Quantum states and intertwining phases in kagome materials

In solid materials, nontrivial topological states, electron correlations, and magnetism are central ingredients for realizing quantum properties, including unconventional superconductivity, charge and spin density waves, and quantum spin liquids. The Kagome lattice, made up of connected triangles and hexagons, can host these three ingredients simultaneously and has proven to be a fertile platform for studying diverse quantum phenomena including those stemming from the interplay of these ingredients. In this review, we introduce the fundamental properties of the Kagome lattice as well as discuss the complex observed phenomena seen in several emergent material systems such as the intertwining of charge order and superconductivity in some Kagome metals, modulation of magnetism and topology in some Kagome magnets, and symmetry breaking with Mott physics in the breathing Kagome insulators. We also highlight many open questions in the field as well as future research directions of Kagome systems.