Inhomogeneous superconductors can host electronic excitations, known as Andreev bound
states (ABSs), below the superconducting energy gap. With the advent of topological …

We review recent progresses in the study of flat band systems, especially focusing on the
fundamental physics related to the singularity of the flat band's Bloch wave functions. We first …

Topology sheds new light on the emergence of unidirectional edge waves in a variety of
physical systems, from condensed matter to artificial lattices. Waves observed in …

We show that flat bands can be categorized into two distinct classes, that is, singular and
nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in …

The fascinating electronic and optoelectronic properties of freestanding graphene and the
possible inclusion of novel two-dimensional (2D) systems in silicon-based electronics have …

In this article, we give a comprehensive review of recent progress in research on symmetry-
protected topological superfluids and topological crystalline superconductors, and their …

A singular flat band (SFB), a distinct class of the flat band, has been shown to exhibit various
intriguing material properties characterized by the quantum distance. We present a general …

Topology plays an increasing role in physics beyond the realm of topological insulators in
condensed mater. From geophysical fluids to active matter, acoustics or photonics, a …

This lecture note adresses the correspondence between spectral flows, often associated to
unidirectional modes, and Chern numbers associated to degeneracy points. The notions of …

We explore the relationship among the magnetic ordering in real space, the resulting spin
texture on the Fermi surface, and the related superconducting gap structure in noncollinear …