Abstract
We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z2 topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.
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References
M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005).
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).
B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006).
R. S. K. Mong, A. M. Essin, and J. E. Moore, Phys. Rev. B 81, 245209 (2010).
C.-X. Liu, ar**v:1304.6455 (2013).
R.-X. Zhang and C.-X. Liu, Phys. Rev. B 91, 115317 (2015).
C.-X. Liu, R.-X. Zhang, and B. K. van Leeuwen, Phys. Rev. B 90, 085304 (2014).
C. Fang and L. Fu, Phys. Rev. B 91, 161105 (2015).
C. Fang, M. J. Gilbert, and B. A. Bernevig, Phys. Rev. B 88, 085406 (2013).
L. Fu, Phys. Rev. Lett. 106, 106802 (2011).
M. Kargarian and G. A. Fiete, Phys. Rev. Lett. 110, 156403 (2013).
J. Liu, W. Duan, and L. Fu, Phys. Rev. B 88, 241303 (2013).
M. Serbyn and L. Fu, Phys. Rev. B 90, 035402 (2014).
P. Jadaun, D. **ao, Q. Niu, and S. K. Banerjee, Phys. Rev. B 88, 085110 (2013).
L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007).
A. A. Soluyanov and D. Vanderbilt, Phys. Rev. B 85, 115415 (2012).
R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, 1651 (1993).
R. Yu et al., Phys. Rev. B 84, 075119 (2011).
A. A. Soluyanov and D. Vanderbilt, Phys. Rev. B 83, 235401 (2011).
N. I. Kulikov and V. V. Tugushev, Phys. Usp. 27, 954 (1984).
R. Ramazashvili, Phys. Rev. Lett. 101, 137202 (2008).
R. Ramazashvili, Phys. Rev. B 79, 184432 (2009).
H. Guo, S. Feng and S.-Q. Shen, Phys. Rev. B 83, 045114 (2011).
M. Fruchart, D. Carpentier, and K. Gawedzki, Europhys. Lett. 106, 60002 (2014).
L. Fu and C. L. Kane, Phys. Rev. B 74, 195312 (2006).
M. Konig et al., J. Phys. Soc. Jpn. 77, 031007 (2008).
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Published in Russian in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 153, No. 1, pp. 108–126.
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Bègue, F., Pujol, P. & Ramazashvili, R. Identifying Two-Dimensional Z2 Antiferromagnetic Topological Insulators. J. Exp. Theor. Phys. 126, 90–105 (2018). https://doi.org/10.1134/S1063776118010028
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DOI: https://doi.org/10.1134/S1063776118010028