General Method to Construct Flat Bands in Two-Dimensional Lattices

Searching for new materials hosting flat bands is pivotal for exploring strongly correlated effects and designing sensitive quantum devices, but remains challenging. We present a general method for realizing flat bands based on mathematical optimization and symmetry analysis. The method enables the discovery of ∼1000 types of two-dimensional lattices that can host flat bands, in sharp contrast with ∼10 flat-band lattices predicted previously besides the well-known ones. We further verify the method using first-principles calculations. Our approach provides new insights for the design of flat-band lattices, particularly when aiming to create experimentally feasible configurations.