Buchanan, M. The unifying role of topology. Nat. Phys. 16, 818 (2020).
Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics Ch. 9 (Cambridge Univ. Press, 1995).
Haldane, F. D. M. Nobel lecture: Topological quantum matter. Rev. Mod. Phys. 89, 040502 (2017).
Wen, X.-G. Colloquium: Zoo of quantum-topological phases of matter. Rev. Mod. Phys. 89, 041004 (2017).
Volovik, G. E. The Universe in a Helium Droplet (Oxford Univ. Press, 2003).
Zang, J., Cros, V. & Hoffmann, A. Topology in Magnetism (Springer, 2018).
Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).
Avron, J. E., Osadchy, D. & Seiler, R. A topological look at the quantum Hall effect. Phys. Today 56, 38–42 (2003).
Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Bernevig, A. Topological Insulators and Topological Superconductors (Princeton Univ. Press, 2013).
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).
Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P. & Ryu, S. Classification of topological quantum matter with symmetries. Rev. Mod. Phys. 88, 035005 (2016).
Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278–1281 (2019).
Chang, G. et al. Topological Hopf and chain link semimetal states and their application to Co2MnGa. Phys. Rev. Lett. 119, 156401 (2017).
Wu, Q., Soluyanov, A. A. & Bzdušek, T. Non-Abelian band topology in noninteracting metals. Science 365, 1273–1277 (2019).
Yan, Z. et al. Nodal-link semimetals. Phys. Rev. B 96, 041103(R) (2017).
Ezawa, M. Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon’s knot, trefoil knot, and other linked nodal varieties. Phys. Rev. B 96, 041202 (2017).
Chang, P.-Y. & Yee, C.-H. Weyl-link semimetals. Phys. Rev. B 96, 081114 (2017).
Zhong, C. et al. Three-dimensional pentagon carbon with a genesis of emergent fermions. Nat. Commun. 8, 15641 (2017).
Bian, G. et al. Topological nodal-line fermions in spin-orbit metal PbTaSe2. Nat. Commun. 7, 10556 (2016).
Watanabe, H., Po, H. C. & Vishwanath, A. Structure and topology of band structures in the 1651 magnetic space groups. Sci. Adv. 4, eaat8685 (2018).
Wang, Y. & Nandkishore, R. Topological surface superconductivity in doped Weyl loop materials. Phys. Rev. B 95, 060506 (2017).
Stenull, O., Kane, C. L. & Lubensky, T. C. Topological phonons and Weyl lines in three dimensions. Phys. Rev. Lett. 117, 068001 (2016).
Nandkishore, R. Weyl and Dirac loop superconductors. Phys. Rev. B 93, 020506(R) (2016).
Sun, X.-Q., Lian, B. & Zhang, S.-C. Double helix nodal line superconductor. Phys. Rev. Lett. 119, 147001 (2017).
Lian, B., Vafa, C., Vafa, F. & Zhang, S.-C. Chern-Simons theory and Wilson loops in the Brillouin zone. Phys. Rev. B 95, 094512 (2017).
Seifert, H. Über das Geschlecht von Knoten. Math. Ann. 110, 571–592 (1935).
Bergholtz, E. J., Budich, J. C. & Kunt, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).
Li, L., Lee, C. H. & Gong, J. Emergence and full 3D-imaging of nodal boundary Seifert surfaces in 4D topological matter. Commun. Phys. 2, 135 (2019).
Carlström, J., Stålhammar, M., Budich, J. C. & Bergholtz, E. J. Knotted non-Hermitian metals. Phys. Rev. B 99, 161115 (2019).
Zhang, X. et al. Tidal surface states as fingerprints of non-Hermitian nodal knot metals. Commun. Phys. 4, 47 (2021).
Sakai, A. et al. Iron-based binary ferromagnets for transverse thermoelectric conversion. Nature 581, 53–57 (2020).
Sakai, A. et al. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14, 1119–1124 (2018).
Guin, S. N. et al. Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co2MnGa. NPG Asia Mater. 11, 16 (2019).
Park, G.-H. et al. Thickness dependence of the anomalous Nernst effect and the Mott relation of Weyl semimetal Co2MnGa thin films. Phys. Rev. B 101, 060406 (2020).
Markou, A. et al. Hard magnet topological semimetals in xPt3 compounds with the harmony of Berry curvature. Commun. Phys. 4, 104 (2021).
Strocov, V. N. et al. High-resolution soft X-ray beamline ADRESS at the Swiss Light Source for resonant inelastic X-ray scattering and angle-resolved photoelectron spectroscopies. J. Synchrotron Radiat. 17, 631–643 (2010).
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).
Wu, L. et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator. Science 354, 1124–1127 (2016).
Zahid Hasan, M. et al. Weyl, Dirac and high-fold chiral fermions in topological quantum matter. Nat. Rev. Mater. 6, 784–803 (2021).
Yin, J.-X., Pan, S. H. & Zahid Hasan, M. Probing topological quantum matter with scanning tunnelling microscopy. Nat. Rev. Phys. 3, 249–263 (2021).
Webster, P. J. Magnetic and chemical order in Heusler alloys containing cobalt and manganese. J. Phys. Chem. Solids 32, 1221–1231 (1971).
Ido, H. & Yasuda, S. Magnetic properties of Co-Heusler and related mixed alloys. J. Phys. 49, C8-141–C8-142 (1988).
Strocov, V. N. et al. Three-dimensional electron realm in VSe2 by soft-X-ray photoelectron spectroscopy: origin of charge-density waves. Phys. Rev. Lett. 109, 086401 (2012).
Kresse, G. & Furthmueller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Belopolski, I. et al. Signatures of Weyl fermion annihilation in a correlated kagome magnet. Phys. Rev. Lett. 127, 256403 (2021).
Salomaa, M. M. & Volovik, G. E. Quantized vortices in superfluid 3He. Rev. Mod. Phys. 59, 533–613 (1987).
Nakahara, M. Geometry, Topology and Physics (Institute of Physics, 2003).
Bansil, A., Lin, H. & Das, T. Colloquium: Topological band theory. Rev. Mod. Phys. 88, 021004 (2016).
Kane, C. L. in Topological Insulators Ch. 1 (Elsevier, 2013).
Tokura, Y., Yasuda, K. & Tsukazaki, A. Magnetic topological insulators. Nat. Rev. Phys. 1, 126–143 (2019).
Hasan, M. Z., Xu, S.-Y. & Bian, G. Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks. Phys. Scr. 2015, T164 (2015).
Yin, J.-X. et al. Quantum-limit Chern topological magnetism in TbMn6Sn6. Nature 583, 533–536 (2020).
Chen, W., Lu, H.-Z. & Hou, J.-M. Topological semimetals with a double-helix nodal link. Phys. Rev. B 96, 041102 (2017).
Muro, T. et al. Soft X-ray ARPES for three-dimensional crystals in the micrometre region. J. Synchr. Radiat. 28, 1631–1638 (2021).
Strocov, V. N. et al. Soft-X-ray ARPES at the Swiss Light Source: from 3D materials to buried interfaces and impurities. Synchrotron Radiat. News 27, 31–40 (2014).