Topological Flat Band Models and Fractional Chern Insulators

TL;DR

This paper reviews topological flat band models and fractional Chern insulators, emphasizing their unique properties, interactions, and potential for applications like topological quantum computation, with insights into models, phenomena, and experimental realizations.

Contribution

It provides a comprehensive overview of models hosting nearly flat topological bands, analyzing interactions, correlated phases, and lattice-specific effects, and discusses experimental prospects.

Findings

Fractional Chern insulators can be stabilized without magnetic fields.

Interactions lead to novel correlated phases in flat topological bands.

Lattice-specific effects include Berry curvature fluctuations and competing instabilities.

Abstract

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 picture and can lead to entirely new insulating phases, with an altogether much richer and less explored phenomenology. Most saliently, lattice generalizations of fractional quantum Hall states, dubbed fractional Chern insulators, have recently been predicted to be stabilized by interactions within nearly dispersionless bands with non-zero Chern number, $C$. Contrary to their continuum analogues, these states do not require an external magnetic field and may potentially persist even at room temperature, which make these systems very attractive for possible applications such as topological quantum computation. This review recapitulates the basics of tight-binding models hosting nearly flat bands with non-trivial topology, $C\neq 0$, and summarizes the present understanding of interactions and strongly correlated phases within these bands. Emphasis is made on microscopic models, highlighting the analogy with continuum Landau level physics, as well as qualitatively new, lattice specific, aspects including Berry curvature fluctuations, competing instabilities as well as novel collective states of matter emerging in bands with $|C|>1$. Possible experimental realizations, including oxide interfaces and cold atom implementations as well as generalizations to flat bands characterized by other topological invariants are also discussed.