Singular flat bands

We review recent progresses in the study of flat band systems, especially focusing on fundamental physics related to singularity band’s Bloch wave functions. first explain that bands can be classified into two classes: singular and non-singular bands, based presence or absence The is generated by crossing with another dispersive band. In band, one find a special kind eigenmodes, called non-contractible loop states robust boundary modes, which exhibit nontrivial real-space topology. Then, we experimental realization these topological eigenmodes photonic lattices. While topologically trivial, show maximum quantum distance around bulk invariant representing strength protects modes. Finally, discuss how manifests itself anomalous Landau level spreading when it has quadratic band-crossing