Topological number of edge states

Koji Hashimoto, Taro Kimura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 - Condensed Matter and Materials Physics
Volume93
Issue number19
DOIs
Publication statusPublished - 2016 May 31

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String theory
Fermions
Momentum
Magnetic fields
monopoles
string theory
equivalence
fermions
analogs
momentum
magnetic fields

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Topological number of edge states. / Hashimoto, Koji; Kimura, Taro.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 93, No. 19, 195166, 31.05.2016.

Research output: Contribution to journalArticle

Hashimoto, Koji ; Kimura, Taro. / Topological number of edge states. In: Physical Review B - Condensed Matter and Materials Physics. 2016 ; Vol. 93, No. 19.
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