Flat Bands on Honeycomb Superlattices

Flat bands on a honeycomb lattice have provided useful platforms to study strong correlation and topological physics. Honeycomb superlattices of s-orbitals have been discovered to host flat bands. We study the origin of the robustness of flat bands in the presence of local perturbations respecting lattice symmetry. Analytically, we derive the flat band energies when various additional hoppings are introduced. Moreover, we argue that we can obtain flat bands at arbitrary energies by tuning the perturbation strengths. We also construct localized states due to destructive interference in real space that give rise to the flat bands. We show that symmetry-protected degeneracy is key to the stability of these states and of the flat bands. Finally, we point out the non-contractible loop states in the flat bands of the system.