Einstein Relation for Electron Diffusion on Arrays of Weakly Coupled Quantum Dots

The transport of electrons on arrays of weakly coupled quantum dots is studied using computer simulations. Distinct minima in the conductivity of the arrays are found for conditions that correspond to filled shells and to integer charging of the quantum dots when the size distribution of the dots is sufficiently small. It is found that the Fickian diffusion coefficient for electrons deviates strongly from that predicted using the Einstein relation, especially in regions where the conductivity spectrum of the array shows minima due to a Coulomb blockade or shell filling.