The influence of architecture of nanoparticle networks on collective charge transport revealed by the fractal time series and topology of phase space manifolds

Abstract

Charge transport in the Coulomb blockade regime of two-dimensional nanoparticle arrays exhibits nonlinear I-V characteristics, where the level of nonlinearity strongly associates with the arrays architecture. Here, we use different mathematical techniques to investigate the collective behavior of the charge transport and quantify its relationship to the structure of the nanoparticle assembly. First, we simulate single-electron tunneling conduction in a class of nanoparticle networks with a controlled variation of the structural characteristics (branching, extended linear segments) which influence the local communication among the conducting paths between the electrodes. Further, by applying an innovative approach based on the algebraic topology of graphs, we analyze the structure of connections in the manifolds, which map the fractal time series of charge fluctuations in the phase space. By tracking the I-V curves in different nanoparticle networks together with the indicators of collective dynamics and the topology of the phase space manifolds, we show that the increased I-V nonlinearity is fully consistent with the enhanced aggregate fluctuations and higher connection complexity among the participating states. Also, by determining shifts in the topology and cooperative transport features, we explore the impact of the size of electrodes and local charge disorder. The results are relevant for designing the nanoparticle devices with improved conduction; they also highlight the significance of topological descriptions for a broader understanding of the nature of fluctuations at the nanoscale.