• atomistic model
• graphene
• plasmonics
• response

The aim of this thesis is the development of a fully atomistic classical model able to describe the optical properties of graphene, i.e. its plasmon resonance and the associated extinction cross section. Over the last years, research has been focused mainly on noble metal plasmonics, that is today the corner stone for the development of new plasmonic structures and gives, at the same time, the theoretical background to understand new physical phenomena involving nanostructured materials. Plasmonics on carbon based nanostructures is a very promising field of research with the potential of revolutionizing several fields of application: photonic devices, biosensing, Surface Enhanced Raman Scattering (SERS) technique and so on.
On the other hand, to the best of my knowledge, the theoretical and computational studies of optical properties of carbon based nanostructures have been limited to ab-initio methods only. In particular, DFT is the most common used method due to its accurate results. However, due to its high computational cost, its application is restricted to nanostructures of few nanometers only, thus strongly limiting the applicability to real cases. For this reason, the development of a fully atomistic classical model able to correctly describe the optical properties of carbon-based nanomaterials and able to treat thousands of atoms, could have high impact, not only for its capability to give theoretical insight into the physical phenomenon, but also for its potentialities to rationalize the design of new experiments.
In this thesis, we propose a fully atomistic classical model, named !FQ, based on the Fluctuating Charge (FQ) Force Field approach, first developed by Rick et al. in 1994 (Steven W Rick, Steven J Stuart, and Bruce J Berne. Dynamical fluctuating charge force fields: Application to liquid water. The Journal of chemical physics, 101(7):6141–6156, 1994.) and successfully applied to the description of bulk solutions. In the FQ force field, each atom is endowed with a charge, which is not fixed, but it can change in response to differences in atomic chemical potentials. Since, the basics formulation of FQ does not take into account the presence of an external oscillating electric field: therefore, a modification of the FQ approach is requested to treat the optical properties of
graphene. Once the model was defined, a lot of calculations have been made in order to compare our model to other DFT and classical calculation results in literature. (see, for example Sukosin Thongrattanasiri, Alejandro Manjavacas, and F Javier Garcia de Abajo. Quantum finite-size effects in graphene plasmons. Acs Nano, 6(2):1766– 1775, 2012.)
In particular, !FQ model has been applied to the optical spectrum of selected graphene disks, which were previously studied with ab-initio and classical continuum models. Such structures were used to study the behavior of the plasmon resonance frequency as a function of the parameters defining our model, that are the grahene surface density, the diameter of the disk, the scattering time, and a free parameter defining !FQ.
The obtained results also prove that !FQ is able to study the tunability of localized plasmon inside graphene disks by exploiting geometrical dimensions or by changing the physical parameters entering the equations. This ascertains that the !FQ Force Field is able to compete with QM approaches in the description of graphene plasmon frequency, also allowing to understand the role of the parameters that influence the intensity of the absorption peak: in particular for small graphene disks of small dimensions (i.e. diameter d between 2 and 5 nm) our results follow the DFT ones, while for the biggest structure (d  8 nm) !FQ returns values for the plasma frequency in accordance with the classical calculations, as expected.