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Localised Wannier Functions in Metallic Systems

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Abstract

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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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220, Aalborg, Denmark

    Horia D. Cornean

  2. Université Paris-Dauphine, PSL Research University, CEREMADE, 75775, Paris, France

    David Gontier

  3. Inria Paris and Université Paris-Est, CERMICS (ENPC), 75589, Paris Cedex 12, France

    Antoine Levitt

  4. Dipartimento di Matematica e Fisica, Università degli Studi di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Rome, Italy

    Domenico Monaco

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  1. Horia D. Cornean
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  2. David Gontier
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  3. Antoine Levitt
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  4. Domenico Monaco
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Correspondence to Domenico Monaco.

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Communicated by Vieri Mastropietro.

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Cornean, H.D., Gontier, D., Levitt, A. et al. Localised Wannier Functions in Metallic Systems. Ann. Henri Poincaré 20, 1367–1391 (2019). https://doi.org/10.1007/s00023-019-00767-6

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  • DOI: https://doi.org/10.1007/s00023-019-00767-6

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