Nearly Flat Conduction Bands from Bond-Centered Orbital Networks in Dense C ₃ N ₄

Nearly flat electronic bands are highly sought after for emergent quantum phenomena yet remain difficult to realize in three-dimensional covalent materials. Here we show that such bands can arise in dense C 3 N 4 through bond-centered orbital networks. A systematic crystal-structure search identifies 110 previously unknown C 3 N 4 frameworks, including two low-energy phases that are dynamically stable and exhibit weakly dispersive band-edge states. In particular, the 176-10-56-0 phase hosts an ultraflat conduction band on the k z = 0 plane with an in-plane bandwidth of only 4 meV, located just 0.06 eV above the true conduction-band minimum. Real-space analysis and effective bond-centered lattices reveal a connectivity-controlled mechanism for dispersion suppression. Moreover, very small strains can directly tune this low-lying flat band into the true conduction-band minimum while preserving weak dispersion, enhancing its experimental relevance. Our results establish bonding topology as a promising route to flat-band engineering in light-element covalent frameworks beyond conventional interference-based scenarios.