A systematic generalised approach to find transport observables for a linear array of different quantum dot (QD) systems has been discussed, using non-equilibrium Green function (NEGF) formalism, in the presence of on-dot Coulomb interaction and inter-dot tunnelling. The equation of motion (EOM) method has been used to derive expressions for Green functions (GFs) within the simplest mean-field approximation to tackle the Coulomb correlation term. Starting from the mathematical structures of GFs for single, double and triple quantum dot systems, the expressions for GFs and transport observables have been generalised for the quantum dot systems containing N number of quantum dots in series as well as parallel linear array of dots. Further, the formulae so obtained have been used for numerical calculations of transmission probability and the I – V characteristics of linear arrays of quantum dots in series as well as parallel configuration containing up to three dots. The results show that, with the increase in number of dots in the scattering region, transmission probability and electron current decrease in series case, while both quantities increase in parallel configuration of dots. The inter-dot tunnelling leads to the splitting of transmission peaks in double QD system in series case whereas, it induces Fano effect in triple QD system in parallel configuration.

中文翻译：

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一种计算串联和并联量子点线性阵列的各种传输可观测值的通用方法

已经讨论了在存在点上库仑相互作用和点间隧道效应的情况下，使用非平衡格林函数 (NEGF) 形式主义，为不同量子点 (QD) 系统的线性阵列寻找传输可观测值的系统通用方法。运动方程 (EOM) 方法已用于在最简单的平均场近似内导出格林函数 (GF) 的表达式，以解决库仑相关项。从单、双和三量子点系统的 GFs 的数学结构开始，GFs 和传输可观测量的表达式已经推广到包含 N 个串联量子点和平行线性点阵列的量子点系统。更多，如此获得的公式已用于传输概率和线性量子点阵列的 I-V 特性的数值计算，以及最多包含三个点的并行配置。结果表明，随着散射区点数的增加，串联情况下传输概率和电子电流减小，而点并联配置时这两个量都增加。点间隧穿导致串联情况下双 QD 系统中传输峰值的分裂，而它在并联配置的三 QD 系统中引起 Fano 效应。在串联情况下，传输概率和电子电流减少，而在点的并联配置中这两个量增加。点间隧穿导致串联情况下双 QD 系统中传输峰值的分裂，而它在并联配置的三 QD 系统中引起 Fano 效应。在串联情况下，传输概率和电子电流减少，而在点的并联配置中这两个量增加。点间隧穿导致串联情况下双 QD 系统中传输峰值的分裂，而它在并联配置的三 QD 系统中引起 Fano 效应。