Anirban, A. 15 years of topological insulators. Nat. Rev. Phys. 5, 267 (2023).
Google Scholar
Tokura, Y. Quantum materials at the crossroads of strong correlation and topology. Nat. Mater. 1, 971–973 (2022).
Google Scholar
Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys. 1, 126–143 (2019).
Google Scholar
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Google Scholar
Hasan, M. Z. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nat. Rev. Mater. 6, 784–803 (2021).
Google Scholar
Bernevig, B. A., Felser, C. & Beidenkopf, H. Progress and prospects in magnetic topological materials. Nature 603, 41–51 (2022).
Google Scholar
Ohno, H. Making nonmagnetic semiconductors ferromagnetic. Science 281, 951–956 (1998).
Google Scholar
Santos-Cottin, D. et al. EuCd2As2: a magnetic semiconductor. Phys. Rev. Lett. 131, 186704 (2023).
Google Scholar
Guo, C. et al. Temperature dependence of quantum oscillations from non-parabolic dispersions. Nat. Commun. 12, 6213 (2021).
Google Scholar
Belopolski, I. et al. Observation of a linked-loop quantum state in a topological magnet. Nature 604, 647–652 (2022).
Google Scholar
Collins, J. L. et al. Electric-field-tuned topological phase transition in ultrathin Na3Bi. Nature 564, 390–394 (2018).
Google Scholar
Osterhoudt, G. B. et al. Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater. 18, 471–475 (2019).
Google Scholar
Tsai, H. et al. Electrical manipulation of a topological antiferromagnetic state. Nature 580, 608–613 (2020).
Google Scholar
Cheng, B. et al. Efficient terahertz harmonic generation with coherent acceleration of electrons in the Dirac semimetal Cd3As2. Phys. Rev. Lett. 124, 117402 (2020).
Google Scholar
Kovalev, S. et al. Non-perturbative terahertz high-harmonic generation in the three-dimensional Dirac semimetal Cd3As2. Nat. Commun. 11, 2451 (2020).
Google Scholar
Baireuther, P., Tworzydło, J., Breitkreiz, M., Adagideli, I. & Beenakker, C. W. J. Weyl-Majorana solenoid. New J. Phys. 19, 025006 (2017).
Google Scholar
Sakai, A. et al. Iron-based binary ferromagnets for transverse thermoelectric conversion. Nature 581, 53–57 (2020).
Google Scholar
Mizuguchi, M. & Nakatsuji, S. Energy-harvesting materials based on the anomalous Nernst effect. Sci. Technol. Adv. Mater. 20, 262–275 (2019).
Google Scholar
Rajamathi, C. R. et al. Weyl semimetals as hydrogen evolution catalysts. Adv. Mater. 29, 1606202 (2017).
Google Scholar
Kotov, V. N., Uchoa, B., Pereira, V. M., Guinea, F. & Neto, A. H. C. Electron-electron interactions in graphene: current status and perspectives. Rev. Mod. Phys. 84, 1067–1125 (2012).
Google Scholar
Elias, D. C. et al. Dirac cones reshaped by interaction effects in suspended graphene. Nat. Phys. 7, 701–704 (2011).
Google Scholar
Witczak-Krempa, W., Knap, M. & Abanin, D. Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown. Phys. Rev. Lett. 113, 136402 (2014).
Google Scholar
Carlström, J. & Bergholtz, E. J. Strongly interacting Weyl semimetals: stability of the semimetallic phase and emergence of almost free fermions. Phys. Rev. B 98, 241102 (2018).
Google Scholar
Isobe, H. & Nagaosa, N. Coulomb interaction effect in Weyl fermions with tilted energy dispersion in two dimensions. Phys. Rev. Lett. 116, 116803 (2016).
Google Scholar
Bulmash, D., Liu, C.-X. & Qi, X.-L. Prediction of a Weyl semimetal in Hg1−x−yCdxMnyTe. Phys. Rev. B 89, 081106 (2014).
Google Scholar
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).
Google Scholar
Hasan, M. Z., Xu, S.-Y., Belopolski, I. & Huang, S.-M. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8, 289–309 (2017).
Google Scholar
Burkov, A. A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).
Google Scholar
Belopolski, I. et al. A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases. Sci. Adv. 3, e1501692 (2017).
Google Scholar
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).
Google Scholar
Nagaosa, N., Morimoto, T. & Tokura, Y. Transport, magnetic and optical properties of Weyl materials. Nat. Rev. Mater. 5, 621–636 (2020).
Google Scholar
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).
Okazaki, Y. et al. Quantum anomalous Hall effect with a permanent magnet defines a quantum resistance standard. Nat. Phys. 18, 25–29 (2022).
Google Scholar
Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).
Google Scholar
Liu, C.-X. et al. Model Hamiltonian for topological insulators. Phys. Rev. B 82, 045122 (2010).
Google Scholar
Burkov, A. A. Anomalous Hall effect in Weyl metals. Phys. Rev. Lett. 113, 187202 (2014).
Google Scholar
Mogi, M. et al. Experimental signature of the parity anomaly in a semi-magnetic topological insulator. Nat. Phys. 18, 390–394 (2022).
Google Scholar
Ong, N. P. & Liang, S. Experimental signatures of the chiral anomaly in Dirac–Weyl semimetals. Nat. Rev. Phys. 3, 394–404 (2021).
Google Scholar
Kandala, A., Richardella, A., Kempinger, S., Liu, C.-X. & Samarth, N. Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator. Nat. Commun. 6, 7434 (2015).
Google Scholar
Liang, S. et al. Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3Bi and GdPtBi. Phys. Rev. X 8, 031002 (2018).
Google Scholar
Onoda, S., Sugimoto, N. & Nagaosa, N. Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets. Phys. Rev. B 77, 165103 (2008).
Google Scholar
Yang, S.-Y. et al. Giant, unconventional anomalous Hall effect in the metallic frustrated magnet candidate, KV3Sb5. Sci. Adv. 6, eabb6003 (2020).
Google Scholar
Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).
Google Scholar
Zhao, Y.-F. et al. Tuning the Chern number in quantum anomalous Hall insulators. Nature 588, 419–423 (2020).
Google Scholar
Lei, C., Chen, S. & MacDonald, A. H. Magnetized topological insulator multilayers. Proc. Natl Acad. Sci. 117, 27224–27230 (2020).
Google Scholar
Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).
Google Scholar
Kresse, G. & Fürthmueller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).
Google Scholar
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
Google Scholar
Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).
Google Scholar
Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982).
Google Scholar
Prodan, E., Hughes, T. L. & Bernevig, B. A. Entanglement spectrum of a disordered topological Chern insulator. Phys. Rev. Lett. 105, 115501 (2010).
Google Scholar
Lee, I. et al. Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi0.1Sb0.9)2−xTe3. Proc. Natl Acad. Sci. 112, 1316–1321 (2015).
Google Scholar
Belopolski, I. et al. Source data for ‘Synthesis of a semimetallic Weyl ferromagnet with point Fermi surface’. Zenodo https://doi.org/10.5281/zenodo.13969155 (2025).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
Google Scholar
