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Localised Wannier Functions in Metallic Systems

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1712.07954.pdf (323.6Kb)
Date
2019-04
Dewey
Analyse
Sujet
Wannier functions; metallic systems; band interpolation; Chern numbers
Journal issue
Annales Henri Poincaré
Volume
20
Number
4
Publication date
04-2019
Article pages
1367–1391
Publisher
Springer
DOI
http://dx.doi.org/10.1007%2Fs00023-019-00767-6
URI
https://basepub.dauphine.fr/handle/123456789/19619
Collections
  • CEREMADE : Publications
Metadata
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Author
Cornean, Horia D.
26709 Department of Mathematical Sciences [Aalborg]
Gontier, David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Levitt, Antoine
2567 Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique [CERMICS]
Monaco, Domenico
139586 Dipartimento di Matematica [Roma TRE]
Type
Article accepté pour publication ou publié
Abstract (EN)
The existence and construction of exponentially localised Wannier functions for insulators are a well-studied problem. In comparison, the case of metallic systems has been much less explored, even though localised Wannier functions constitute an important and widely used tool for the numerical band interpolation of metallic condensed matter systems. In this paper, we prove that, under generic conditions, N energy bands of a metal can be exactly represented by N+1 Wannier functions decaying faster than any polynomial. We also show that, in general, the lack of a spectral gap does not allow for exponential decay.

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