Quantum master equation for electron transport through quantum dots and single molecules

TL;DR

This paper derives a quantum master equation for electron transport in quantum dots and molecules, analyzing how coherences affect transport properties under various conditions and approximations.

Contribution

It introduces a quantum master equation that accounts for system-lead interactions and coherences, providing insights into transport dynamics and steady states.

Findings

Coherences between states with different electron numbers do not affect second-order transport.

Coherences between same-electron-number states can influence transport when damping is rapid.

In the rotating wave approximation, the dynamics simplify to a birth-death process.

Abstract

A quantum master equation (QME) is derived for the many-body density matrix of an open current-carrying system weakly coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of number of electrons in the system. We show that coherences between system states with different number of electrons, n, (Fock space coherences) do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order or faster then the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation (when the damping is slow compared to the Bohr frequencies of the system), the dynamics of populations and the coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.