  We examine the low energy effective theory of phase oscillations in a
two-dimensional granular superconducting sheet where the grains are arranged in
honeycomb lattice structure. Using the example of graphene we present the
evidence for the engineered Dirac nodes in the bosonic excitations: the spectra
of the collective bosonic modes cross at the K and K points in the Brillouin
zone and form Dirac nodes. We show how two different types of collective phase
oscillations are obtained and that they are analogous to the Leggett and the
Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the
Dirac node is preserved in the presence of an inter-grain interaction, despite
induced changes of the qualitative features of the two collective modes.
Finally, breaking the sublattice symmetry by choosing different on-site
potentials for the two sublattices leads to a gap opening near the Dirac node,
in analogy with Fermionic Dirac materials. Dirac node dispersion of bosonic
excitations is thus expanding the discussion of the conventional Dirac cone
excitations to the case of bosons. We call this case as a representative of
Bosonic Dirac Materials (BDM), similar to the case of Fermionic Dirac materials
extensively discussed in the literature.
