General construction of flat bands with and without band crossings based on wave function singularity

In this work, we develop a systematic method of constructing flat band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS), and also the singularity of the flat-band wave function obtained by a Fourier transformation of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific...