  We propose a distant-neighbor quantum-mechanical (DNQM) approach to study the
linear and nonlinear optical properties of graphene nanoflakes (GNFs). In
contrast to the widely used tight-binding description of the electronic states
that considers only the nearest-neighbor coupling between the atoms, our
approach is more accurate and general, as it captures the electron-core
interactions between all atoms in the structure. Therefore, as we demonstrate,
the DNQM approach enables the investigation of the optical coupling between two
closely separated, but chemically unbound GNFs. We also find that the optical
response of GNFs depends crucially on their shape, size, and symmetry
properties. Specifically, increasing the size of nanoflakes is found to shift
their accommodated quantum plasmon oscillations to lower frequency.
Importantly, we show that by embedding a cavity into GNFs, one can change their
symmetry properties, tune their optical properties, or enable otherwise
forbidden second-harmonic generation processes.
