Incompleteness of the Landauer Formula for Electronic Transport

TL;DR

This paper demonstrates that the Landauer formula for nanoscale conductance is incomplete because it neglects many-body effects, which are linked to the viscous behavior of electron liquids, and proposes a perturbative correction method using current-density-functional theory.

Contribution

It introduces a perturbative formalism based on time-dependent current-density-functional theory to account for many-body effects missing in the Landauer conductance formula.

Findings

Landauer formula neglects many-body effects.

Viscous electron liquid influences conductance.

Proposed perturbative corrections to resistance.

Abstract

We show that the Landauer multi-terminal formula for the conductance of a nanoscale system is incomplete because it does not take into account many-body effects which cannot be treated as contributions to the single-particle transmission probabilities. We show that the physical origin of these effects is related to the viscous nature of the electron liquid, and develop a perturbative formalism, based on the time-dependent current-density-functional theory, for calculating the corrections to the resistance in terms of the ``Kohn-Sham current distribution'' and the exchange-correlation kernel. The difficulties that still remain in calculating the latter are critically discussed.