The kagome lattice is a tiling of two-dimensional space comprised of corner-sharing triangles, having the same point symmetries as the honeycomb lattice (graphene) but a richer electronic structure. Recent theoretical developments suggest that the combination of magnetism, spin-orbit coupling, and geometric frustration in kagome metals is a promising platform to realize phenomena at the intersection of topology and strong correlations, such as the fractional quantum Hall and intrinsic anomalous Hall effect. Here, a major role is played by the three distinctive features of the kagome electronic band structure, namely the Dirac points, the van Hove singularity, and the flat bands. In this talk, I will report on studies of the experimental band structure of various kagome compounds to highlight the rich physics arising from the combination of topology, magnetism, and correlations, and the prospects for realizing new quantum matter phenomena in this class of materials.
In the first part, I will discuss the family of transition metal stannides (Fe3Sn2, FeSn, and CoSn). In these systems which intertwine robust magnetism and electronic topology, we observed various manifestations of topological physics. These include the realization of the Kane-Mele model for 2D Dirac fermions with a spin-orbit-induced topological gap, as well as the discovery of the elusive flat bands with nontrivial topology.
In the second part, I will discuss our most recent studied of the AV3Sb5 family of correlated kagome metals, where superconductivity and charge-density-waves have been found to coexist. Here, I will focus on the role of the van Hove singularity in creating the conditions for multiple instabilities of the Fermi surface and the emergence of collective electronic phases.