Phys. Rev. Lett. 101, 186805 (2008) [4 pages]
Topological Surface States in Three-Dimensional Magnetic Insulators
Abstract
References (24)
Citing Articles
Joel E. Moore, 1,2 Ying Ran, 1 and Xiao-Gang Wen31Department of Physics, University of California, Berkeley, California 94720, USA
2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
3Department of Physics, University of California, Berkeley, California 94720, USA
Received 9 May 2008; published 31 October 2008
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these “Hopf insulators” are characterized by a topological invariant as in quantum Hall states and ![[openface Z]](http://scitation.aip.org/servlet/GetImg?key=PRLTAO000101000018186805000001%3A0%3A0%3A28&t=a&d=a) 2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.
©2008 The American Physical Society
REFERENCES (24)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
- 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).
- K. Ohgushi, S. Murakami, and N. Nagaosa, Phys. Rev. B 62, R6065 (2000).
- M. Taillefumier, B. Canals, C. Lacroix, V. K. Dugaev, and P. Bruno, Phys. Rev. B 74, 085105 (2006).
- J. E. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 51, 51 (1983).
- Y. G. Makhlin and T. S. Misirpashaev, JETP Lett. 61, 49 (1995).
- F. Wilczek and A. Zee, Phys. Rev. Lett. 51, 2250 (1983).
- L. Fu and C. L. Kane, Phys. Rev. B 74, 195312 (2006).
- A. M. Essin and J. E. Moore, Phys. Rev. B 76, 165307 (2007).
- W.-Y. Hsiang and D.-H. Lee, Phys. Rev. A 64, 052101 (2001).
- P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett. 98, 256801 (2007).
- C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006).
- C. Wu, B. A. Bernevig, and S.-C. Zhang, Phys. Rev. Lett. 96, 106401 (2006).
- J. Ye, Y. B. Kim, B. I. Shraiman, P. Majumdar, and Z. Tesanovic, Phys. Rev. Lett. 83, 3737 (1999).
CITING ARTICLES
For access to citing articles, you need to log in.For access to citing articles, you need to Log in.
|
A new free weekly publication from APS
|
You are not logged in to this journal. Log in
| Subscription Information
View Cart
Download Citation
MyScitation
Print View