# Flat bands in lattices with non-Hermitian coupling

## TL;DR

This paper investigates non-Hermitian photonic lattices with flat bands caused by bipartite symmetry, revealing unique phenomena like non-diffracting states, exceptional points, and effects of effective flux tuning on diffraction and amplification.

## Contribution

It introduces the concept of non-Hermitian flat bands in photonic lattices and explores their properties, including the effects of flux tuning and the emergence of exceptional points.

## Key findings

- Existence of non-Hermitian flat bands enforced by bipartite symmetry
- Observation of non-diffracting compact localized states
- Identification of non-Hermitian degeneracies and their effects

## Abstract

We study non-Hermitian photonic lattices that exhibit competition between conservative and non-Hermitian (gain/loss) couplings. A bipartite sublattice symmetry enforces the existence of non-Hermitian flat bands, which are typically embedded in an auxiliary dispersive band and give rise to non-diffracting "compact localized states". Band crossings take the form of non-Hermitian degeneracies known as exceptional points. Excitations of the lattice can produce either diffracting or amplifying behaviors. If the non-Hermitian coupling is fine-tuned to generate an effective $\pi$ flux, the lattice spectrum becomes completely flat, a non-Hermitian analogue of Aharonov-Bohm caging in which the magnetic field is replaced by balanced gain and loss. When the effective flux is zero, the non-Hermitian band crossing points give rise to asymmetric diffraction and anomalous linear amplification.