Bulk-edge correspondence and trapping at a non-Hermitian topological interface

TL;DR

This paper investigates the bulk-edge correspondence in non-Hermitian topological systems, revealing that unlike Hermitian cases, edge states do not necessarily trap light at interfaces between different topological media.

Contribution

It demonstrates that in non-Hermitian systems, multiple edge states can exist without trapping light, challenging the conventional bulk-edge correspondence understanding.

Findings

Multiple edge states can exist at non-Hermitian interfaces.

Light trapping at the interface is not guaranteed despite edge states.

Bulk-edge correspondence can be violated in non-Hermitian systems.

Abstract

In Hermitian systems, according to the bulk-edge correspondence interfacing two topological optical media with different bulk topological numbers implies the existence of edge states, which can trap light at the interface. However, such a general scenario can be violated when dealing with non-Hermitian systems. Here we show that interfacing two semi-infinite Hatano-Nelson chains with different bulk topological numbers can result in the existence of infinitely many edge (interface) states, however light waves cannot be rather generally trapped at the interface.