Phonon affected transport through molecular quantum dots

TL;DR

This paper develops an analytical method to study how molecular vibrations influence electron transport in quantum dots, covering a wide range of coupling strengths and phonon frequencies.

Contribution

It extends a variational Lang-Firsov approach with perturbation theory to analyze electron-phonon interactions in molecular quantum dots.

Findings

Spectral function analysis reveals polaron formation effects.

Transport coefficients show dependence on electron-phonon coupling.

Limitations of the approach are discussed in the context of polaron physics.

Abstract

To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variational Lang-Firsov transformation, combined with a perturbative calculation of the electron-phonon self-energy in the framework of generalised Matsubara functions. This allows us to describe the system at weak to strong coupling and intermediate to large phonon frequencies. We present results for the quantum dot spectral function and for the kinetic coefficient that characterises the electron transport through the dot. With these results we critically examine the strengths and limitations of our approach, and discuss the properties of the molecular quantum dot in the context of polaron physics. We place particular emphasis on the importance of corrections to the concept of an antiadiabatic dot polaron suggested by the complete Lang-Firsov transformation.