Phys. Rev. Lett. 98, 046402 (2007) [4 pages]
Exponential Localization of Wannier Functions in Insulators
Abstract
References (37)
Citing Articles
Christian Brouder, 1 Gianluca Panati, 2 Matteo Calandra, 1 Christophe Mourougane, 3 and Nicola Marzari41Institut de Minéralogie et de Physique des Milieux Condensés, CNRS UMR 7590, Universités Paris 6 et 7, IPGP, 140 rue de Lourmel, 75015 Paris, France
2Zentrum Mathematik and Physik Department, Technische Universität München, 80290 München, Germany
3Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, 75013 Paris, France
4Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA
Received 28 June 2006; published 25 January 2007
The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.
©2007 The American Physical Society
| URL: |
http://link.aps.org/doi/10.1103/PhysRevLett.98.046402
|
| DOI: |
10.1103/PhysRevLett.98.046402 |
| PACS: |
71.23.An;
03.65.Vf
|
REFERENCES (37)
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