Dirac returns: Non-Abelian statistics of vortices with Dirac fermions

Shigehiro Yasui, Kazunori Itakura, Muneto Nitta

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Topological superconductors classified as type D admit zero-energy Majorana fermions inside vortex cores, and consequently the exchange statistics of vortices becomes non-Abelian, giving a promising example of non-Abelian anyons. On the other hand, types C and DIII admit zero-energy Dirac fermions inside vortex cores. It has been long believed that an essential condition for the realization of non-Abelian statistics is non-locality of Dirac fermions made of two Majorana fermions trapped inside two well-separated vortices as in the case of type D. Contrary to this conventional wisdom, however, we show that vortices with local Dirac fermions also obey non-Abelian statistics.

Original languageEnglish
Pages (from-to)261-268
Number of pages8
JournalNuclear Physics B
Issue number2
Publication statusPublished - 2012 Jun 11


  • Non-Abelian statistics
  • Quantum vortices
  • Topological superconductors and insulators

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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