Kagome metals

Three important driving forces for creating qualitatively new phases in quantum materials are the topology of the materials’ electronic band structures, frustration in the electrons’ motion or magnetic interactions, and strong correlations between their charge, spin, and orbital degrees of freedom. In few material systems do all of these aspects come together to contribute on an equal footing to stabilize new electronic states with unprecedented properties; however, the search for such systems can be guided by models of configurational motifs or key sublattices that can host such physics. One of the most fascinating structural motifs for realizing this rich interplay of frustration, electronic topology, and electron correlation effects is the kagome lattice. This review provides an overview of the theoretical underpinnings driving the physics of kagome lattices and a subsequent discussion on experimental progress in realizing novel states enabled by kagome networks in crystalline materials. Different material classes are discussed, with an emphasis on the phenomenologies of their electronic states and how they map to interactions arising from their kagome lattices. The kagome lattice is a two-dimensional tiling of hexagons and triangles named after a Japanese basket weaving technique. Its geometry gives rise to highly frustrated interactions and interference effects experienced by electrons and their multiple degrees of freedom. In metals, the exploration of materials with kagome conduction networks is driven by predictions of realizing new electronic states where these interference effects are dominant, amplifying electronic interactions and many-body effects. In these kagome metals, these amplified correlation effects in combination with spin-orbit coupling and other forms of frustration have given rise to a wealth of phenomena beyond expectations. These include unusual states and responses born from topological flat bands, massive Dirac fermions, sublattice interference effects at saddle points such as unconventional superconductivity, orbital antiferromagnetism and flux phases, amplified anomalous Hall effects, and electronic nematic states. This review examines the theoretical and experimental work on kagome metals, with the aim of elucidating fundamental mechanisms underlying the observed exotic phenomena.