Topological insulators and topological nonlinear {sigma} models
- Department of Physics, University of California at Berkeley, Berkeley, California 94720 (United States) and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
In this paper we link the physics of topological nonlinear {sigma} models with that of Chern-Simons insulators. We show that corresponding to every 2n-dimensional Chern-Simons insulator there is a (n-1)-dimensional topological nonlinear {sigma} model with the Wess-Zumino-Witten term. Breaking internal symmetry in these nonlinear {sigma} models leads to nonlinear {sigma} models with the {theta} term. [This is analogous to the dimension reduction leading from 2n-dimensional Chern-Simons insulators to (2n-1) and (2n-2)-dimensional topological insulators protected by discrete symmetries.] The correspondence described in this paper allows one to derive the topological term in a theory involving fermions and order parameters (we shall referred to them as ''fermion-{sigma} models'') when the conventional gradient-expansion method fails. We also discuss the quantum number of solitons in topological nonlinear {sigma} model and the electromagnetic action of the (2n-1)-dimensional topological insulators. Throughout the paper we use a simple model to illustrate how things work.
- OSTI ID:
- 21502916
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 82, Issue 24; Other Information: DOI: 10.1103/PhysRevB.82.245117; (c) 2010 American Institute of Physics; ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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SOLITONS
SYMMETRY
SYMMETRY BREAKING
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