Effective field theory of a topological insulator and the Foldy-Wouthuysen transformation

Ömer F. Dayi*, Mahmut Elbistan, Elif Yunt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Employing the Foldy-Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern-Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern-Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy-Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.

Original languageEnglish
Pages (from-to)935-951
Number of pages17
JournalAnnals of Physics
Volume327
Issue number3
DOIs
Publication statusPublished - Mar 2012

Keywords

  • Berry gauge field
  • Chern-Simons action
  • Foldy-Wouthuysen transformation
  • Topological insulator

Fingerprint

Dive into the research topics of 'Effective field theory of a topological insulator and the Foldy-Wouthuysen transformation'. Together they form a unique fingerprint.

Cite this