Title: Three-dimensional flat bands in pyrochlore metals

Abstract: In an electronic flat band, the kinetic energy of electrons is quenched by a destructive interference of hopping pathways intrinsic to the crystal structure. Such a flat band allows electron-electron interactions to energetically dominate, providing a promising route towards realizing exotic and correlated ground states. While recent efforts have demonstrated intriguing flat band phase diagrams, these have largely been limited to quasi-two-dimensional materials such as Kagome metals and van der Waals structures. Here I discuss the design and characterization of materials that realize three-dimensional (3D) flat bands, focusing on the pyrochlore lattice as a 3D analogy to the Kagome network. Our spectroscopic and thermodynamic measurements reveal multiple flat bands in prototypical pyrochlore metals of the C15 Laves family. We further demonstrate chemical tunability of these flat bands to the Fermi level and establish both single-orbital and multi-orbital destructive interference patterns as essential for accurately describing the flat bands in these systems. I conclude by discussing recent efforts to further characterize flat bands in correlated pyrochlore materials, highlighting the rich phenomena within this material family.