Non-Hermitian Topological Phases: Principles and Prospects

TL;DR

This review explores the principles, models, and recent experimental progress in non-Hermitian topological phases, emphasizing unique phenomena like exceptional points, the skin effect, and their implications for future research.

Contribution

It provides a comprehensive overview of the fundamental principles, models, and experimental advances in non-Hermitian topological phases, highlighting new phenomena and future directions.

Findings

Identification of key non-Hermitian topological phenomena

Analysis of the non-Hermitian skin effect and generalized Brillouin zone

Survey of recent experimental progress in the field

Abstract

The synergy between non-Hermitian concepts and topological ideas have led to very fruitful activity in the recent years. Their interplay has resulted in a wide variety of new non-Hermitian topological phenomena being discovered. In this review, we present the key principles underpinning the topological features of non-Hermitian phases. Using paradigmatic models -- Hatano-Helson, non-Hermitian Su-Schrieffer-Heeger and non-Hermitian Chern insulator -- we illustrate the central features of non-Hermitian topological systems, including exceptional points, complex energy gaps and non-Hermitian symmetry classification. We discuss the non-Hermitian skin effect and the notion of the generalized Brillouin zone, which allows restoring the bulk-boundary correspondence. Using concrete examples, we examine the role of disorder, present the linear response framework, and analyze the Hall transport properties of non-Hermitian topological systems. We also survey the rapidly growing experimental advances in this field. Finally, we end by highlighting possible directions which, in our view, may be promising for explorations in the near future.