Resistance and localization in thin films and wires

Abstract

The zero temperature resistance of a container gives a measure of the degree of localization of the electrons within the container. At very low temperatures hopping between localized states occurs, but at higher temperatures electrons may diffuse as if they were in a metal until their motion is limited by their localization. A recent scaling theory of conductance suggests that conductance is a smoothly varying function of a length scale that is set by the distance an electron travels before it suffers inelastic scattering by a phonon. In this theory all states are localized in one and two dimensions, and there is no minimum metallic conductivity in three dimensions. There is other evidence that all states are localized in two dimensions. Recent experiments on low temperature conduction in thin wires and thin films are discussed. The question of whether which are supposed to demonstrate a minimum metallic conductivity at the mobility edge must be faced.