Topological quantum chemistry and symmetry-based indicators have facilitated large-scale
searches for materials with topological properties at the Fermi energy (EF). We report the …

Chiral edge states are highly sought after as paradigmatic topological states relevant to both
quantum information processing and dissipationless electron transport. Using …

Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple
point always appears in phonon spectrum because of the Nambu–Goldstone theorem. Here …

Establishing the fundamental relation between the homotopy invariants and the band
topology of Hamiltonians has played a critical role in the recent development of topological …

The theory of the shift current is thus far geometrical without being topological. This means
that the real-space displacement of a photoexcited quasiparticle depends on the geometric …

Boundary obstructed topological phases caused by Wannier orbital shift between ordinary
atomic sites are proposed, which, however, cannot be indicated by symmetry eigenvalues at …

We study the generalization of the three-dimensional two-band Hopf insulator to the case of
many bands, where all the bands are separated from each other by band gaps. The …

The interplay between ferroelectricity and band topology can give rise to a wide range of
both fundamental and applied research. Here, we map out the emergence of nontrivial …

We study the conditions for Bloch bands to be spanned by symmetric and strictly compact
Wannier states that have zero overlap with all lattice sites beyond a certain range. Similar to …

The topological classification of gapped band structures depends on the particular definition
of topological equivalence. For translation-invariant systems, stable equivalence is defined …