Time-dependent quantum transport through an interacting quantum dot beyond sequential tunneling: second-order quantum rate equations

TL;DR

This paper develops a comprehensive theoretical framework using second-order quantum rate equations to analyze time-dependent electron transport through an interacting quantum dot, capturing transient dynamics and the Kondo effect.

Contribution

It introduces the SOQREs method, combining auxiliary-mode expansion and Lacroix's decoupling, for accurate transient analysis beyond sequential tunneling.

Findings

Successfully describes the Kondo effect qualitatively.

Accurately models transient current responses to voltage pulses.

Provides a comparison with other approaches like the von Neumann method.

Abstract

A general theoretical formulation for the effect of a strong on-site Coulomb interaction on the time-dependent electron transport through a quantum dot under the influence of arbitrary time-varying bias voltages and/or external fields is presented, based on slave bosons and the Keldysh nonequilibrium Green's function (GF) techniques. To avoid the difficulties of computing double-time GFs, we generalize the propagation scheme recently developed by Croy and Saalmann to combine the auxiliary-mode expansion with the celebrated Lacroix's decoupling approximation in dealing with the second-order correlated GFs and then establish a closed set of coupled equations of motion, called second-order quantum rate equations (SOQREs), for exact description of transient dynamics of electron correlated tunneling. We verify that the stationary solution of our SOQREs is able to correctly describe the Kondo effect on a qualitative level. Moreover, a comparison with other methods, such as the second-order von Neumann approach and Hubbard-I approximation, is performed. As illustrations, we investigate the transient current behaviors in response to a step voltage pulse and a harmonic driving voltage, and linear admittance as well, in the cotunneling regime.