Material Lattice Design of 3D Flat Bands

The realization of bulk flat bands owing to destructive hopping of model lattice systems is a promising route that can be expected to lead to exotic correlated and topological phenomena. However, most current experimental work is limited to twisted moiré heterostructures and 2D toy model systems such as Kagome materials. In bulk materials a 2D sublattice pattern can only guarantee band flatness in the 3D dimension via a generic lack of hopping weights rather than the deconstructive interference of the wavefunction that guarantees the band flatness within the 2D plane. We here discuss material structures for 3D hopping networks that become topological upon inclusion of spin orbit coupling. We demonstrate different origins for band flatness and their potential electronic signatures.