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Weyl, Dirac and high-fold chiral fermions in topological quantum matter

Abstract

Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in the context of particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin–orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk–boundary correspondence, giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss several exotic optical and magnetic responses observed in these materials, as well as progress in developing related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities.

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Fig. 1: Topology and classification of Weyl fermions.
Fig. 2: Weyl semimetal states in the noncentrosymmetric TaAs family of crystals.
Fig. 3: Chern numbers and Fermi arc surface states.
Fig. 4: Type-II Weyl semimetals: LaAlGe and MoxW1−xTe2.
Fig. 5: Topological chiral crystals in the RhSi family.
Fig. 6: Topological nodal lines in PbTaSe2 and ZrSiS.
Fig. 7: Magnetic Weyl lines and drumhead surface states in Co2MnGa.
Fig. 8: Magnetic tunability of topological kagome magnets.

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Acknowledgements

We acknowledge P. W. Anderson, D. A. Huse, F. D. M. Haldane, N. P. Ong and E. Lieb for discussions on quantum magnets, topological matter, spin liquids and superconductivity. We further acknowledge insightful discussions with Alexei V. Federov, Arun Bansil, BaoKai Wang, Benjamin J Wieder, Biao Lian, Chang Liu, Chenglong Zhang, Chi-Cheng Lee, Ching-Kai Chiu, Claudia Felser, Daniel Multer, Daniel S. Sanchez, David Hsieh, Dong Qian, Donghui Lu, Fangcheng Chou, Hao Zheng, Hechang Lei, Horng-Tay Jeng, Hsin Lin, Huibin Zhou, Jie Ma, Jonathan Denlinger, Kaustuv Manna, L. Andrew Wray, Madhab Neupane, Makoto Hashimoto, Maksim Litskevich, Md Shafayat Hossain, Nana Shumiya, Nasser Alidoust, Niels B. M. Schröter, Pavel P. Shibayev, Qi Zhang, Raman Sankar, Shik Shin, Shin-Ming Huang, Shuang Jia, Songtian S. Zhang, Stepan S Tsirkin, Sung-Kwan Mo, Takeshi Kondo, Tay-Rong Chang, Titus Neupert, Tyler A. Cochran, Weiwei Xie, Vicky Süß, Vladimir N. Strocov, Xian P Yang, Yukiaki Ishida, Yuqi Xia, Yuxiao Jiang, Zahid Hussain, Zheng Liu, Zhujun Yuan, Zi-Jia Cheng and Zurab Guguchia. We acknowledge experimental collaboration with Vladimir N. Strocov, Niels B. M. Schröter and Alla Chikina (ADRESS endstation, Swiss Light Source, Paul Scherrer Institut, Proposal #20180896) in acquiring data presented in Fig. 5c, the details of which will be published in a forthcoming article. Spectroscopy work led by Princeton University was supported by the United States Department of Energy (U.S. DOE) under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200; M.Z.H.). The theoretical work and sample characterization are supported by the Gordon and Betty Moore Foundation (GBMF4547 and GBMF9461; M.Z.H.). The sample characterization related to topological magnetism and superconductivity is partly based on support by the U.S. DOE, Office of Science through the Quantum Science Center (QSC), a National Quantum Information Science Research Center at the Oak Ridge National Laboratory. G.C. would like to acknowledge the support of the National Research Foundation, Singapore under its NRF Fellowship Award (NRF-NRFF13-2021-0010) and the Nanyang Assistant Professorship grant from Nanyang Technological University. S.Y.X. was supported by the Center for the Advancement of Topological Semimetals, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE) Office of Science, through the Ames Laboratory under contract DE-AC0207CH11358. S.Y.X. acknowledges the Corning Fund for Faculty Development. G.B. was supported by the US National Science Foundation under Grant No. NSF DMR-1809160.

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Hasan, M.Z., Chang, G., Belopolski, I. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nat Rev Mater 6, 784–803 (2021). https://doi.org/10.1038/s41578-021-00301-3

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