Onsager, L. Interpretation of the de Haas–van Alphen effect. Philos. Mag. 43, 1006–1008 (1952).
Roth, L. M. Semiclassical theory of magnetic energy levels and magnetic susceptibility of Bloch electrons. Phys. Rev. 145, 434–448 (1966).
Mikitik, G. P. et al. Manifestation of Berry’s phase in metal physics. Phys. Rev. Lett. 82, 2147–2150 (1999).
Gao, Y. & Niu, Q. Zero-field magnetic response functions in Landau levels. Proc. Natl Acad. Sci. USA 114, 7295–7300 (2017).
Fuchs, J.-N. et al. Landau levels, response functions and magnetic oscillations from a generalized onsager relation. SciPost Phys. 4, 024 (2018).
Zhang, Y. et al. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2, 177–180 (2006).
Rhim, J.-W. & Yang, B.-J. Classification of flat bands according to the band-crossing singularities of Bloch wave functions. Phys. Rev. B 99, 045107 (2019).
Bužek, V. & Hillery, M. Quantum copying: beyond the no-cloning theorem. Phys. Rev. A 54, 1844–1852 (1996).
Dodonov, V. V. et al. Hilbert–Schmidt distance and non-classicality of states in quantum optics. J. Mod. Opt. 47, 633–654 (2000).
Berry, M. V. in Geometric Phases in Physics (eds Shapere, A. & Wilczek, F.) 7–28 (World Scientific, 1989).
Haldane, F. D. M. Dirac-point models: Hilbert space geometry and topology http://wwwphy.princeton.edu/~haldane/talks/nobel_jpeg.pdf (2010).
Neupert, T. et al. Measuring the quantum geometry of Bloch bands with current noise. Phys. Rev. B 87, 245103 (2013).
Peotta, S. et al. Superfluidity in topologically nontrivial flat bands. Nat. Commun. 6, 8944 (2015).
Piéchon, F. et al. Geometric orbital susceptibility: quantum metric without Berry curvature. Phys. Rev. B 94, 134423 (2016).
Gianfrate, A. et al. Measurement of the quantum geometric tensor and of the anomalous Hall drift. Nature 578, 381–385 (2020).
Ozawa T. & Goldman N. Extracting the quantum metric tensor through periodic driving. Phys. Rev. B 97, 201117 (2018).
Park, S. & Yang, B.-J. Classification of accidental band crossings and emergent semimetals in two dimensional noncentrosymmetric systems. Phys. Rev. B 96, 125127 (2017).
Yang, B.-J. & Nagaosa, N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5, 4898 (2014).
Xiao, Y. et al. Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum. Phys. Rev. B 67, 104505 (2003).
Yamada M. G. et al. First-principles design of a half-filled flat band of the kagome lattice in two-dimensional metal–organic frameworks. Phys. Rev. B 94, 081102 (2016).
Chen, Y. et al. Ferromagnetism and Wigner crystallization in kagome graphene and related structures. Phys. Rev. B 98, 035135 (2018).
You, J.-Y. et al. Flat band and hole-induced ferromagnetism in a novel carbon monolayer. Sci. Rep. 9, 20116 (2019).
Lee, J. M. et al. Stable flatbands, topology, and superconductivity of magic honeycomb networks. Phys. Rev. Lett. 124, 137002 (2020).
Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).
Lin, Z. et al. Flatbands and emergent ferromagnetic ordering in Fe3Sn2 kagome lattices. Phys. Rev. Lett. 121, 096401 (2018).
Kang, M. et al. Dirac fermions and flat bands in the ideal kagome metal FeSn. Nat. Mater. 19, 163–169 (2020).
Kang, M. et al. Topological flat bands in frustrated kagome lattice CoSn. Preprint at https://arxiv.org/abs/2002.01452 (2020).
Li, Z. et al. Realization of flat band with possible nontrivial topology in electronic kagome lattice. Sci. Adv. 4, eaau4511 (2018).
Yin, J.-X. et al. Negative flat band magnetism in a spin–orbit-coupled correlated kagome magnet. Nat. Phys. 15, 443–448 (2019).
Min, H. et al. Intrinsic and Rashba spin–orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006).
Ramachandran A. et al. Chiral flat bands: existence, engineering, and stability. Phys. Rev. B 96, 161104 (2017).
Ihn, T. Semiconductor Nanostructures: Quantum States and Electronic Transport (Oxford Univ. Press, 2010).
Terashima, T. T. et al. Magnetization process of the Kondo insulator YbB12 in ultrahigh magnetic fields. J. Phys. Soc. Jpn. 86, 054710 (2017).
Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).
Stoner, E. Atomic moments in ferromagnetic metals and alloys with nonferromagnetic elements. Phil. Mag. 15, 1018–1034 (1933).
Kopnin N. P. et al. High-temperature surface superconductivity in topological flat-band systems. Phys. Rev. B 83, 220503 (2011).
Hanaguri T. et al. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2Se3. Phys. Rev. B 82, 081305 (2010).
Sadowski, M. L. et al. Landau level spectroscopy of ultrathin graphite layers. Phys. Rev. Lett. 97, 266405 (2006).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).
Kresse, G. & Furthmüller, 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. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
Perdew, J. P. et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Dudarev, S. L. et al. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).
Po, H. C. et al. Faithful tight-binding models and fragile topology of magic-angle bilayer graphene. Phys. Rev. B 99, 195455 (2019).