Inspired by graphene, I investigate the properties of several different real and artificial Dirac
materials. Firstly, I consider a two-dimensional honeycomb lattice of metallic nanoparticles, each
supporting localised surface plasmons, and study the quantum properties of the collective plasmons
resulting from the near field dipolar interaction between the nanoparticles. I analytically
investigate the dispersion, the effective Hamiltonian and the eigenstates of the collective plasmons
for an arbitrary orientation of the individual dipole moments. When the polarisation points close
to normal to the plane the spectrum presents Dirac cones, similar to those present in the electronic
band structure of graphene. I derive the effective Dirac Hamiltonian for the collective plasmons
and show that the corresponding spinor eigenstates represent chiral Dirac-like massless bosonic
excitations that present similar effects to those of electrons in graphene, such as a non-trivial Berry
phase and the absence of backscattering from smooth inhomogeneities. I further discuss how one
can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon
dispersion by modifying the polarisation of the localized surface plasmons, paving the way for a
fully tunable plasmonic analogue of graphene. I present a phase diagram of gapless and gapped
phases in the collective plasmon dispersion depending on the dipole orientation.
When the inversion symmetry of the honeycomb structure is broken, the collective plasmons
become gapped chiral Dirac modes with an energy-dependent Berry phase. I show that this
concept can be generalised to describe many real and artificial graphene-like systems, labeling
them Dirac materials with a linear gapped spectrum. I also show that biased bilayer graphene is
another Dirac material with an energy dependent Berry phase, but with a parabolic gapped spectrum.
I analyse the relativistic phenomenon of Klein Tunneling in both types of system.
The Klein paradox is one of the most counter-intuitive results from quantum electrodynamics
but it has been seen experimentally to occur in both monolayer and bilayer graphene, due to
the chiral nature of the Dirac quasiparticles in these materials. The non-trivial Berry phase of
pi in monolayer graphene leads to remarkable effects in transmission through potential barriers,
whereas there is always zero transmission at normal incidence in unbiased bilayer graphene in the
npn regime. These, and many other 2D materials have attracted attention due to their possible
usefulness for the next generation of nano-electronic devices, but some of their Klein tunneling
results may be a hindrance to this application. I will highlight how breaking the inversion symmetry
of the system allows for results that are not possible in these system’s inversion symmetrical
counterparts
