Generalization and applicability of the Landauer formula for non-equilibrium current in the presence of interactions

Abstract

Using non-equilibrium Green's functions (NEGF), we calculate the current through an interacting region connected to non-interacting leads. The problem is reformulated in such a way that a Landauer-like term appears in the current as well as extra terms corresponding to non-equilibrium many-body effects. The interaction in the central region renormalizes not only the Green's functions but also the coupling at the contacts between the central region and the leads, allowing the total current to be further expressed as a generalized Landauer-like current formula. The general expression for the dynamical functional that renormalizes the contacts is provided. We analyze in detail under what circumstances Landauer-like approaches to the current, i.e. without contact renormalization, are valid for interacting electron-electron and/or electron-phonon systems. Numerical NEGF calculations are then performed for a model electron-phonon coupled system in order to validate our analytical approach. We show that the conductance for the off-resonant transport regime is adequately described by Landauer-like approach in the small-bias limit, while for the resonant regime the Landauer-like approach results depart from the exact results even at small finite bias. The validity of applying a Landauer-like approach to inelastic electron tunneling spectroscopy is also studied in detail.

13 pages, 5 figures. Accepted for publication in PRB

References in corpus (33)

• Density functional method for nonequilibrium electron transport
• Low Temperature Transport through a Quantum Dot: The Anderson Model out of Equilibrium
• Phonon effects in molecular transistors: Quantum and classical treatment
• Inelastic transport theory from first-principles: methodology and applications for nanoscale devices
• Probability of anomalously large Bit-Error-Rate in long haul optical transmission
• Microscopic study of electrical transport through individual molecules with metallic contacts: I. "Band" lineup, voltage drop and high-field transport
• Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips
• Transmission eigenchannels from non-equilibrium Green's functions
• Time-Dependent Partition-Free Approach in Resonant Tunneling Systems
• Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
• Inelastic scattering and local heating in atomic gold wires
• Modeling inelastic phonon scattering in atomic- and molecular-wire junctions
• Real-time Kadanoff-Baym approach to plasma oscillations in a correlated electron gas
• Electron-vibration interaction in transport through atomic gold wires
• Many Body Effects on the Transport Properties of Single-Molecule Devices
• Spin-Dependent Transport Through An Interacting Quantum Dot
• Effects of electron-phonon interaction on non-equilibrium transport through single-molecule transistor
• Time-dependent quantum transport: an exact formulation based on TDDFT
• Ab initio analysis of electron-phonon coupling in molecular devices
• Universal features of electron-phonon interactions in atomic wires
• Inelastic current-voltage characteristics of atomic and molecular junctions
• Inelastic effects on the transport properties of alkanethiols
• An `all-carbon' molecular device
• Vibration-induced correction to the current through a single molecule
• Incompleteness of the Landauer Formula for Electronic Transport
• Electronic Transport in Fullerene C20 Bridge Assisted by Molecular Vibrations
• Kadanoff-Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation
• Single channel conductance of H${}_2$ molecules attached to platinum or palladium electrodes
• Properties of multi-particle Green and vertex functions within Keldysh formalism
• Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling
• Inelastic resonant tunneling through single molecules and quantum dots: spectrum modification due to nonequilibrium effects
• Fermi-liquid theory for a conductance through an interacting region attached to noninteracting leads
• A Landauer transport formulation with inelastic scattering

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