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Localised Wannier Functions in Metallic Systems

Cornean, Horia D.; Gontier, David; Levitt, Antoine; Monaco, Domenico (2019), Localised Wannier Functions in Metallic Systems, Annales Henri Poincaré, 20, 4, p. 1367–1391. 10.1007%2Fs00023-019-00767-6

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Type
Article accepté pour publication ou publié
Date
2019-04
Journal name
Annales Henri Poincaré
Volume
20
Number
4
Publisher
Springer
Pages
1367–1391
Publication identifier
Metadata
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Author(s)
Cornean, Horia D.
Department of Mathematical Sciences [Aalborg]
Gontier, David cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Levitt, Antoine
Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique [CERMICS]
Monaco, Domenico
Dipartimento di Matematica [Roma TRE]
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.
Subjects / Keywords
Wannier functions; metallic systems; band interpolation; Chern numbers