Bergholtz, Emil J.
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≠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.
500 Naturwissenschaften und Mathematik::530 Physik
Topological Flat Band Models and Fractional Chern Insulators
International Journal of Modern Physics B. - 27 (2013), 24, Artikel Nr.
Institut für Theoretische Physik