Insulator/Chern-insulator transition in the Haldane model

Abstract

References (31)

Citing Articles

Download: PDF (789 kB) or Buy this Article (US$25) (Use Article Pack)

T. Thonhauser and David Vanderbilt
Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA

Received 24 August 2006; published 20 December 2006

Westudy the behavior of several physical properties of the Haldanemodel as the system undergoes its transition from the normal-insulatorto the Chern-insulator phase. We find that the density matrixhas exponential decay in both insulating phases, while having apower-law decay, more characteristic of a metallic system, precisely atthe phase boundary. The total spread of the maximally localizedWannier functions is found to diverge in the Chern-insulator phase.However, its gauge-invariant part, related to the localization length ofResta and Sorella, is finite in both insulating phases anddiverges as the phase boundary is approached. We also clarifyhow the usual algorithms for constructing Wannier functions break downas one crosses into the Chern-insulator region of the phasediagram.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.74.235111
DOI:	10.1103/PhysRevB.74.235111
PACS:	73.43.-f; 73.20.At; 11.30.Rd 73.43.-f Quantum Hall effects 73.20.At Surface states, band structure, electron density of states 11.30.Rd Chiral symmetries in particles and fields YEAR: 2006
KEYWORDS:	electrical conductivity transitions, Wannier functions, phase diagrams

REFERENCES (31)

View in Separate Window/Tab

For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.

F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).
R. D. King-Smith and D. Vanderbilt, Phys. Rev. B 47, R1651 (1993);

ibid. 48, 4442 (1993)

T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. 95, 137205 (2005).
D. Ceresoli, T. Thonhauser, D. Vanderbilt, and R. Resta, Phys. Rev. B 74, 024408 (2006).
N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997).
L. He and D. Vanderbilt, Phys. Rev. Lett. 86, 5341 (2001).
R. Resta and S. Sorella, Phys. Rev. Lett. 82, 370 (1999).
I. Souza, T. Wilkens, and R. M. Martin, Phys. Rev. B 62, 1666 (2000).
X.-G. Wen, Phys. Rev. Lett. 84, 3950 (2000).
C. Day, Phys. Today 58(2), 17 (2005).
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Phys. Rev. Lett. 97, 036808 (2006).
B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
S. F. Boys, Rev. Mod. Phys. 32, 296 (1960);

ibid. 32, 300 (1960)

B. C. Carlson and J. M. Keller, Phys. Rev. 105, 102 (1957).
R. Resta, Phys. Rev. Lett. 95, 196805 (2005).
S. N. Taraskin, D. A. Drabold, and S. R. Elliott, Phys. Rev. Lett. 88, 196405 (2002).
S. N. Taraskin, P. A. Fry, Xiaodong Zhang, D. A. Drabold, and S. R. Elliott, Phys. Rev. B 66, 233101 (2002).
S. Goedecker, Rev. Mod. Phys. 71, 1085 (1999).