We study the bulk and boundary properties of fragile topological insulators (TIs) protected
by inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification. …

According to the Onsager’s semiclassical quantization rule, the Landau levels of a band are
bounded by its upper and lower band edges at zero magnetic field. However, there are two …

Symmetry-protected topological crystalline insulators (TCIs) have primarily been
characterized by their gapless boundary states. However, in time-reversal- ( T \documentclass[12pt]{…

In this work, we develop a systematic method of constructing flat-band models with and
without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a …

We introduce stable real-space invariants (SRSIs), topological invariants defined from
adiabatic deformations between Wannier states, generalizing previously discovered local and …

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…

Axion insulators are 3D magnetic topological insulators supporting hinge states and quantized
magnetoelectric effects, recently proposed for detecting dark-matter axionic particles via …

Geometry of the wave function is a central pillar of modern solid state physics. In this work,
we unveil the wave-function geometry of two-dimensional semimetals with band crossing …

Tight-binding models can accurately replicate the band structure and topology of crystalline
systems. They have been widely used in solid-state physics due to their versatility and low …

Flat bands have band crossing points with other dispersive bands in many systems including
the canonical flat-band models in the Lieb and kagome lattices. Here we show that some of …