$\mathcal{PT}$-Symmetric Topological Edge-Gain Effect

TL;DR

This paper introduces a novel non-Hermitian topological effect where only edge states exhibit complex eigenvalues, enabling robust, topologically protected edge lasing in photonic systems with uniform gain.

Contribution

It presents a new topological phenomenon with complex eigenvalues confined to edge states in uniform materials, useful for topological lasers.

Findings

Edge states have complex eigenvalues only, despite uniform material.

The effect is robust against defects due to topological protection.

Potential application in reciprocal topological lasers.

Abstract

We demonstrate a non-Hermitian topological effect that is characterized by having complex eigenvalues only in the edge states of a topological material, despite the fact that the material is completely uniform. Such an effect can be constructed in any topological structure formed by two gapped sub-systems, e.g., a quantum spin-Hall system, with a suitable non-Hermitian coupling between the spins. The resulting complex-eigenvalued edge state is robust against defects due to the topological protection. In photonics, such an effect can be used for the implementation of topological lasers, in which a uniform pumping provides gain only in the edge lasing state. Furthermore, such a topological lasing model is reciprocal and is thus compatible with standard photonic platforms.