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 …

The discovery of the quantum spin Hall effect and topological insulators more than a decade
ago has revolutionized modern condensed matter physics. Today, the field of topological …

We discuss phenomena arising from the combined influence of electron correlation and spin-
orbit coupling (SOC), with an emphasis on emergent quantum phases and transitions in …

Topological insulators and their intriguing edge states can be understood in a single-particle
picture and can as such be exhaustively classified. Interactions significantly complicate this …

The electronic structure of transition metal oxides featuring correlated electrons can be
rationalized within the Zaanen-Sawatzky-Allen framework. Following a brief description of …

We present a pedagogical review of the physics of fractional Chern insulators with a
particular focus on the connection to the fractional quantum Hall effect. While the latter …

The kagome lattice has long been regarded as a theoretical framework that connects lattice
geometry to unusual singularities in electronic structure. Transition metal kagome …

Recently, the long-sough quantum anomalous Hall effect was realized in a magnetic
topological insulator. However, the requirement of an extremely low temperature …

Topological insulators are characterized by a non-trivial band topology driven by the spin-
orbit coupling. To fully explore the fundamental science and application of topological …

The quantum anomalous Hall effect (QAHE) is a quantized Hall effect that occurs at zero
magnetic field. Its mechanism and properties are different from those of conventional …