Fractional quantum Hall physics in topological flat bands

By S. Parameswaran, Rahul Roy, Shiv Sondhi. 2013

375 citations recorded by the source corpus.

Abstract 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 conventionally arises in semiconductor heterostructures at low temperatures and in high magnetic fields, interacting Chern insulators at fractional band filling may host phases with the same topological properties, but stabilized at the lattice scale, potentially leading to high-temperature topological order. We discuss the construction of topological flat band models, provide a survey of numerical results, and establish the connection between the Chern band and the continuum Landau problem. We then briefly summarize various aspects of Chern band physics that have no natural continuum analogs, before turning to a discussion of possible experimental realizations. We close with a survey of future directions and open problems, as well as a discussion of extensions of these ideas to higher dimensions and to other topological phases.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6329ac4392584e434c4b44cd10229da81f576c68

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms (2014, background): “While the former will be crucial to understand and experimentally minimize heating effects, the latter might provide a novel route for revealing interacting bosonic or fermionic many-body states in Chern bands, such as those introduced in the context of fractional Chern insulators [29].”
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].”
Artificial gauge fields in materials and engineered systems (2017, positive): “We point out that a similar scheme was originally proposed in an optical-lattice context [62] to generate fractional Chern insulators [53].”
Topological bands for ultracold atoms (2018, neutral): “model) which are far-removed from the continuum Landau level (Parameswaran et al., 2013).”