Localised Wannier Functions in Metallic Systems

  • Horia D. Cornean
  • David Gontier
  • Antoine Levitt
  • Domenico MonacoEmail author


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.

Mathematics Subject Classification

35Q40 81Q30 81Q70 


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Financial support from Grant 8021-00084B of the Danish Council for Independent Research | Natural Sciences, from the ERC Consolidator Grant 2016 “UniCoSM—Universality in Condensed Matter and Statistical Mechanics” and from PEPS JC 2017 is gratefully acknowledged.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horia D. Cornean
    • 1
  • David Gontier
    • 2
  • Antoine Levitt
    • 3
  • Domenico Monaco
    • 4
    Email author
  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark
  2. 2.Université Paris-Dauphine, PSL Research University, CEREMADEParisFrance
  3. 3.Inria Paris and Université Paris-Est, CERMICS (ENPC)Paris Cedex 12France
  4. 4.Dipartimento di Matematica e FisicaUniversità degli Studi di Roma TreRomeItaly

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