Localised Wannier Functions in Metallic systems

Decebal Horia Cornean, David Gontier, Antoine Levitt, Domenico Monaco

Research output: Contribution to journalJournal articleResearchpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
JournalAnnales Henri Poincare
Volume20
Issue number4
Pages (from-to)1367-1391
Number of pages25
ISSN1424-0637
Publication statusPublished - 2019

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Spectral Gap
Insulator
Exponential Decay
energy bands
interpolation
polynomials
Metals
Interpolate
insulators
Polynomial
decay
Energy
metals

Cite this

Cornean, D. H., Gontier, D., Levitt, A., & Monaco, D. (2019). Localised Wannier Functions in Metallic systems. Annales Henri Poincare, 20(4), 1367-1391.
Cornean, Decebal Horia ; Gontier, David ; Levitt, Antoine ; Monaco, Domenico. / Localised Wannier Functions in Metallic systems. In: Annales Henri Poincare. 2019 ; Vol. 20, No. 4. pp. 1367-1391.
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Cornean, DH, Gontier, D, Levitt, A & Monaco, D 2019, 'Localised Wannier Functions in Metallic systems', Annales Henri Poincare, vol. 20, no. 4, pp. 1367-1391.

Localised Wannier Functions in Metallic systems. / Cornean, Decebal Horia; Gontier, David; Levitt, Antoine; Monaco, Domenico.

In: Annales Henri Poincare, Vol. 20, No. 4, 2019, p. 1367-1391.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Localised Wannier Functions in Metallic systems

AU - Cornean, Decebal Horia

AU - Gontier, David

AU - Levitt, Antoine

AU - Monaco, Domenico

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

M3 - Journal article

VL - 20

SP - 1367

EP - 1391

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 4

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Cornean DH, Gontier D, Levitt A, Monaco D. Localised Wannier Functions in Metallic systems. Annales Henri Poincare. 2019;20(4):1367-1391.