Isolated flat bands in a lattice of interlocking circles

Flat-band physics has attracted much attention in recent years because of its interesting properties and important applications. Some typical lattices have been proposed to generate flat bands, such as Kagome and Lieb lattices. The flat bands in these lattices contact with other bands rather than being isolated. However, an ideal flat band should be isolated, because isolation is a prerequisite for a number of important applications. Here, we propose a lattice that can produce isolated flat bands. The lattice is named an interlocking-circles lattice because its pattern seems like interlocking circles. Moreover, the lattice is realized in graphene by hydrogenation. In the hydrogenated graphene, there are two nontrivial isolated flat bands appearing around the Fermi level. Upon hole or electron doping, the flat bands split into spin-polarized bands and then result in a ferromagnetic graphene. Our work not only proposes a type of lattice but also opens a way to find systems with isolated flat bands.