Graphene as a Metal without the Negative Dielectric Constant in the Designed Mono – Layer Graphene Waveguide at a Chemical Potential of 450meV

Graphene's electronic properties come from its halffilled band structure formed from the $\pi$ -bond which hybridizes together to form the $\pi$-band and $\pi^{\ast}$-bands. Due to its almost zero bandgap, Graphene can be tuned as a metal by applying a chemical potential to the 2D material, as it has high electron mobility at atomic level thickness. Using this property, Graphene was tuned to chemical potentials from 350meV − 500meV, where it showed semi-conductor behaviour below 400meV and metallic behaviour above 450meV. The Group III and V elements of the periodic table combine well to bond with Graphene due to their sp2 hybridisation and hexagonal crystalline bonding, and this property was further used in building a mono-layer Graphene waveguide structure using silicon nitride as the outer core, silica as the substrate and air as the cladding, to further investigate the behaviour of Graphene as a metal. The modal solutions in this structure were obtained by solving the full-vectorial H-field formulation using the finite element method (FEM) which showed the hybrid plasmonic mode generation at the silicon nitride-graphene-silica interface, thereby confirming the behaviour of Graphene as a metal at 450meV without its negative dielectric constant. This however contradicts the surface plasmon theory which states that at a metal-dielectric surface, surface plasmon polaritons (SPP's) are only formed if k1/k2 = −ε1/ε2 is satisfied. This work needs further experimental evaluation to confirm the behaviour of Graphene as a metal without the negative dielectric constant at 450meV as it would then open doors to a new understanding of solid-state physics, thereby leading to new applications in this field of science.