Physics – Condensed Matter – Materials Science
Scientific paper
1998-05-13
Physical Review Letters, Vol 82, issue 10
Physics
Condensed Matter
Materials Science
Will appear in March 8th 1999 issue of Physical Review Letters
Scientific paper
We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ 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 $\gamma$ behaves contrary to the conventional wisdom that generically $\gamma\propto\sqrt{\Delta}$ in insulators and $\gamma\propto\sqrt{T}$ in metals, where $\Delta$ is the direct band gap and $T$ the temperature. Rather, in semiconductors $\gamma\propto\Delta$, and in metals at low temperature $\gamma\propto T$.
Arias Tomas
Ismail-Beigi Sohrab
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