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 …

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 …

Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas
past decades witnessed their new physics, the unified understanding has yet to be obtained …

Topological materials have become the focus of intense research in recent years, since they
exhibit fundamentally new physical phenomena with potential applications for novel devices …

Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one
of the most actively studied subjects in condensed matter physics, as correlations and SOC …

Exotic phases of matter can emerge from the interplay between strong electron interactions
and non-trivial topology. Materials that have non-dispersing bands in their electronic band …

As opposed to ordinary metals, whose Fermi surfaces are two dimensional, topological
(semi) metals can exhibit protected one-dimensional Fermi lines or zero-dimensional Fermi …

The link between chemical orbitals described by local degrees of freedom and band theory,
which is defined in momentum space, was proposed by Zak several decades ago for …

We study a topological band degeneracy in non-Hermitian systems with parity-time (PT) and
parity-particle-hole (CP) symmetries. In d-dimensional non-Hermitian systems, it is shown …

While the topological classification of insulators, semimetals, and superconductors in terms
of nonspatial symmetries is well understood, less is known about topological states …