Impurity induced parallel multi-flat bands in graphene

The electronic structure of graphene suppresses the transfer of the single active electron when the adjacent carbon atom is doped. This causes the emergence of a robust and universal flat band in the band structure and subsequently a mid-gap state in the DOS diagram close to the zero of the energy. This effect can be modified by adding extra impurities to the graphene supercells. We found that one can observe multiple flat bands by adding the odd number of epoxy groups around the initial impurity point. In addition, different types of neighbor impurities are compared with each other in their impurity-induced flat band effect. The origin of the multiple flat bands is investigated by a series of analyses with different types of impurities and configurations. Therefore, any periodic arrangement of impurity strongly localizes electrons and produces alternated superlattice bands whose width depends on the parameters of the added impurity. Accessing multiple flat bands can pave the way in the engineering of suitable platforms in studying other phenomena such as superconductivity and fractional quantum Hall effect.