Incompleteness of the Landauer Formula for Electronic Transport

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.

arXiv comment11 pages, 4 figures, submitted to Phys. Rev. B

References in corpus (19)

• Current-dependent exchange-correlation potential for dynamical linear response theory
• Self-interaction errors in density functional calculations of electronic transport
• Time-dependent density functional theory beyond the adiabatic local density approximation
• A first-principles approach to electrical transport in atomic-scale nanostructures
• Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula
• Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems
• Transport in nanoscale systems: the microcanonical versus grand-canonical picture
• The Elasticity of an Electron Liquid
• Microscopic Current Dynamics in Nanoscale Junctions
• Local electron heating in nanoscale conductors
• Landauer Conductance without Two Chemical Potentials
• Hydrodynamic approach to transport and quantum turbulence in nanoscale conductors
• Treatment of electron viscosity in quantum conductance
• Electron turbulence at nanoscale junctions
• DC Conductance of Molecular Wires
• Ab-initio formulation of the 4-point conductance of interacting electronic systems
• Turbulence-induced magnetic flux asymmetry at nanoscale junctions
• Reply to Comment on "Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems"
• Ballistic transport is dissipative: the why and how

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