Levy statistics in quasi one-dimensional percolation paths in nano-patterned quantum dot solids

Quantum dot (QD) solids hold promise as a tunable platform for applications such as quantum computation and spintronics, and for exploring many-body physics. However, the predicted, novel electronic properties in QD solids have been obscured by disorder caused by structural defects, variability in electronic energy levels of the QDs and charge traps on the QD surfaces. We nano-pattern QD solids with dimensions ~10−100 nm that are free of structural defects found in many larger superlattices. The QDs are strongly coupled (≤1 nm inter-dot spacing), which offsets inhomogeneities in the electronic energy levels in the QD. We find current noise that increases linearly with the average current at high temperatures, and we find random telegraph noise at low temperatures. We show that charge is transmitted along quasi-one-dimensional channels, which open and close at a rate given by Levy statistics. The trapping and release of charge in the QD matrix is the likely cause for these fluctuations. These nano-patterned QD solids enable measurement of the charge transport mechanism intrinsic to the QDs; and, they offer a direct measurement of the influence of charge trapping on the charge transport mechanism.