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Phys. Rev. Lett. 98, 106803 (2007) [4 pages]

Topological Insulators in Three Dimensions

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Liang Fu, C. L. Kane, and E. J. Mele
Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

Received 26 July 2006; published 7 March 2007

Westudy three-dimensional generalizations of the quantum spin Hall (QSH) effect.Unlike two dimensions, where a single Z₂ topological invariant governsthe effect, in three dimensions there are 4 invariants distinguishing16 phases with two general classes: weak (WTI) and strong(STI) topological insulators. The WTI are like layered 2D QSH states,but are destroyed by disorder. The STI are robust andlead to novel “topological metal” surface states. We introduce atight binding model which realizes the WTI and STI phases,and we discuss its relevance to real materials, including bismuth.

©2007 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevLett.98.106803
DOI:	10.1103/PhysRevLett.98.106803
PACS:	73.43.-f; 72.25.Hg; 73.20.-r; 85.75.-d 73.43.-f Quantum Hall effects 72.25.Hg Electrical injection of spin polarized carriers 73.20.-r Electron states at surfaces and interfaces 85.75.-d Magnetoelectronics; spintronics: devices exploiting spin polarized transport or integrated magnetic fields YEAR: 2007

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