Series of Abelian and non-Abelian states in C>1 fractional Chern insulators

A. Sterdyniak, C. Repellin, B. Andrei Bernevig, N. Regnault

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Abstract

We report the observation of a series of Abelian and non-Abelian topological states in fractional Chern insulators (FCIs). The states appear at bosonic filling ν=k/(C+1) (k,C integers) in several lattice models, in fractionally filled bands of Chern numbers C≥1 subject to on-site Hubbard interactions. We show strong evidence that the k=1 series is Abelian while the k>1 series is non-Abelian. The energy spectrum at both ground-state filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the fractional quantum Hall (FQH) SU(C) (color) singlet k-clustered states (including Halperin, non-Abelian spin singlet states and their generalizations). The ground-state momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU(C) color singlets, but offers anomalies in the counting for C>1, possibly related to dislocations that call for the development of alternative counting rules of these topological states.

Original languageEnglish (US)
Article number205137
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume87
Issue number20
DOIs
StatePublished - May 29 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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