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 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 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 …

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity
to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non …

We establish exact relations between the winding of “energy”(eigenvalue of Hamiltonian) on
the complex plane as momentum traverses the Brillouin zone with periodic boundary …

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 …

In spatially periodic Hermitian systems, such as electronic systems in crystals, the band
structure is described by the band theory in terms of the Bloch wave functions, which …

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 …