There are two prominent applications of the mathematical concept of topology to the physics
of materials: band topology, which classifies different topological insulators and semimetals …

The concept of topological energy bands and their manifestations have been demonstrated
in condensed matter systems as a fantastic paradigm toward unprecedented physical …

Non-Hermitian band theory distinguishes between line gaps and point gaps. While point
gaps can give rise to intrinsic non-Hermitian band topology without Hermitian counterparts …

Symmetry-protected topological crystalline insulators (TCIs) have primarily been
characterized by their gapless boundary states. However, in time-reversal-(T-) invariant …

Higher-order topological phases in crystalline and non-crystalline systems: a review Page 1
Journal of Physics: Condensed Matter ACCEPTED MANUSCRIPT • OPEN ACCESS Higher-order …

Chern insulators, and more broadly, topological insulators, present an obstruction to the
construction of exponentially localized electronic Wannier functions. This implies a …

Axion insulators possess a quantized axion field θ= π protected by combined lattice and
time-reversal symmetry, holding great potential for device applications in layertronics and …

Topological defects in solid-state materials are crystallographic imperfections that local
perturbations cannot remove. Owing to their nontrivial real-space topology, topological …

The discovery of quantum spin Hall effect characterized by the first spin-Chern numbers in
2D systems has significantly advanced topological materials. To explore its 4D counterpart …

The capacity to custom tailor the properties of quantum matter and materials is a central
requirement for enlarging their range of possible functionalities. A particularly promising …