Landauer Theory, Inelastic Scattering and Electron Transport in Molecular Wires

TL;DR

This paper extends Landauer theory to include inelastic scattering in molecular wires by developing a self-consistent method for non-equilibrium electron distributions, accounting for elastic and inelastic processes in quantum transport.

Contribution

It introduces a self-consistent formalism for inelastic electron transport that incorporates Pauli exclusion and particle conservation, generalizing Landauer theory for molecular conductors.

Findings

Inelastic scattering significantly affects electron conduction in molecular wires.

The developed model accurately predicts current-voltage characteristics considering phonon interactions.

Elastic and inelastic processes compete, influencing transport properties in nanoscale systems.

Abstract

In this paper we address the topic of inelastic electron scattering in mesoscopic quantum transport. For systems where only elastic scattering is present, Landauer theory provides an adequate description of transport that relates the electronic current to single-particle transmission and reflection probabilities. A formalism proposed recently by Bonca and Trugman facilitates the calculation of the one-electron transmission and reflection probabilities for inelastic processes in mesoscopic conductors connected to one-dimensional ideal leads. Building on their work, we have developed a self-consistent procedure for the evaluation of the non-equilibrium electron distributions in ideal leads connecting such mesoscopic conductors to electron reservoirs at finite temperatures and voltages. We evaluate the net electronic current flowing through the mesoscopic device by utilizing these non-equilibrium distributions. Our approach is a generalization of Landauer theory that takes account of the Pauli exclusion principle for the various competing elastic and inelastic processes while satisfying the requirement of particle conservation. As an application we examine the influence of elastic and inelastic scattering on conduction through a two site molecular wire with longitudinal phonons using the Su-Schrieffer-Heeger model of electron-phonon coupling.