Electronic properties of graphene antidot lattices

We study graphene antidot lattices -- superlattices made by perforating voids in a graphene sheet. We show that, due to their bipartite structure, such lattices display zero-energy flat bands . We also find quasi-flat bands at low energies resulting from the presence of lattice-scale defects in the system and argue that the ensuing localized electron states compete with the states induced by the superlattice-scale defects that have been proposed as hosts for electron-spin qubits. For representative antidot lattices, we predict the real-space electron density profiles due to both flat and quasi-flat bands. We also investigate the effect of phonons in antidot lattices using a model that accounts for the phonon-modulation of the hopping integrals. Based on the adopted model, we quantify the nature of charge carriers by computing the conduction-band quasiparticle weight due to the electron-phonon coupling. We find a strong phonon-induced renormalization, which provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of graphene antidot lattices.