Scanning probe microscopy (SPM), a key invention in nanoscience, has by now been
extended to a wide spectrum of basic and applied fields. Its application to basic science led …

Certain lattice wave systems in translationally invariant settings have one or more spectral
bands that are strictly flat or independent of momentum in the tight binding approximation …

Electronic flat bands in momentum space, arising from strong localization of electrons in real
space, are an ideal stage to realize strongly-correlated phenomena. Theoretically, the flat …

Quantum simulators are essential tools for understanding complex quantum materials.
Platforms based on ultracold atoms in optical lattices and photonic devices have led the field …

The dimensionality of an electronic quantum system is decisive for its properties. In one
dimension, electrons form a Luttinger liquid, and in two dimensions, they exhibit the …

Achieving time-domain control of quantum states with atomic-scale spatial resolution in
nanostructures is a long-term goal in quantum nanoscience and spintronics. Here, we …

A flatband representing a highly degenerate and dispersionless manifold state of electrons
may offer unique opportunities for the emergence of exotic quantum phases. To date …

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 …

Advances in high-resolution and spin-resolved scanning tunnelling microscopy, as well as
atomic-scale manipulation, have enabled the bottom-up, atom-by-atom creation and …

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 …