# Chiral Flat Bands: Existence, Engineering and Stability

## TL;DR

This paper investigates the existence, design principles, and stability of chiral flat bands in bipartite lattice networks, revealing their robustness under various perturbations and proposing new realizations across different dimensions.

## Contribution

It introduces a simple generating principle for chiral flat bands and identifies new potentially realizable lattice configurations with these features.

## Key findings

- Chiral flat bands host compact localized states at zero energy.
- Chiral symmetry-preserving perturbations do not destroy flat bands.
- Flat bands are protected by spectral gaps and pseudogaps under disorder.

## 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 flatband and the modified compact localized states. Chiral flatbands are spectrally protected by gaps, and pseudogaps in the presence of disorder due to Griffiths effects.