Architecture with designer atoms: Simple theoretical considerations

The distinct electronic states of assemblies of metallic quantum dots are discussed in a simple approximation where each dot is mimicked as an “atom” that carries one valence electron. Because of their large size, the charging energy of the dots, I = energy required to add another electron, is much smaller than for ordinary atoms. The Coulomb blocking of charge migration is therefore easier to overcome. For the theory, however, this is a challenge, because ionic states, which are typically higher in energy, come down, so the density of electronic states is high, and special methods need to be adapted. Quantum dots are prepared by wet chemical methods and accordingly are not quite identical. They will have a size distribution that can be narrow (when the dots can be assembled into an ordered array) or broad. Other sources of disorder are packing imperfections, which are characteristic of a wider size distribution, ligand deformations, and chemical unevenness. Two experimental control parameters are the size of the dots and the spacing between them. We discuss the combined effects of the low charging energy and disorder and examine the distinct electronic phases that can be realized.