Topological number of edge states

Koji Hashimoto, Taro Kimura

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

Original languageEnglish
Article number195166
JournalPhysical Review B
Issue number19
Publication statusPublished - 2016 May 31
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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