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 (1/2ℏω), 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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Klitzing, K. v., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).
Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).
Yang, K., Haldane, F. D. M. & Rezayi, E. H. Wigner crystals in the lowest Landau level at low-filling factors. Phys. Rev. B 64, 081301 (2001).
Staromlynska, J., Finlayson, D. M. & Stradling, R. A. Shubnikov–de Haas measurements in indium antimonide. J. Phys. C 16, 6373–6386 (1983).
Zheng, G. et al. Transport evidence for the three-dimensional Dirac semimetal phase in ZrTe5 . Phys. Rev. B 93, 115414 (2016).
Physics in High Magnetic Fields (eds Chikazumiand, S. & Miura, N.) (Springer, 1981).
Behnia, K., Balicas, L. & Kopelevich, Y. Signatures of electron fractionalization in ultraquantum bismuth. Science 317, 1729–1731 (2007).
Li, L. et al. Phase transitions of Dirac electrons in bismuth. Science 321, 547–550 (2008).
Zhang, C.-L. et al. Ultraquantum magnetoresistance in single-crystalline β-Ag2Se. Preprint at http://arxiv.org/abs/1502.02324 (2015).
Iye, Y. et al. High-magnetic-field electronic phase transition in graphite observed by magnetoresistance anomaly. Phys. Rev. B 25, 5478–5485 (1982).
Fauqué, B. et al. Two phase transitions induced by a magnetic field in graphite. Phys. Rev. Lett. 110, 266601 (2013).
Grüner, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129–1181 (1988).
Fauqué, B., Vignolle, B., Proust, C., Issi, J.-P. & Behnia, K. Electronic instability in bismuth far beyond the quantum limit. New J. Phys. 11, 113012 (2009).
Zhu, Z. et al. Emptying Dirac valleys in bismuth by magnetic field. Preprint at http://arxiv.org/abs/1608.06199 (2016).
Weyl, H. Elektron und gravitation. I. Z. Phys. 56, 330–352 (1929).
Herring, C. Accidental degeneracy in the energy bands of crystals. Phys. Rev. 52, 365–373 (1937).
Murakami, S. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9, 356 (2007).
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).
Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).
Huang, S. M. et al. A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).
Weng, H. et al. Weyl semimetal phase in non-centrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11, 748–754 (2015).
Zhang, C.-L. et al. Electron scattering in tantalum monoarsenide. Phys. Rev. B 95, 085202 (2017).
Xu, S.-Y. et al. Experimental discovery of a topological Weyl semimetal state in TaP. Sci. Adv. 1, e1501092 (2015).
Zhang, C.-L. et al. Large magnetoresistance over an extended temperature regime in monophosphides of tantalum and niobium. Phys. Rev. B 92, 041203(R) (2015).
Abrikosov, A. A. Quantum magnetoresistance. Phys. Rev. B 58, 2788–2794 (1998).
Wang, C. M., Lu, H. Z. & Shen, S. Q. Anomalous phase shift of quantum oscillations in 3D topological semimetals. Phys. Rev. Lett. 117, 077201 (2016).
Lu, H. Z., Zhang, S. B. & Shen, S. Q. High-field magnetoconductivity of topological semimetals with short-range potential. Phys. Rev. B 92, 045203 (2015).
Cohen, M. H. & Falicov, L. M. Magnetic breakdown in crystals. Phys. Rev. Lett. 7, 231–233 (1961).
Sasaki, T., Sato, H. & Toyota, N. Magnetic breakdown effect in organic superconductor κ-(BEDT-TTF)2Cu(NCS)2 . Solid State Commun. 76, 507–510 (1990).
Chen, C.-Z. et al. Disorder and metal-insulator transitions in Weyl semimetals. Phys. Rev. Lett. 115, 246603 (2015).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Strocov, V. N. et al. Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, technical realisation and scientific applications. J. Synchrotron Radiat. 21, 32–44 (2014).
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
Authors and Affiliations
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.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 2065 kb)
Rights and permissions
About this article
Cite this article
Zhang, CL., Xu, SY., Wang, C. et al. Magnetic-tunnelling-induced Weyl node annihilation in TaP. Nature Phys 13, 979–986 (2017). https://doi.org/10.1038/nphys4183
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys4183
This article is cited by
-
Light control with Weyl semimetals
eLight (2023)
-
Field-induced Lifshitz transition in the magnetic Weyl semimetal candidate PrAlSi
npj Quantum Materials (2023)
-
Quantum-limit phenomena and band structure in the magnetic topological semimetal EuZn2As2
Communications Physics (2023)
-
Quantum transport in topological semimetals under magnetic fields (III)
Frontiers of Physics (2023)
-
Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe5
Nature Communications (2022)