Spectroscopy of the transition-rate matrix for molecular junctions: dynamics in the Franck-Condon regime

TL;DR

This paper introduces a spectral analysis of the transition-rate matrix in quantum master equations to study the dynamics of electronic transport in molecular junctions, especially under Franck-Condon blockade conditions.

Contribution

It proposes using the eigenvalues spectrum of the transition-rate matrix as a new tool to analyze nanoscopic transport dynamics, offering insights beyond stationary state observables.

Findings

Eigenvalues spectrum reveals transport dynamics in molecular junctions.

Application to Franck-Condon blockade demonstrates the method's effectiveness.

Provides a complementary perspective to traditional stationary state analysis.

Abstract

The quantum master equation applied to electronic transport through nanoscopic devices provides information not only on the stationary state but also on the dynamics. The dynamics is characterized by the eigenvalues of the transition-rate matrix, or generator, of the master equation. We propose to use the spectrum of these eigenvalues as a tool for the study of nanoscopic transport. We illustrate this idea by analyzing a molecular quantum dot with an electronic orbital coupled to a vibrational mode, which shows the Franck-Condon blockade if the coupling is strong. Our approach provides complementary information compared to the study of observables in the stationary state.