Combinatorics

Physics

Topology (electrical circuits)

Mathematics

Topological order

Topological quantum number

Gravitational singularity

Topological insulator

Magnetism

Condensed matter physics

Theoretical physics

Fermion

Superconductivity

Quantum mechanics

Quantum

Nature

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&nbsp;magnetism, and van Hove singularities can lead to instabilities towards long-range many-body&nbsp;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&nbsp;superconductors,&nbsp;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. Recent key developments in the exploration of kagome materials are reviewed, including fundamental concepts of a kagome lattice, realizations of Chern and Weyl topological magnetism, flat-band many-body correlations, and unconventional charge-density waves and superconductivity.

Topological kagome magnets and superconductors