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.
Localised Wannier functions in metallic systems / Cornean, Horia D; Gontier, David; Levitt, Antoine; Monaco, Domenico. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 20:(2019), pp. 1367-1391. [10.1007/s00023-019-00767-6]
Localised Wannier functions in metallic systems
Monaco, Domenico
2019
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.File | Dimensione | Formato | |
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