Transient dynamics of a molecular quantum dot with a vibrational degree of freedom

TL;DR

This paper studies the transient behavior of a molecular quantum dot with vibrational modes, using perturbation theory and mean-field methods to analyze electron transport and inelastic effects under bias voltage.

Contribution

It introduces a combined approach of perturbation theory and mean-field approximation to analyze transient dynamics in a vibrational quantum dot.

Findings

Identification of inelastic effects when bias exceeds phonon frequency

Observation of bistability in the quantum dot dynamics

Characterization of transient current and population behavior

Abstract

We investigate the transient effects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian which is instantly coupled to two fermionic leads biased by a finite voltage. In the limit of weak electron-phonon interaction, we use perturbation theory to determine the time-dependence of the dot population and the average current. The limit of strong coupling is accessed by means of a self-consistent time-dependent mean-field approximation. These comple- mentary approaches allow us to investigate the dynamics of the inelastic effects occurring when the applied bias voltage exceeds the phonon frequency and the emergence of bistability.