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P. Weinberger:
"Ab initio theories of electric transport in solid systems with reduced dimensions ";
Physics Reports, 377 (2003), 281 - 387.

Ab initio theories ofelectric transport in solid systems with reduced dimensions, i.e., systems that at best
are characterized by two-dimensional translational invariance, are reviewed in terms ofa fully relativistic description
ofthe Kubo-Greenwood equation. As the use ofthis equation requires concepts such as collinearity
and non-collinearity in order to properly de1ne resistivities or resistances corresponding to particular magnetic
con1gurations, respective consequences ofthe (local) density functional theory are recalled in quite a detailed
manner. Furthermore, since theoretical descriptions ofsolid systems with reduced dimensions require quantum
mechanical methods di3erent from bulk systems (three-dimensional periodicity), the so-called Screened
Korringa-Kohn-Rostoker (SKKR-) method for layered systems is introduced together with a matching coherent
potential approximation (inhomogeneous CPA).
The applications shown are mainly meant to illustrate various aspects ofelectric transport in solid systems
with reduced dimensions and comprise not only current-in-plane (CIP) experiments, but also current
perpendicular to the planes ofatoms geometries, consequences oftunneling, and 1nite nanostructures at or on
metallic substrates.
In order to give a more complete view ofavailable ab initio methods also a non-relativistic approach
based on the Tight Binding Linear Combination ofmu;n tin orbitals (TB-LMTO-) method and the so-called
Kubo-Landauer equation in terms oftransmission and re=ection matrices is presented.
A compilation ofref erences with respect to ab-initio type approaches not explicitly discussed in here 1nally
concludes the discussion ofelectric properties in solid systems with reduced dimensions.
c
2003 Elsevier Science B.V. All rights reserved.
PACS: 75.30.Gw; 75.70.Ak; 75.70.Cn

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http://www.cms.tuwien.ac.at/publications/pdf2003/pr377-281-03.pdf