Bloch bundles, Marzari-Vanderbilt functional and maximally localized   Wannier functions
  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. 
Gianluca Panati and Adriano Pisante
math-ph cond-mat.mes-hall math.MP