# Defect states emerging from a non-Hermitian flat band of photonic zero modes

## TL;DR

This paper demonstrates the existence of a non-Hermitian flat band of photonic zero modes in gain-loss modulated lattices, revealing new defect states and their behaviors influenced by non-Hermitian symmetries, with practical photonic design implications.

## Contribution

It uncovers a non-Hermitian flat band of photonic zero modes due to particle-hole symmetry and explores defect states and their localization in such systems.

## Key findings

- Existence of a non-Hermitian flat band of photonic zero modes.
- Defect states behave as a chain with rigid and soft links.
- Localization of defect states increases with gain and loss strength.

## Abstract

We show the existence of a flat band consisting of photonic zero modes in a gain and loss modulated lattice system, as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudo-spin under the influence of a complex-valued pseudo-magnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength. A realistic photonic design is presented based on coupled InP/InGaAsP waveguides, and we also extend the discussion to two- and three-dimensional lattices.