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. PACS numbers: 73.20.Mf, 78.67.Bf, 73.22.Lp, 73.22.Pr Light has been the source of inspiration for scientific thinking for millennia. Ancient Assyrians developed the first lenses in order to bend the trajectory of light and control its propagation. In contrast to the macroscopic scale, the use of light to observe microscopic structures poses difficulties due to the diffraction limit [1]. In an attempt to overcome this limit and observe subwavelength structures, plasmonic nanostructures have been created [2,3], like isolated metallic nanoparticles [4]. The evanescent field at the surface of the nanoparticle, associated to the localized surface plasmon (LSP) resonance [5], produces strong optical field enhancement in the subwavelength region, allowing one to overcome the diffraction limit and achieve resolution at the molecular level [6].While the field of plasmonics mostly focuses on single or few structures, the creation of ordered arrays of nanoparticles constitutes a bridge to the realm of metamaterials. Plasmonic metamaterials exhibit unique properties beyond traditional optics, like negative refractive index [7], perfect lensing [8], the exciting perspective of electromagnetic invisibility cloaking [9], and "trapped rainbow" slow light exploiting the inherent broadband nature of plasmonics [10]. Indeed, in plasmonic metamaterials the interaction between LSPs on individual nanoparticles generates extended plasmonic modes involving all LSPs at once [11,12]. Understanding the nature and properties of these plasmonic modes [referred to as "collective plasmons" (CPs) in what follows] is of crucial importance as they are the channel guiding electromagnetic radiation with strong lateral confinement over macroscopic distances.CPs in periodic arrays of metallic nanoparticles are an active area of research in plasmonics because the interaction of ...

We study theoretically "graphene-like" plasmonic metamaterials constituted by two-dimensional arrays of metallic nanoparticles, including perfect honeycomb structures with and without inversion symmetry, as well as generic bipartite lattices. The dipolar interactions between localised surface plasmons in different nanoparticles gives rise to collective plasmons that extend over the whole lattice. We study the band structure of collective plasmons and unveil its tunability with the orientation of the dipole moments associated with the localised surface plasmons. Depending on the dipole orientation, we identify a phase diagram of gapless or gapped phases in the collective plasmon dispersion. We show that the gapless phases in the phase diagram are characterised by collective plasmons behaving as massless chiral Dirac particles, in analogy with electrons in graphene. When the inversion symmetry of the honeycomb structure is broken, collective plasmons are described as gapped chiral Dirac modes with an energy-dependent Berry phase. We further relax the geometric symmetry of the honeycomb structure by analysing generic bipartite hexagonal lattices. In this case we study the evolution of the phase diagram and unveil the emergence of a sequence of topological phase transitions when one hexagonal sublattice is progressively shifted with respect to the other.