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  • Perspective
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Flat bands, strange metals and the Kondo effect

Nature Reviews Materials volume 9, pages 509–526 (2024)Cite this article

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Abstract

Flat-band materials such as the kagome metals or moiré superlattices are of intense current interest. Flat bands can result from the electron motion on numerous (special) lattices and usually exhibit topological properties. Their reduced bandwidth proportionally enhances the effect of Coulomb interaction, even when the absolute magnitude of the latter is relatively small. Seemingly unrelated to these materials is the large family of strongly correlated electron systems, which include the heavy-fermion compounds, and cuprate and pnictide superconductors. In addition to itinerant electrons from large, strongly overlapping orbitals, they frequently contain electrons from more localized orbitals, which are subject to a large Coulomb interaction. The question then arises as to what commonality in the physical properties and microscopic physics, if any, exists between these two broad categories of materials. A rapidly increasing body of strikingly similar phenomena across the different platforms — from electronic localization–delocalization transitions to strange-metal behaviour and unconventional superconductivity — suggests that similar underlying principles could be at play. Indeed, it has recently been suggested that flat-band physics can be understood in terms of Kondo physics. Inversely, the concept of electronic topology from lattice symmetry, which is fundamental in flat-band systems, is enriching the field of strongly correlated electron systems, in which correlation-driven topological phases are increasingly being investigated. In this Perspective article, we elucidate this connection, survey the new opportunities for cross-fertilization across platforms and assess the prospect for new insights that may be gained into correlation physics and its intersection with electronic topology.

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Fig. 1: Platforms for topology and correlation phenomena.
Fig. 2: Experimental measures of correlation strength across materials platforms.
Fig. 3: Strange-metal phenomena in the extreme correlation regime.
Fig. 4: Strange-metal phenomena in the extreme correlation regime: shot-noise suppression.
Fig. 5: Flavours of topology in correlated systems.
Fig. 6: Signatures of correlated topology in insulators, semimetals and superconductors.
Fig. 7: Heavy-fermion physics as a unifying view?

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Acknowledgements

The authors thank J. Analytis, D. Calugaru, J. Cano, L. Chen, R. Comin, L. Crippa, P. Dai, X. Dai, L. Deng, D. Efetov, S. Fang, S. Grefe, P. Guinea, T. Hazra, J. Hertzog Arbeitman, J. Hoffman, H. Hu, J. Huang, K. Ingersent, O. Jansen, P. Jarillo-Herrero, A. Kandala, S. Kirchner, D. Kirschbaum, L. Lau, G. Le Roy, X. Li, G. Lonzarich, M. Lužnik, V. Madhavan, M. Mahankali, D. Natelson, J. P. Paglione, A. Panigrahi, J. Pixley, G. Rai, N. Regnault, G. Sangiovanni, S. Sebastian, T. Senthil, C. Setty, Z. Song, F. Steglich, S. Sur, M. Taupin, A. Tsvelik, O. Vafek, R. Valenti, M. Vergniory, Y. Wang, T. Wehling, F. Xie, B. J. Yang, L. Ye, M. Yi, J. Yu, R. Yu and Z. Zhuang for collaborations and discussions, which were in part conducted at the Kavli Institute for Theoretical Physics at UC Santa Barbara, where support was provided by the US National Science Foundation (NSF) under Grant No. NSF PHY-1748958, and at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-2210452. J.G.C. was supported by the Gordon and Betty Moore Foundation EPiQS Initiative (Grant No. GBMF9070). The work of B.A.B. was primarily supported by the US Department of Energy (DOE) Grant No. DE-SC0016239 and the Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF11070). Q.S. is primarily supported by the US DOE, BES, under Award No. DE-SC0018197, by the Robert A. Welch Foundation Grant No. C-1411 and by the Vannevar Bush Faculty Fellowship ONR-VB N00014-23-1-2870. P.C. was supported by NSF grant DMR-1830707. S.P. acknowledges funding from the Austrian Science Fund (I5868-FOR 5249 QUAST, F86-SFB Q-M&S), the European Union’s Horizon 2020 Research and Innovation Programme (824109, EMP) and the European Research Council (ERC Advanced Grant 101055088, CorMeTop).

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Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Joseph G. Checkelsky

  2. Department of Physics, Princeton University, Princeton, NJ, USA

    B. Andrei Bernevig

  3. Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, San Sebastián, Spain

    B. Andrei Bernevig

  4. IKERBASQUE, Basque Foundation for Science, Bilbao, Spain

    B. Andrei Bernevig

  5. Center for Materials Theory, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, USA

    Piers Coleman

  6. Department of Physics, Royal Holloway University of London, Egham, UK

    Piers Coleman

  7. Department of Physics and Astronomy, Rice Center for Quantum Materials, Rice University, Houston, TX, USA

    Qimiao Si

  8. Institute of Solid State Physics, Vienna University of Technology, Vienna, Austria

    Silke Paschen

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Checkelsky, J.G., Bernevig, B.A., Coleman, P. et al. Flat bands, strange metals and the Kondo effect. Nat Rev Mater 9, 509–526 (2024). https://doi.org/10.1038/s41578-023-00644-z

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