Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

TL;DR

This paper evaluates various approximation methods within the nonequilibrium Green function formalism to accurately model steady state transport in double quantum dot arrays, highlighting the most effective closure for complex systems.

Contribution

The study develops and compares four closure schemes for the equation-of-motion Green function approach applied to double quantum dot arrays, identifying the most accurate method for strong interactions.

Findings

One closure accurately describes transport in double quantum dots.

All closures work well for single quantum dots.

The poles of Green functions correlate with many-particle energy differences.

Abstract

We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations, however its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results.This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.