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 …

Non-Hermitian theory is a theoretical framework used to describe open systems. It offers a
powerful tool in the characterization of both the intrinsic degrees of freedom of a system and …

This article reviews recent developments in the non-Hermitian skin effect (NHSE),
particularly on its rich interplay with topology. The review starts off with a pedagogical …

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 …

The past decades have witnessed the flourishing of non-Hermitian physics in non-
conservative systems, leading to unprecedented phenomena of unidirectional invisibility …

Non-Hermitian topological effects are of crucial importance both in fundamental physics and
applications. Here we discover the gain-loss-induced hybrid second-order skin-topological …

The combination of broken Hermiticity and band topology in physical systems unveils a
novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that …

Exceptional points and skin effect, as the two distinct hallmark features unique to the non-
Hermitian physics, have each attracted enormous interests. Recent theoretical works reveal …

Recent years have seen remarkable development in open quantum systems effectively
described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological …

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 …