Vacancy-Engineered Flat-Band Superconductivity in Holey Graphene

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 $\sim 0.5$eV 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.