Optimally localized Wannier functions for quasi onedimensional nonperiodic insulators
Abstract
It is proved that for general, not necessarily periodic quasi one dimensional systems, the band position operator corresponding to an isolated part of the energy spectrum has discrete spectrum and its eigenfunctions have the same spatial localization as the corresponding spectral projection. As a consequence, an eigenbasis of the band position operator provides a basis of optimally localized (generalized) Wannier functions for quasi one dimensional systems, thus proving the "strong conjecture" of Marzari and Vanderbilt. If the system has some translation symmetries (e.g. usual translations, screw transformations), they are "inherited" by the Wannier basis.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.3392
 Bibcode:
 2007arXiv0709.3392C
 Keywords:

 Condensed Matter  Other;
 Mathematical Physics
 EPrint:
 15 pages, final version. Accepted for publication in J.Phys.A