Ab initio theories of electric transport in solid systems with reduced dimensions

Ab initio theories of electric transport in solid systems with reduced dimensions, i.e., systems that at best are characterized by two-dimensional translational invariance, are reviewed in terms of a fully relativistic description of the Kubo–Greenwood equation. As the use of this equation requires concepts such as collinearity and non-collinearity in order to properly define resistivities or resistances corresponding to particular magnetic configurations, respective consequences of the (local) density functional theory are recalled in quite a detailed manner. Furthermore, since theoretical descriptions of solid systems with reduced dimensions require quantum mechanical methods different 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). plications shown are mainly meant to illustrate various aspects of electric transport in solid systems with reduced dimensions and comprise not only current-in-plane (CIP) experiments, but also current perpendicular to the planes of atoms geometries, consequences of tunneling, and finite nanostructures at or on metallic substrates. er to give a more complete view of available ab initio methods also a non-relativistic approach based on the Tight Binding Linear Combination of muffin tin orbitals (TB-LMTO-) method and the so-called Kubo–Landauer equation in terms of transmission and reflection matrices is presented. ilation of references with respect to ab-initio type approaches not explicitly discussed in here finally concludes the discussion of electric properties in solid systems with reduced dimensions.