Exponential localization of Wannier functions in insulators
Materials Science
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.cond-mat/0606726,
title = {Exponential localization of Wannier functions in insulators},
author = {Christian Brouder and Gianluca Panati and Matteo Calandra and Christophe Mourougane and Nicola Marzari},
journal= {arXiv preprint arXiv:cond-mat/0606726},
year = {2007}
}
Comments
Four pages, two figures