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Charge transport within Coulomb blockade regime in two-dimensionalnanoparticle arrays exhibits nonlinear I-V characteristics, where the level ofnonlinearity strongly associates with the array's architecture. Here, we usedifferent mathematical approaches to quantify collective behavior in the chargetransport inside the sample and its relationship to the structuralcharacteristics of the assembly and the presence of charge disorder. Inparticular, we simulate single-electron tunneling conduction in severalassemblies with controlled variation of the structural components (branching,extended linear segments) that influence the local communication among theconducting paths between the electrodes. Furthermore, by applying the fractalanalysis of time series of the number of tunnelings and the technique ofalgebraic topology, we unravel the temporal correlations and structure of thephase-space manifolds corresponding to the cooperative fluctuations of charge.By tracking the I-V curves in different assemblies together with the indicatorsof collective dynamics and topology of manifolds in the state space, we showthat the increased I-V nonlinearity is fully consistent with the enhancedaggregate fluctuations and topological complexity of the participating states.The architecture that combines local branching and global topological disorderenables the creation of large drainage basins of nano-rivers leading tostronger cooperation effects. Also, by determining shifts in the topology andcollective transport features, we explore the impact of the size of electrodesand local charge disorder. The results are relevant for designing thenanoparticle devices with improved conduction; they also highlight thesignificance of topological descriptions for a broader understanding of thenature of fluctuations at the nanoscale.

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