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 …

Abstracts In solid materials, non-trivial topological states, electron correlations and
magnetism are central ingredients for realizing quantum properties, including …

The destructive interference of wavefunctions in a kagome lattice can give rise to topological
flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been …

The introduction of the concept of topology into condensed matter physics has greatly
deepened our fundamental understanding of transport properties of electrons as well as all …

Fractional Chern insulators (FCIs) are lattice generalizations of the conventional fractional
quantum Hall effect (FQHE) in two-dimensional (2D) electron gases. They typically arise in a …

The topological flat band (TFB) has been proposed theoretically in various lattice models, to
exhibit a rich spectrum of intriguing physical behaviors. However, the experimental …

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 …

Recently there has been intense interest in kagome metals, which are expected to host flat
bands (FBs). However, the observed “FBs” are not flat over the whole two-dimensional …

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively
studied as a toy model, while material design and synthesis remain elusive. Here, we report …

We study two models of correlated bond and site disorder on the kagome lattice considering
both translationally invariant and completely disordered systems. The models are shown to …