Non-Hermitian topological phenomena: A review

TL;DR

This review explores recent advances in non-Hermitian topological physics, focusing on boundary phenomena like the skin effect and the interplay between non-Hermiticity and topology.

Contribution

It provides a comprehensive overview of non-Hermitian topological phases, emphasizing boundary phenomena and the intrinsic topological nature of non-Hermiticity.

Findings

Discussion of the non-Hermitian skin effect as a boundary phenomenon

Analysis of the competition between non-Hermitian and topological boundary effects

Insights into the topological nature inherent in non-Hermitian systems

Abstract

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.