for trivial and Weyl semimetals. H.Liu and X.-C.X. contributed the Landau band indexation. S.-M.H. also performed Landau level simulations. T.N. performed the major part of theoretical analyses and gave the k p model. S.-Y.X., C.-L.Z., C.M.W., H.-Z.L., T.N. and S.J. wrote the paper. S.-Y.X. and S.J. were responsible for the overall direction, planning and integration among different research units.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Hai-Zhou Lu or Junfeng Wang or Shuang Jia.

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https://doi.org/10.1038/nphys4183

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