Generalized many-channel conductance formula with application to small rings

TLDR

The authors model a multi‑channel scatterer by assuming all incident channels on one side share a common chemical potential, with transmitted and reflected currents determined solely by the sample’s multichannel scattering matrix, and without assuming inter‑channel equilibration. They derive a generalized conductance formula for a multi‑channel scatterer that differs from previous results except Azbel’s, confirm it for a single channel at finite temperature, and show that in a small ring the h/e and h/2e periodic contributions to conductance scale inversely with channel number N.

Abstract

The conductance of a sample scattering elastically and coupled to leads with many channels is derived. We assume that all the incident channels on one side of the sample are fed from the same chemical potential. The transmitted and reflected streams are determined by the incident streams through the multichannel scattering properties of the sample. We do not assume that the channels equilibrate with each other. Our result differs from those given earlier by other authors, except for that of Azbel [J. Phys. C 14, L225 (1981)], which is confirmed. We point out that a similar result is obtained for the conductance in a single channel at a temperature above zero. As an application, we obtain the dependence on channel number N of the contributions to the conductance of a small ring, periodic in the Aharonov-Bohm flux through it. Terms whose period is h/e as well as those with period h/2e vary with N as 1/N.