Topological field theory of timereversal invariant insulators
Abstract
We show that the fundamental timereversal invariant (TRI) insulator exists in 4+1 dimensions, where the effectivefield theory is described by the (4+1) dimensional ChernSimons 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 reversalbreaking 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 Z_{2} 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 finestructure constant α=e^{2}/ℏc . Finally, we present a general classification of all topological insulators in various dimensions and describe them in terms of a unified topological ChernSimons field theory in phase space.
 Publication:

Physical Review B
 Pub Date:
 November 2008
 DOI:
 10.1103/PhysRevB.78.195424
 arXiv:
 arXiv:0802.3537
 Bibcode:
 2008PhRvB..78s5424Q
 Keywords:

 73.43.f;
 78.20.e;
 78.20.Ls;
 03.65.Vf;
 Quantum Hall effects;
 Optical properties of bulk materials and thin films;
 Magnetooptical effects;
 Phases: geometric;
 dynamic or topological;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Theory
 EPrint:
 47 pages, 21 figures. Submitted to PRB. For high resolution figures please see final published version