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26 April 2024

» arxiv » cond-mat/0606726

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Exponential localization of Wannier functions in insulators
Christian Brouder ; Gianluca Panati ; Matteo Calandra ; Christophe Mourougane ; Nicola Marzari ;
Date:	28 Jun 2006
Subject:	Materials Science
Abstract:	The exponential localization of Wannier functions is proved in dimensions 2 and 3, settling a long-standing conjecture. The proof relies on an equivalence between the nullity of the first Chern class defined by the Berry connection and the triviality of the Bloch bundle. The analytic quasi-Bloch functions are shown to satisfy an explicit equation and a condition for the reality of the Wannier functions is given. More generally, the vanishing of the Hall current or of the Chern numbers is equivalent to the exponential localization of the Wannier functions.
Source:	arXiv, cond-mat/0606726
Other source:	[GID 1014279] pmid17358792
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