# Topology and exceptional points of massive Dirac models with generic non-Hermitian perturbations

## TL;DR

This paper systematically classifies and analyzes massive Dirac models with various non-Hermitian perturbations, revealing their exceptional points, boundary modes, and topological properties, which are relevant for photonic applications like topological lasers.

## Contribution

It provides a comprehensive classification of non-Hermitian Dirac models, detailing their topological features and exceptional points, filling a gap in the understanding of experimental non-Hermitian topological systems.

## Key findings

- Identified three types of non-Hermitian terms in Dirac models.
- Determined bulk exceptional points and boundary modes for each case.
- Suggested applications in photonic topological lasers and optical devices.

## Abstract

Recently, there has been a lot of activity in the research field of topological non-Hermitian physics, partly driven by fundamental interests and partly driven by applications in photonics. However, despite these activities, a general classification and characterization of non-Hermitian Dirac models that describe the experimental systems is missing. Here, we present a systematic investigation of massive Dirac models on periodic lattices, perturbed by general non-Hermitian terms. We find that there are three different types of non-Hermitian terms. For each case we determine the bulk exceptional points, the boundary modes, and the band topology. Our findings serve as guiding principles for the design of applications, for example, in photonic lattices. For instance, periodic Dirac systems with non-Hermitian mass terms can be used as topological lasers. Periodic Dirac systems with non-Hermitian anti-commuting terms, on the other hand, exhibit exceptional points at the surface, whose non-trivial topology could be utilized for optical devices.