Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic
excitations that are protected by topology and symmetry. As three-dimensional analogs 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 …

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal
resistance, is the characteristic experimental fingerprint of Chern insulators—topologically …

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 …

The physics of quantum materials is dictated by many-body interactions and mathematical
concepts such as symmetry and topology that have transformed our understanding of matter …

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 …

Topological insulators are new states of quantum matter which cannot be adiabatically
connected to conventional insulators and semiconductors. They are characterized by a full …

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 …

Topological insulators are electronic materials that have a bulk band gap like an ordinary
insulator but have protected conducting states on their edge or surface. These states are …

We develop the topological band theory for systems described by non-Hermitian
Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of …