# Classification of Exceptional Points and Non-Hermitian Topological Semimetals

## TL;DR

This paper provides a comprehensive classification of exceptional points in non-Hermitian systems, revealing new topological structures and predicting novel non-Hermitian semimetals and nodal superconductors.

## Contribution

It introduces a complete classification scheme based on energy gaps and symmetries, uncovering unique non-Hermitian topological phases with no Hermitian counterparts.

## Key findings

- Classification of exceptional points based on complex-energy gaps and symmetries
- Prediction of new non-Hermitian semimetals and nodal superconductors
- Construction of a topological dumbbell of exceptional points in 3D

## Abstract

Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal. This classification reveals unique non-Hermitian gapless structures with no Hermitian analogs and systematically predicts unknown non-Hermitian semimetals and nodal superconductors; a topological dumbbell of exceptional points in three dimensions is constructed as an illustration. Our work paves the way toward richer phenomena and functionalities of exceptional points and non-Hermitian topological semimetals.