  Charge transport within Coulomb blockade regime in two-dimensional
nanoparticle arrays exhibits nonlinear I-V characteristics, where the level of
nonlinearity strongly associates with the array's architecture. Here, we use
different mathematical approaches to quantify collective behavior in the charge
transport inside the sample and its relationship to the structural
characteristics of the assembly and the presence of charge disorder. In
particular, we simulate single-electron tunneling conduction in several
assemblies with controlled variation of the structural components (branching,
extended linear segments) that influence the local communication among the
conducting paths between the electrodes. Furthermore, by applying the fractal
analysis of time series of the number of tunnelings and the technique of
algebraic topology, we unravel the temporal correlations and structure of the
phase-space manifolds corresponding to the cooperative fluctuations of charge.
By tracking the I-V curves in different assemblies together with the indicators
of collective dynamics and topology of manifolds in the state space, we show
that the increased I-V nonlinearity is fully consistent with the enhanced
aggregate fluctuations and topological complexity of the participating states.
The architecture that combines local branching and global topological disorder
enables the creation of large drainage basins of nano-rivers leading to
stronger cooperation effects. Also, by determining shifts in the topology and
collective 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.
