Localised Wannier Functions in Metallic systems

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

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

2 Citationer (Scopus)

Resumé

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.
OriginalsprogEngelsk
TidsskriftAnnales Henri Poincare
Vol/bind20
Udgave nummer4
Sider (fra-til)1367-1391
Antal sider25
ISSN1424-0637
DOI
StatusUdgivet - 2019

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

Citer dette

Cornean, Decebal Horia ; Gontier, David ; Levitt, Antoine ; Monaco, Domenico. / Localised Wannier Functions in Metallic systems. I: Annales Henri Poincare. 2019 ; Bind 20, Nr. 4. s. 1367-1391.
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Localised Wannier Functions in Metallic systems. / Cornean, Decebal Horia; Gontier, David; Levitt, Antoine; Monaco, Domenico.

I: Annales Henri Poincare, Bind 20, Nr. 4, 2019, s. 1367-1391.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer 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.

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DO - 10.1007/s00023-019-00767-6

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