Exceptional Topology of Non-Hermitian Systems

TL;DR

This paper reviews the unique topological phenomena in non-Hermitian systems, highlighting exceptional degeneracies, novel phases, and boundary effects, with applications across classical and quantum platforms.

Contribution

It provides a comprehensive overview of non-Hermitian topological phases, emphasizing exceptional points, new classifications, and boundary phenomena, integrating recent theoretical and experimental advances.

Findings

Exceptional degeneracies lead to unique topological phases.

Non-Hermitian systems exhibit anomalous bulk-boundary correspondence.

Applications span optical, electronic, and cold-atom systems.

Abstract

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits,s and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.