Electron transport in nanoscale junctions with local anharmonic modes

TL;DR

This paper compares electron transport in nanoscale junctions with local anharmonic modes, analyzing the differences between harmonic and two-state impurity models in high-temperature and low-temperature regimes.

Contribution

It demonstrates the absence of Franck-Condon blockade in the spin-fermion model and explores nonlinear effects predicted by mean-field analysis.

Findings

Franck-Condon blockade is absent in the spin-fermion model.

Nonlinear phenomena like bistability are predicted by mean-field in the Anderson-Holstein model but not in the spin-fermion model.

High-temperature transport characteristics differ significantly between the two models.

Abstract

We study electron transport in nanojunctions in which an electron on a quantum dot or a molecule is interacting with an N-state local impurity, a harmonic ("Holstein") mode, or a two-state system ("spin"). These two models, the Anderson-Holstein model and the spin-fermion model, can be conveniently transformed by a shift transformation into a form suitable for a perturbative expansion in the tunneling matrix element. We explore the current-voltage characteristics of the two models in the limit of high temperature and weak electron-metal coupling using a kinetic rate equation formalism, considering both the case of an equilibrated impurity, and the unequilibrated case. Specifically, we show that the analog of the Franck-Condon blockade physics is missing in the spin-fermion model. We complement this study by considering the low-temperature quantum adiabatic limit of the dissipative spin-fermion model, with fast tunneling electrons and a slow impurity. While a mean-field analysis of the Anderson-Holstein model suggests that nonlinear functionalities, bistability and hysteresis may develop, such effects are missing in the spin-fermion model at the mean-field level.