Abstract
This paper focuses on modeling a disordered system of quantum dots (QDs) by using complex networks with spatial and physical-based constraints. The first constraint is that, although QDs (=nodes) are randomly distributed in a metric space, they have to fulfill the condition that there is a minimum inter-dot distance that cannot be violated (to minimize electron localization). The second constraint arises from our process of weighted link formation, which is consistent with the laws of quantum physics and statistics: it not only takes into account the overlap integrals but also Boltzmann factors to include the fact that an electron can hop from one QD to another with a different energy level. Boltzmann factors and coherence naturally arise from the Lindblad master equation. The weighted adjacency matrix leads to a Laplacian matrix and a time evolution operator that allows the computation of the electron probability distribution and quantum transport efficiency. The results suggest that there is an optimal inter-dot distance that helps reduce electron localization in QD clusters and make the wave function better extended. As a potential application, we provide recommendations for improving QD intermediate-band solar cells.
Highlights
This paper has proposed the modeling of a quantum system, S, made up of N disordered quantum dots (QDs), by using complex networks (CN) with spatial and physicalbased constraints
While discerning what a node is seems easy (QD ≡ node), more care and physical intuition is required when determining how the links between QDs are formed in such a way that they have physical meaning
The novelty of our model is threefold: first, we have considered the QDs (=nodes) to be randomly distributed in a metric space, they have to fulfill the key condition that there is a minimum distance between dot centers that cannot be violated; second, our model allows nodes with different attributes to be considered—in particular, with different energy levels; third, the link formation and the weighting process that we have proposed are consistent with the laws of quantum physics and statistics
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. With this motivation in mind, our object of study is a special kind of disordered system of QDs. We speak of disorder in two senses: on the one hand, QDs are placed randomly with the only restriction that there is a minimum Euclidean distance (d E,min = rmin ) between dot centers (Figure 1g); on the other hand, QDs are not identical: during the growth process, each individual QD may have a slightly different size.
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