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# Topological kagome magnets and superconductors

## Abstract

A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin and correlation. Here we review these key developments in this field, starting from the fundamental concepts of a kagome lattice, to the realizations of Chern and Weyl topological magnetism, to various flat-band many-body correlations, and then to the puzzles of unconventional charge-density waves and superconductivity. We highlight the connection between theoretical ideas and experimental observations, and the bond between quantum interactions within kagome magnets and kagome superconductors, as well as their relation to the concepts in topological insulators, topological superconductors, Weyl semimetals and high-temperature superconductors. These developments broadly bridge topological quantum physics and correlated many-body physics in a wide range of bulk materials and substantially advance the frontier of topological quantum matter.

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## Acknowledgements

We thank our research collaborators for various discussions on kagome physics. M.Z.H. acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center and Princeton University; visiting scientist support at Berkeley Lab (Lawrence Berkeley National Laboratory) during the early phases of this work; support from the Gordon and Betty Moore Foundation (GBMF9461) for the STM and the theory work; and support from the US DOE under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200) for the theory and angle-resolved photoemission spectroscopy work. B.L. is supported by the Alfred P. Sloan Foundation, the National Science Foundation through Princeton University’s Materials Research Science and Engineering Center DMR-2011750; and the National Science Foundation under award DMR-2141966. J.-X.Y. acknowledges support from Princeton University, as well as the support from South University of Science and Technology of China principal research grant (number Y01202500). M.Z.H. also acknowledges visiting scientist support from Stanford University during the last phase of this work.

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Yin, JX., Lian, B. & Hasan, M.Z. Topological kagome magnets and superconductors. Nature 612, 647–657 (2022). https://doi.org/10.1038/s41586-022-05516-0

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