Phys. Rev. B 78, 195424 (2008) [43 pages]
Topological field theory of time-reversal invariant insulators
Abstract
References (80)
Citing Articles
Received 27 February 2008; published 24 November 2008
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  =e2/![[h-bar]](http://scitation.aip.org/stockgif3/planck.gif) c. 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.
©2008 The American Physical Society
REFERENCES (80)
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- K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
- D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).
- R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).
- R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
- D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
- Q. Niu, D. J. Thouless, and Y.-S. Wu, Phys. Rev. B 31, 3372 (1985).
- S. C. Zhang, T. H. Hansson, and S. Kivelson, Phys. Rev. Lett. 62, 82 (1989).
- W. P. Su, J. R. Schrieffer, and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979).
- R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).
- G. Ortiz and R. M. Martin, Phys. Rev. B 49, 14202 (1994).
- D. J. Thouless, Phys. Rev. B 27, 6083 (1983).
- J. Goldstone and F. Wilczek, Phys. Rev. Lett. 47, 986 (1981).
- C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
- B. A. Bernevig and S. C. Zhang, Phys. Rev. Lett. 96, 106802 (2006).
- C. Wu, B. A. Bernevig, and S. C. Zhang, Phys. Rev. Lett. 96, 106401 (2006).
- C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006).
- L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
- J. E. Moore and L. Balents, Phys. Rev. B 75, 121306(R) (2007).
- S. Murakami, N. Nagaosa, and S. C. Zhang, Phys. Rev. Lett. 93, 156804 (2004).
- C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005).
- L. Fu and C. L. Kane, Phys. Rev. B 74, 195312 (2006).
- L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007).
- X. L. Qi and S. C. Zhang, Phys. Rev. Lett. 101, 086802 (2008).
- Y. Ran, A. Vishwanath, and D.-H. Lee, Phys. Rev. Lett. 101, 086801 (2008).
- A. J. Niemi and G. W. Semenoff, Phys. Rev. Lett. 51, 2077 (1983).
- X. L. Qi, Y. S. Wu, and S. C. Zhang, Phys. Rev. B 74, 045125 (2006).
- F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
- Chaoxing Liu, Xiaoliang Qi, Xi Dai, Zhong Fang, and Shoucheng Zhang, Phys. Rev. Lett. 101, 146802 (2008).
- Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
- R. Jackiw and C. Rebbi, Phys. Rev. D 13, 3398 (1976).
- S. Murakami, N. Nagaosa, and S. C. Zhang, Phys. Rev. B 69, 235206 (2004).
- M. Creutz, Rev. Mod. Phys. 73, 119 (2001).
- J. E. Avron, L. Sadun, J. Segert, and B. Simon, Phys. Rev. Lett. 61, 1329 (1988).
- S. Adler, Phys. Rev. 177, 2426 (1969).
- M. C. Huang and P. Sikivie, Phys. Rev. D 32, 1560 (1985).
- F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987).
- K. Lee, Phys. Rev. D 35, 3286 (1987).
- R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977).
- R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37, 172 (1976).
- X. Dai, T. L. Hughes, X. L. Qi, Z. Fang, and S.-C. Zhang, Phys. Rev. B 77, 125319 (2008).
- E. Fradkin, E. Dagotto, and D. Boyanovsky, Phys. Rev. Lett. 57, 2967 (1986).
- A. N. Redlich, Phys. Rev. D 29, 2366 (1984).
- C. Chamon, C.-Y. Hou, R. Jackiw, C. Mudry, S.-Y. Pi, and A. P. Schnyder, Phys. Rev. Lett. 100, 110405 (2008).
- T. Grover and T. Senthil, Phys. Rev. Lett. 100, 156804 (2008).
- B. Julia and A. Zee, Phys. Rev. D 11, 2227 (1975).
- N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).
- D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001).
- M. Stone and R. Roy, Phys. Rev. B 69, 184511 (2004).
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