Many-body current formula and current conservation for non-equilibrium fully interacting nanojunctions

Abstract

We consider the electron transport properties through fully interacting nanoscale junctions beyond the linear-response regime. We calculate the current flowing through an interacting region connected to two interacting leads, with interaction crossing at the left and right contacts, by using a non-equilibrium Green's functions (NEGF) technique. The total current at one interface (the left one for example) is made of several terms which can be regrouped into two sets. The first set corresponds to a very generalised Landauer-like current formula with physical quantities defined only in the interacting central region and with renormalised lead self-energies. The second set characterises inelastic scattering events occurring in the left lead. We show how this term can be negligible or even vanish due to the pseudo-equilibrium statistical properties of the lead in the thermodynamic limit. The expressions for the different Green's functions needed for practical calculations of the current are also provided. We determine the constraints imposed by the physical condition of current conservation. The corresponding equation imposed on the different self-energy quantities arising from the current conservation is derived. We discuss in detail its physical interpretation and its relation with previously derived expressions. Finally several important key features are discussed in relation to the implementation of our formalism for calculations of quantum transport in realistic systems.

References in corpus (47)

• Density functional method for nonequilibrium electron transport
• Phonon effects in molecular transistors: Quantum and classical treatment
• Microscopic study of electrical transport through individual molecules with metallic contacts: I. "Band" lineup, voltage drop and high-field transport
• Probability of anomalously large Bit-Error-Rate in long haul optical transmission
• Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips
• 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
• A first-principles approach to electrical transport in atomic-scale nanostructures
• Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula
• The effect of inelastic processes on tunneling
• Electron-vibration interaction in transport through atomic gold wires
• Density functional calculations of nanoscale conductance
• Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects
• Fullerene-based molecular nanobridges: A first-principles study
• Effects of electron-phonon interaction on non-equilibrium transport through single-molecule transistor
• Quantum inelastic conductance through molecular wires
• Landauer Theory, Inelastic Scattering and Electron Transport in Molecular Wires
• Time-dependent quantum transport: an exact formulation based on TDDFT
• Ab initio analysis of electron-phonon coupling in molecular devices
• Coherent electron-phonon coupling and polaron-like transport in molecular wires
• Non-equilibrium GW approach to quantum transport in nano-scale contacts
• Universal features of electron-phonon interactions in atomic wires
• An `all-carbon' molecular device
• Vibration-induced correction to the current through a single molecule
• Conserving Approximations in Time-Dependent Density Functional Theory
• Introduction to Nonequilibrium Statistical Mechanics with Quantum Field
• Inelastic tunneling through mesoscopic structures
• Electron transport through an interacting region: The case of a nonorthogonal basis set
• Incompleteness of the Landauer Formula for Electronic Transport
• Generalization and applicability of the Landauer formula for non-equilibrium current in the presence of interactions
• Electronic Transport in Fullerene C20 Bridge Assisted by Molecular Vibrations
• Molecular transport junctions: Current from electronic excitations in the leads
• Single channel conductance of H${}_2$ molecules attached to platinum or palladium electrodes
• Correlation induced memory effects in the transport properties of low dimensional systems
• Non-equilibrium electronic structure of interacting single-molecule nanojunctions: vertex corrections and polarization effects for the electron-vibron coupling
• Non-equilibrium inelastic electronic transport: Polarization effects and vertex corrections to the self-consistent Born approximation
• Transport through a molecular quantum dot in the polaron crossover regime
• Inelastic resonant tunneling through single molecules and quantum dots: spectrum modification due to nonequilibrium effects
• Non-equilibrium quantum transport in fully interacting single-molecule nanojunctions
• Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields
• Initial correlations in nonequilibrium Falicov-Kimball model
• An embedding potential definition of channel functions
• A Landauer transport formulation with inelastic scattering
• Nonequilibrium Keldysh Formalism for Interacting Leads -- Application to Quantum Dot Transport Driven by Spin Bias
• Microscopic mechanisms of dephasing due to electron-electron interactions
• Time-dependent embedding

Cited by in corpus (5)

• Improvements on non-equilibrium and transport Green function techniques: the next-generation transiesta
• Ab initio complex band structure of conjugated polymers: Effects of hydrid DFT and GW schemes
• Nonequilibrium fluctuation-dissipation relations for one- and two-particle correlation functions in steady-state quantum transport
• Non-equilibrium renormalised contacts for transport in nanodevices with interaction: a quasi-particle approach
• Non-equilibrium transport with self-consistent renormalised contacts for a single-molecule nanodevice with electron-vibron interaction