  A bipartite lattice with chiral symmetry is known to host zero energy flat
bands if the numbers of the two sublattices are different. We demonstrate that
this mechanism of producing flat bands can be realized on graphene by
introducing periodic vacancies. Using first-principle calculations, we
elaborate that even though the pristine graphene does not exactly preserve
chiral symmetry, this mechanism applied to holey graphene still produces single
or multiple bands as narrow as ~0.5eV near the Fermi surface throughout the
entire Brillouin zone. Moreover, this mechanism can combine with
vacancy-engineered nonsymmorphic symmetry to produce band structures with
coexisting flat bands and nodal lines. A weak coupling mean-field treatment
suggests the stabilization of superconductivity by these vacancy-engineered
narrow bands. In addition, superconductivity occurs predominantly on the
majority sublattices, with an amplitude that increases with the number of
narrow bands.
