Electronic response of assemblies of designer atoms: The metal-insulator transition and the role of disorder

Quantum dots present the chemist with the opportunity to synthesize atomic- like building blocks with made-to-measure electronic properties. For the th eorists this allows a study of the same Hamiltonian for a range of paramete rs. Hen we consider a lattice of quantum dots, where the dots can be prepar ed with a narrow distribution of properties but are never quite identical. This is unlike an ordered lattice of atoms or molecules. We report computat ions of the frequency-dependent dielectric response of a two-dimensional ar ray of quantum dots, as a function of the distance between the dots. When t he dots are not closely packed, the response is dominated by the Coulomb re pulsion of electrons (of opposite spin) on a given dot. This gives rise to an insulator-metal transition as the expanded array is compressed. The inte rplay between the three effects, the "disorder" due to the size, shape, and environmental fluctuations of the dots, the coupling of adjacent dots, and the Coulomb repulsion are studied as functions of the lattice spacing. The computations are performed in the approximation where each dot carries one valence electron, but these electrons are fully correlated so as to fully account for the Coulomb blocking. This is possible by a diagonalization of the Hamiltonian in a many-electron basis. Comparison is made with experimen tal results for the dielectric response, as described in a companion to thi s paper.