The transition from localized to collective electronic states in a silver quantum dots monolayer examined by nonlinear optical response

The optical second-harmonic response of a finite hexagonal lattice is computed as a function of the inter particle separation. In agreement with experiments on Langmuir monolayers of silver quantum dots, the computed response exhibits a peak due to a transition from localized electronic states to a band-like structure. The localization is due to the fluctuations in the particle size and position. For a perfect lattice the variation of the nonlinear response with the inter particle separation is qualitatively different. The role of the symmetry breaking is demonstrated at the tight binding level of electronic structure computations.