On the Locality of Physics in Metals, Semiconductors, and Insulators

Details On the Locality of Physics in Metals, Semiconductors, and Insulators On the Locality of Physics in Metals, Semiconductors, and Insulators

1998-05-13

arxiv.org/abs/cond-mat/9805147v4

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 $\gamma\propto T$.

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