Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints

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.