  We consider a two-dimensional honeycomb lattice of metallic nanoparticles,
each supporting a localized surface plasmon, and study the quantum properties
of the collective plasmons resulting from the near field dipolar interaction
between the nanoparticles. We 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 polarization
points close to the normal to the plane the spectrum presents Dirac cones,
similar to those present in the electronic band structure of graphene. We
derive the effective Dirac Hamiltonian for the collective plasmons and show
that the corresponding spinor eigenstates represent Dirac-like massless bosonic
excitations that present similar effects to electrons in graphene, such as a
non-trivial Berry phase and the absence of backscattering off smooth
inhomogeneities. We 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 polarization of the localized surface plasmons, paving the way
for a fully tunable plasmonic analogue of graphene.
