Topological field theory of time-reversal invariant insulators
2008/02/24 by Xiao-Liang Qi, Xiao‐Liang Qi, Taylor L. Hughes +2 · 3,347 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Atomic and Subatomic Physics Research #Invariant (physics) #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological degeneracy #Topological entropy in physics #Topological insulator #Topological order #Topological quantum field theory #Topological quantum number #Topological ring #Topological space #Topological vector space #Topology (electrical circuits) #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1103/physrevb.78.195424
published in Physical Review B 78(19) (American Physical Society) · 47 pages, 21 figures. Submitted to PRB. For high resolution figures please see final published version
arxiv created 2008/02/24 · openalex publication_date 2008/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
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 \ensuremathα=e2∕\ensuremathℏc. 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.
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