Molecular transistor coupled to phonons and Luttinger-liquid leads

TL;DR

This paper investigates how electron-phonon interactions influence transport and noise in a molecular quantum dot connected to Luttinger-liquid leads, revealing suppression of current and noise, and super-Poissonian noise at strong coupling.

Contribution

It introduces a semi-classical rate equation approach to analyze the combined effects of electron-electron and electron-phonon interactions on transport in Luttinger-liquid systems.

Findings

Electron-electron interactions suppress current and noise.

Stronger intralead interactions enhance the Fano factor.

High electron-phonon coupling leads to super-Poissonian noise.

Abstract

We study the effects of electron-phonon interactions on the transport properties of a molecular quantum dot coupled to two Luttinger-liquid leads. In particular, we investigate the effects on the steady state current and DC noise characteristics. We consider both equilibrated and unequilibrated on-dot phonons. The density matrix formalism is applied in the high temperature approximation and the resulting semi-classical rate equation is numerically solved for various strengths of electron-electron interactions in the leads and electron-phonon coupling. The current and the noise are in general smeared out and suppressed due to intralead electron interaction. On the other hand, the Fano factor, which measures the noise normalized by the current, is more enhanced as the intralead interaction becomes stronger. As the electron-phonon coupling becomes greater than order one, the Fano factor exhibits super-Poissonian behaviour.