The crossover from two dimensions to one dimension in granular electronic materials

Granular conductors are solids comprising densely packed nanoparticles, and have electrical properties that are determined by the size, composition and packing of the composite nanoparticles. The ability to control these properties in two- and three-dimensional granular conductors has made such systems appropriate for use as prototypes for investigating new physics. However, the fabrication of strictly one-dimensional granular conductors remains challenging. Here, we describe a method for the assembly of nanoparticles into granular solids that can be tuned continuously from two to one dimension, and establish how electron transport evolves between these limits. We find that the energy barriers to transport increase in the one-dimensional limit, in both the variable-range-hopping (low-voltage) and sequential-tunnelling (high-voltage) regimes. Furthermore, in the sequential-tunnelling regime we find an unexpected relationship between the temperature and the voltage at which the conductance becomes appreciable a relationship that appears peculiar to one-dimensional systems. These results are explained by extrapolating existing granular conductor theories to one dimension.