Abstract
We show that the fundamental time-reversal invariant (TRI) insulator exists in dimensions, where the effective-field theory is described by the -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 dimensions. The TRI quantum spin Hall insulator in dimensions and the topological insulator in dimensions can be obtained as descendants from the fundamental TRI insulator in dimensions through a dimensional reduction procedure. The effective topological field theory and the topological classification for the TRI insulators in and 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 . 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.
14 More- Received 27 February 2008
DOI:https://doi.org/10.1103/PhysRevB.78.195424
©2008 American Physical Society
Erratum
Erratum: Topological field theory of time-reversal invariant insulators [Phys. Rev. B 78, 195424 (2008)]
Xiao-Liang Qi, Taylor L. Hughes, and Shou-Cheng Zhang
Phys. Rev. B 81, 159901 (2010)
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Physical Review B 50th Anniversary Milestones
These Milestone studies represent lasting contributions to physics by way of reporting significant discoveries, initiating new areas of research, or substantially enhancing the conceptual tools for making progress in the burgeoning field of condensed matter physics.
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