On Electronic Properties of Assemblies of Quantum Nanodots

The electronic response of a 2D hexagonal array of quantum dots is computed as a function of the distance between the dots. The electronic properties result from the interplay between three factors: (i) the “inherent disorder” due to the size, shape, and environmental fluctuations of the dots, (ii) the coupling of adjacent dots, and (iii) the role of the Coulombic repulsion. The computations are carried out using a Pariser−Parr−Pople type Hamiltonian, which is fully diagonalized in a many-electron basis as a function of the interdot separation. At high compression, the dots nearly touch one another and the electronic response is dominated by the coupling between the dots. An Anderson-like delocalized to localized transition arises as the lattice is expanded because the interdot coupling decreases. When the dots are further apart, the electronic response is dominated by the Coulombic repulsion of electrons (of opposite spin) on a given dot. The latter gives rise to a Mott-type insulator to metal transition as the extended array is compressed. In addition, we also discuss the case where large fluctuations in size are able to overcome the Coulombic effects. For such arrays, the Mott-type insulator to metal transition is smeared out by the disorder effects. Moreover, at large interdot separation, the ground state is found to be ionic while for moderately disordered arrays, the ground state is covalent. Comparison is made with the experimental results of the Heath group.