Fractional S -duality, classification of fractional topological insulators, and surface topological order

Peng Ye, Meng Cheng, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a generalization of the S-duality of four-dimensional quantum electrodynamics (QED4) to QED4 with fractionally charged excitations, the fractional S-duality. Such QED4 can be obtained by gauging the U(1) symmetry of a topologically ordered state with fractional charges. When time-reversal symmetry is imposed, the axion angle (θ) can take a nontrivial but still time-reversal-invariant value π/t2 (t Z). Here, 1/t specifies the minimal electric charge carried by bulk excitations. Such states with time-reversal and U(1) global symmetry (fermion number conservation) are fractional topological insulators (FTIs). We propose a topological quantum field theory description, which microscopically justifies the fractional S-duality. Then, we consider stacking operations (i.e., a direct sum of Hamiltonians) among FTIs. We find that there are two topologically distinct classes of FTIs: type I and type II. Type I (t Zodd) can be obtained by directly stacking a noninteracting topological insulator and a fractionalized gapped fermionic state with minimal charge 1/t and vanishing θ. But type II (t Zeven) cannot be realized through any stacking. Finally, we study the surface topological order of fractional topological insulators.

Original languageEnglish (US)
Article number085125
JournalPhysical Review B
Issue number8
StatePublished - Aug 18 2017

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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