Scattering approach to quantum electronic transport.

Abstract

We study the problem of quantum electronic transport in a mesoscopic disordered system arranged in a two-probe configuration, using the transfer-matrix scattering formalism. We calculate the statistical average of quantities of physical interest starting from single-scattering units and working our way to the n-unit system by successive multiplication of the single-transfer matrices. In the weak-scattering limit discussed in the text, results are described by a diffusion equation in transfer-matrix space. Second moments of the departure of the single-transfer matrices from the unit matrix give rise to generalized diffusion coefficients: once these are specified, results are universal, in the sense that higher-order moments are irrelevant. The isotropy assumption (N-channel generalization of a random-phase assumption) made in some of our previous publications is not needed: we show that, as a consequence, the present results are physically more reasonable than those involving the isotropy assumption. We study the reflection and transmission amplitudes and coefficients for individual pairs of channels in the ballistic regime and the total-reflection coefficient in the ballistic and metallic regimes (the latter in the approximation of ``equivalent channels''). The failure of isotropy in the localized regime is shown in one example. The present model, and not the one involving isotropy, is appropriate for the description of nonlocal quantum effects in multiprobe measurements, as well as persistent currents in normal metal rings.