Fermi-liquid theory for a conductance through an interacting region attached to noninteracting leads

TL;DR

This paper establishes a Fermi-liquid framework linking dc conductance to transmission in an interacting region connected to noninteracting leads, showing vertex corrections vanish at zero temperature, simplifying conductance calculation.

Contribution

It extends the Landauer formula to interacting regions by demonstrating vertex corrections disappear at zero temperature, enabling a Landauer-type expression for conductance.

Findings

Vertex corrections vanish at T=0 in noninteracting leads.

Conductance can be expressed using single-particle transmission at Fermi energy.

Generalization to multiple scattering channels is achieved.

Abstract

We study the relation between the dc conductance and the transmission through an interacting region based on the Kubo formalism using the perturbation analysis in the Coulomb interaction developed by Yamada-Yosida and Shiba. We find that the contributions of the vertex correction to the dc conductance disappear at T=0 if the currents are measured in the noninteracting leads. Consequently, the dc conductance is written in a Landauer-type form using the transmission coefficient for single-particle-like excitation at the Fermi energy. The results are generalized to a system with a number of scattering channels, and may be regarded as an extension of the relation derived by Fisher-Lee.