Optical properties of geometrically optimized graphene quantum dots

We derive effective tight-binding model for geometrically optimized graphene quantum dots and based on it we investigate corresponding changes in their optical properties in comparison to ideal structures. We consider hexagonal and triangular dots with zigzag and armchair edges. Using density functional theory methods we show that displacement of lattice sites leads to changes in atomic distances and in consequence modifies their energy spectrum. We derive appropriate model within tight-binding method with edge-modified hopping integrals. Using group theoretical analysis, we determine allowed optical transitions and investigate oscillatory strength between bulk-bulk, bulk-edge and edge-edge transitions. We compare optical joint density of states for ideal and geometry optimized structures. We also investigate an enhanced effect of sites displacement which can be designed in artificial graphene-like nanostructures. A shift of absorption peaks is found for small structures, vanishing with increasing system size.