Topological Flat Band Models and Fractional Chern Insulators

By E. Bergholtz, Zhao Liu. 2013

332 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/55a3de1e5a8a6aaca0fb9c9123c90603043a2d80

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Artificial flat band systems: from lattice models to experiments (2018, background): “Such models are frequently referred to as fractional Chern insulators in the literature [2, 3].”
Novel effects of strains in graphene and other two dimensional materials (2015, background): “Interestingly, the possibility of realizing the elusive fractional Chern insulators (FCI) (for a review see [21]), zeromagnetic field analogues of the fractional quantum Hall effect, has also been proposed within this scenario [1, 102].”
Topological quantum matter with ultracold gases in optical lattices (2016, methodology): “In gases of neutral atoms, analogues of the gauge field A appearing in (4) can be generated artificially, using the atom–light interaction.”