Transport as a Consequence of Incident Carrier Flux

Abstract

The electrical resistance of a one-dimensional metal, with no inelastic scattering, is [1,2]

$$\Re _{e1} = \left( {\hbar \pi /e^2 } \right)R/\left( {1 - R} \right).$$

((1.1))

where R is the reflection probability for a carrier entering the specimen, at the Fermi level. Equation (1.1) allows for a two-fold spin degeneracy. This relationship received widespread attention in the localization literature, following the work of ANDERSON, et al. [3]. As an example of the many further extensions, we cite only [4]. The opportunities for generalizations of (1.1), as well as its limitations, are, perhaps, still inadequately appreciated. In that connection, I will stress the utility of a viewpoint taken over from circuit theory. It was originally invoked [5] in a paper treating the metallic residual resistance problem from a viewpoint in which the current flow into the specimen is taken as the causal agent, and the electric field is built up as the consequence of a continued flow of charges against scattering centers. The duality of currents and fields as source agents is, of course, very familiar in electrical engineering, but has not become a common viewpoint in transport theory.