# Spontaneous topological pumping in non-Hermitian systems

## TL;DR

This paper demonstrates that non-Hermitian systems can exhibit spontaneous topological pumping via modulational instability, enabling edge state transfer without external driving, contrasting with Hermitian systems.

## Contribution

It introduces the concept of spontaneous topological pumping in non-Hermitian systems through modulational instability, a novel mechanism for topological state transfer.

## Key findings

- Spontaneous topological pumping occurs in non-Hermitian systems.
- State conversion of edge states is achieved without external modulation.
- Topological edge states can transfer spontaneously from one edge to the opposite.

## Abstract

We introduce modulational instability in non-Hermitian systems to study state conversion of topological edge states. We show that state conversion in non-Hermitian systems leads to topological pumping, which is a way of transferring topological edge state from one edge to the opposite edge. In contrast to Hermitian systems, topological pumping can occur spontaneously in non-Hermitian systems.