# Flat band induced by the interplay of synthetic magnetic flux and non-Hermiticity

## TL;DR

This paper introduces a tunable, real-energy flat band in a non-Hermitian, parity-time symmetric lattice, achieved through the interplay of synthetic magnetic flux and non-Hermiticity, with potential for localized eigenstates.

## Contribution

It demonstrates the realization of a flat band with real energy in a non-Hermitian system, a novel concept combining synthetic flux and non-Hermiticity effects.

## Key findings

- Flat band has entirely real energy.
- Flat band energy is tunable.
- Eigenstates are compact localized states.

## Abstract

A flat band is nondispersive and formed under destructive interference. Although flat bands are found in various Hermitian systems, to realize a flat band in non-Hermitian systems is an interesting task. Here, we propose a flat band in a parity-time symmetric non-Hermitian lattice. The proposed flat band has entirely real energy and is formed at an appropriate match between synthetic magnetic flux and non-Hermiticity. The flat band energy is tunable. At a weak intercell coupling, the flat band is isolated, whereas at a strong intercell coupling, it intersects with the dispersive band at the non-Hermitian phase transition point. The eigenstates of the flat band are compact localized states and are confined in one, two, or three unit cells at the edges or inside the non-Hermitian lattice.