We consider a periodic Schrödinger 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 in Marzari and Vanderbilt (Phys Rev B 56:12847-12865, 1997) and we prove some results about the existence and exponential localization of its minimizers, in dimension d le; 3. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds. © 2013 Springer-Verlag Berlin Heidelberg.
Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions / Panati, Gianluca; Pisante, Adriano. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 322:3(2013), pp. 835-875. [10.1007/s00220-013-1741-y]
Bloch Bundles, Marzari-Vanderbilt Functional and Maximally Localized Wannier Functions
PANATI, GIANLUCA;PISANTE, Adriano
2013
Abstract
We consider a periodic Schrödinger 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 in Marzari and Vanderbilt (Phys Rev B 56:12847-12865, 1997) and we prove some results about the existence and exponential localization of its minimizers, in dimension d le; 3. The proof exploits ideas and methods from the theory of harmonic maps between Riemannian manifolds. © 2013 Springer-Verlag Berlin Heidelberg.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
