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 (1/2ℏω), 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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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.
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Physical Review B (2019)