A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

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 …

A conventional topological insulator (TI) has gapped bulk states but gapless edge states.
The emergence of the gapless edge states is dictated by the bulk topological invariant of the …

Over the past decade, topology has emerged as a major branch in broad areas of physics,
from atomic lattices to condensed matter. In particular, topology has received significant …

Recent research in topological photonics has not only proposed and realized novel
topological phenomena such as one‐way broadband propagation and robust transport of …

Recently, higher-order topological phases that do not obey the usual bulk-edge
correspondence principle have been introduced in electronic insulators and brought into …

The topological phases of matter are characterized using the Berry phase, a geometrical
phase associated with the energy-momentum band structure. The quantization of the Berry …

Photonic topological insulators enable topological boundary modes that are resilient to
defects and disorder, irrespective of manufacturing precision. This property is known as …

The topological properties of an object, associated with an integer called the topological
invariant, are global features that cannot change continuously but only through abrupt …

Topological photonics provides a fundamental framework for robust manipulation of light,
including directional transport and localization with built-in immunity to disorder. Combined …