Lateral conductance of perfect and disordered dot lattices

A theoretical treatment is given of the onset of lateral conductance in a dot lattice, which occurs as the number of electrons per dot is increased, thereby enlarging the dots until they touch. This is the threshold point between a dot and an antidot lattice. The conductance rise has been experimentally measured and we compare our predictions to those results. Two conduction mechanisms are considered in detail; band conductance in a perfect lattice and hopping conduction in a lattice with slight disorder. Both give an exponential rise of the lattice conductance with electron number. The effect of strong disorder is discussed, and using a mapping to a random resistor network it is shown to lead to a far more gradual rise in the conductance.