Flat Band Effects in Model Lattice Crystals

The notion of an electronic flat band refers to a collectively degenerate set of quantum mechanical eigenstates in periodic solids. The vanishing kinetic energy of flat bands relative to the electron-electron interaction is expected to result in a variety of many-body quantum phases of matter. Here we present recent developments in realizing flat bands in transition element-based crystalline materials. We will discuss recent experiments in which three dimensional flat bands are realized and connections to magnetism and other emergent states. We will also comment on the potential role of band topology and prospects for using similar lattice and orbital engineering to realize new correlated systems.