Classification and analysis of two-dimensional Abelian fractional topological insulators

Michael Levin, Ady Stern

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


We present a general framework for analyzing fractionalized, time-reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have Abelian braiding statistics. First, we construct the most general Chern-Simons theories that can describe these states. We then derive a criterion for when these systems have protected gapless edge modes, that is, edge modes that cannot be gapped out without breaking time-reversal or charge-conservation symmetry. The systems with protected edge modes can be regarded as fractionalized analogues of topological insulators. We show that previous examples of 2D fractional topological insulators are special cases of this general construction. As part of our derivation, we define the concept of "local Kramers degeneracy" and prove a local version of Kramers theorem.

Original languageEnglish
Article number115131
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - 21 Sep 2012
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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