Transport with Microscopic Inhomogeneities. Residual Resistivity Dipole, Landauer Formula, and the Three‐Dimensional Impurity Case

Abstract

AbstractA superposition method for the density matrix of stationary transport processes is developed where an arbitrary perturbation is superimposed on a weakly scattering background. Additional scatterers, areal perturbations of the grain boundary type and/or geometrical confinements in wires or films are candidates for applications. In the present paper an arbitrarily strong added scatterer is treated whose linear size remains small compared with the mean free path within the background. This problem is solved for a one‐channel quantum wire and for the three‐dimensional bulk. In both cases the evolving residual resistivity dipole (RRD) is determined. Already existing results are confirmed, generalized, and complemented by the inclusion of oscillatory density terms. A comparison of both the cases demonstrates the decisive role played by the topology of the problem. Within the scope of a completely formalized nonclassical transport theory, the internal mechanism producing the RRD is analysed. In this way it is shown that the voltage drop due to an added scatterer is given correctly, in the one‐channel case, by an expression of the (R/T)‐type quite similar to the original Landauer formula (LF). This derivation of a modified LF abandons the concept of dissipative reservoirs and ideal leads. The physical difference between ideal and resistive leads yields different results, too. These agree completely only for a sharp Fermi energy while, in the general case of finite temperatures, non‐negligible energy dependences destroy the full equivalence of both approaches.