Fractional quantum Hall physics in topological flat bands

Siddharth A. Parameswaran, Rahul Roy, Shivaji Lal Sondhi

Research output: Contribution to journalShort survey

136 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)816-839
Number of pages24
JournalComptes Rendus Physique
Volume14
Issue number9-10
DOIs
StatePublished - Nov 1 2013

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Keywords

  • Chern insulators
  • Flat bands
  • Fractional quantum Hall effect
  • Topological order

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