Topological states of non-Hermitian systems

TL;DR

This paper reviews the emerging field of topological states in non-Hermitian systems, highlighting their unique properties and the extension of topological concepts beyond Hermitian models, especially in photonics and condensed matter.

Contribution

It provides a concise overview of the recent developments in topological phases of non-Hermitian systems, including bulk-boundary correspondence and potential physical realizations.

Findings

Non-Hermitian systems exhibit unique topological properties.

Bulk-boundary correspondence extends to non-Hermitian models.

Applications in photonics and condensed matter are discussed.

Abstract

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the context of photonic systems, where one needs to account for gain and loss, circuits of resonators, and also when modeling the lifetime due to interactions in condensed matter systems. Here we provide a brief overview of this rapidly growing subject, the search for topological states and a bulk-boundary correspondence in non-Hermitian systems.