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Exponential decay properties of Wannier functions and related quantities

Lixin He·David Vanderbilt
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Abstract

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of non-orthonormal Wannier-like functions.

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Lixin He, David Vanderbilt. 2001-02-01. Exponential decay properties of Wannier functions and related quantities. https://doi.org/10.1103/physrevlett.86.5341

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