  In this paper, we investigate the band properties of 2D honeycomb plasmonic
lattices consisting of metallic nanoparticles. By means of the coupled dipole
method and quasi-static approximation, we theoretically analyze the band
structures stemming from near-field interaction of localized surface plasmon
polaritons for both the infinite lattice and ribbons. Naturally, the
interaction of point dipoles decouples into independent out-of-plane and
in-plane polarizations. For the out-of-plane modes, both the bulk spectrum and
the range of the momentum $k_{\parallel}$ where edge states exist in ribbons
are similar to the electronic bands in graphene. Nevertheless, the in-plane
polarized modes show significant differences, which do not only possess
additional non-flat edge states in ribbons, but also have different
distributions of the flat edge states in reciprocal space. For in-plane
polarized modes, we derived the bulk-edge correspondence, namely, the relation
between the number of flat edge states at a fixed $k_\parallel$, Zak phases of
the bulk bands and the winding number associated with the bulk hamiltonian, and
verified it through four typical ribbon boundaries, i.e. zigzag, bearded
zigzag, armchair, and bearded armchair. Our approach gives a new topological
understanding of edge states in such plasmonic systems, and may also apply to
other 2D "vector wave" systems.
