# Alice string in Non-Hermitian Systems

## TL;DR

This paper introduces the concept of Alice strings in non-Hermitian systems, showing how band-structure nodes can act as topological defects that alter Chern numbers, with implications for topological phases and surface states.

## Contribution

It generalizes Alice strings to momentum space in non-Hermitian media, revealing their role in topological charge changes and braiding phenomena in crystalline systems.

## Key findings

- Band-structure nodes act as Alice strings in non-Hermitian systems.
- Alice strings can flip the Chern number of Weyl points and exceptional rings.
- Signatures include non-trivial braiding and surface state features.

## Abstract

Alice string is a topological defect with a very peculiar feature. When a defect with a monopole charge encircles an Alice string, the monopole charge changes sign. In this work, we generalize this notion to momentum space of periodic media with loss and gain. In particular, we find that the generic band-structure node for a three-dimensional non-Hermitian crystalline system acts as an Alice string, which can flip the Chern number charge carried by Weyl points and by exceptional-line rings. We discuss signatures of this topological structure for a lattice model with one tuning parameter, including non-trivial braiding of bulk band nodes, and the spectroscopic features of both the bulk and the surface states. We also explore how an Alice string affects the validity of the Nielsen-Ninomiya theorem, and present a mathematical description of the braiding phenomenon.