Topological field theory of time-reversal invariant insulators

Xiao Liang Qi, Taylor L. Hughes, Shou Cheng Zhang

Research output: Contribution to journalArticlepeer-review


We show that the fundamental time-reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective-field theory is described by the (4+1) -dimensional Chern-Simons theory and the topological properties of the electronic structure are classified by the second Chern number. These topological properties are the natural generalizations of the time reversal-breaking quantum Hall insulator in 2+1 dimensions. The TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimensions can be obtained as descendants from the fundamental TRI insulator in 4+1 dimensions through a dimensional reduction procedure. The effective topological field theory and the Z2 topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of measurable phenomena, the most striking of which is the topological magnetoelectric effect, where an electric field generates a topological contribution to the magnetization in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine-structure constant α=e2/ℏc. Finally, we present a general classification of all topological insulators in various dimensions and describe them in terms of a unified topological Chern-Simons field theory in phase space.

Original languageEnglish (US)
Article number195424
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number19
StatePublished - Nov 24 2008
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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