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

TL;DR

This paper extends the Landauer formula to interacting systems using NEGF, revealing when a Landauer-like approach is valid for non-equilibrium current calculations involving interactions.

Contribution

It derives a generalized Landauer-like formula incorporating contact renormalization due to interactions and analyzes its validity for electron-electron and electron-phonon systems.

Findings

Landauer-like approach valid in off-resonant, small-bias regime

Departures from Landauer-like results in resonant transport

Validated analytical approach with NEGF numerical calculations

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.