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 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 …

Topological semimetals (TSMs) are characterized by bulk band crossings in their electronic
structures, which are expected to give rise to gapless electronic excitations and topological …

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

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 …

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 …

Using a recently developed formalism called topological quantum chemistry, we perform a
high-throughput search of 'high-quality'materials (for which the atomic positions and …

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 …

Most natural and artificial materials have crystalline structures from which abundant
topological phases emerge,,,,–. However, the bulk–edge correspondence—which has been …

Topological systems are inherently robust to disorder and continuous perturbations,
resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless …