School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
J Chem Phys. 2013 Apr 28;138(16):164125. doi: 10.1063/1.4802752.
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.
我们使用非平衡格林函数的运动方程方法研究了通过双量子点阵列的稳态输运。这种流行的技术依赖于不可控的近似来获得方程组的封闭解;然而，它的准确性受到质疑。我们专注于 4 种不同的封闭解，其中 2 种以前在单量子点系统(安德森杂质模型)的背景下提出，并扩展到双量子点阵列，并开发了 2 种新的封闭解。与已知在弱系统-引导耦合和高温下准确的主方程方法相比，我们比较了微分电导的结果。虽然所有 4 种封闭解都为单量子点情况下的库仑阻塞和其他输运性质提供了准确的描述，但在双量子点阵列的情况下，只有开发的封闭解之一提供了令人满意的结果。通过将格林函数的极点与隔离系统的精确多粒子能差进行比较，可以对这种情况进行合理化解释。我们的分析为将运动方程技术扩展到具有强电子相互作用的大型桥系统的更精细模型提供了手段。
