Chiral flat bands: Existence, engineering, and stability

Abstract

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. ©2017 American Physical Society