Chiral flat bands: Existence, engineering, and stability

We study flat bands in bipartite tight-binding networks with discrete translational invariance. Chiral flat bands with chiral symmetry eigenenergy E=0 and host compact localized eigenstates for finite range hopping. For a bipartite network with a majority sublattice chiral flat bands emerge. We present a simple generating principle of chiral flat-band networks and as a showcase add to the previously observed cases a number of new potentially realizable chiral flat bands in various lattice dimensions. Chiral symmetry respecting network perturbations---including disorder and synthetic magnetic fields---preserve both the flat band and the modified compact localized states. Chiral flat bands are spectrally protected by gaps and pseudogaps in the presence of disorder due to Griffiths effects.