It has long been noticed that special lattices contain single-electron flat bands (FB) without
any dispersion. Since the kinetic energy of electrons is quenched in the FB, this highly …

Topological insulators have become one of the most active research areas in condensed
matter physics. This article reviews progress on the topic of electronic correlation effects in …

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing
magnetic field is a long-standing quest of solid state physics. Recent experiments have …

Recent experiments have produced evidence for fractional quantum anomalous Hall
(FQAH) states at zero magnetic field in the semiconductor moiré superlattice system t MoTe …

Fractional Chern insulators realize the remarkable physics of the fractional quantum Hall
effect (FQHE) in crystalline systems with Chern bands. The lowest Landau level (LLL) is …

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 …

We study topological phases of interacting systems in two spatial dimensions in the absence
of topological order (ie, with a unique ground state on closed manifolds and no fractional …

An exciting new prospect in condensed matter physics is the possibility of realizing fractional
quantum Hall states in simple lattice models without a large external magnetic field. A …

Lattice models forming bands with higher Chern number offer an intriguing possibility for
new phases of matter with no analogue in continuum Landau levels. Here, we establish the …

Recent numerical simulations of flat-band models with interactions which show clear
evidence of fractionalized topological phases in the absence of a net magnetic field have …