Materials with an underlying kagome lattice provide a unique window into the collective behavior of interacting electrons. In insulating kagome systems, the magnetic frustration introduced by the lattice can promote exotic magnetic quantum states. In metallic kagome systems, the typical electronic dispersion displays features usually associated with strong correlations and topological phenomena, such as flat bands, Dirac points, and van Hove singularities. Recently, a new family of metallic kagome compounds AV3Sb5 (with A=Cs, K, Rb) has been found to display superconductivity, which is preceded by the onset of a charge-density wave (CDW). Interestingly, the three-dimensional CDW has been reported to display unusual features, some of which are suggestive of time-reversal symmetry-breaking. In this talk, I will introduce a phenomenological model, constructed from the low-energy states near the van Hove points, for the complex-valued CDW order parameter. This model features a rich interplay between the real component of the CDW – which describes bond distortions – and its imaginary component – which describes loop currents. As a result, a broad landscape of secondary orders emerges, displaying threefold rotational symmetry breaking, ferromagnetism, octupolar magnetic moment, and toroidal magnetic order. The unique experimental manifestations of these different types of CDW will be presented. I will also discuss the importance of the out-of-plane electronic dispersion for both CDW and superconductivity, focusing on the key role played by the apical Sb p-orbitals.
