Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions
Mathematical Physics
2013-09-26 v3 Mesoscale and Nanoscale Physics
math.MP
Abstract
We consider a periodic Schroedinger operator and the composite Wannier functions corresponding to a relevant family of its Bloch bands, separated by a gap from the rest of the spectrum. We study the associated localization functional introduced by Marzari and Vanderbilt, and we prove some results about the existence and exponential localization of its minimizers, in dimension d < 4. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds.
Keywords
Cite
@article{arxiv.1112.6197,
title = {Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions},
author = {Gianluca Panati and Adriano Pisante},
journal= {arXiv preprint arXiv:1112.6197},
year = {2013}
}
Comments
37 pages, no figures. V2: the appendix has been completely rewritten. V3: final version, to appear in Commun. Math. Physics