Flat bands without twists: periodic holey graphene.

(HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. The electronic properties of a periodic distribution of lattice holes are explored here, demonstrating the emergence of flat bands. It is established that such flat bands arise as a consequence of an induced sublattice site imbalance, i.

Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with - orbitals.

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with - orbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by themetric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands.