1998/05/31 by Sohrab Ismail-Beigi, Tomas Arias
Physics and Astronomy · #cond-mat.mtrl-sci
published as Physical Review Letters, Vol 82, issue 10 · Will appear in March 8th 1999 issue of Physical Review Letters
arxiv created 1999/02/22 · arxiv updated 2009/11/30
We present an analytical study of the spatial decay rate γ of the one-particle density matrix ρ( r, r')∼exp(-γ| r- r'|) for systems described by single particle orbitals in periodic potentials in arbitrary dimensions. This decay reflects electronic locality in condensed matter systems and is also crucial for O(N) density functional methods. We find that γ behaves contrary to the conventional wisdom that generically γ∝√Δ in insulators and γ∝√(T) in metals, where Δ is the direct band gap and T the temperature. Rather, in semiconductors γ∝Δ, and in metals at low temperature γ∝ T.