Coupling double flat bands in a quadrangular-star lattice.

Most special two-dimensional (2D) lattices, such as Kagome and Lieb lattices, can only generate a single flat band. Here, we propose a 2D lattice named a quadrangular-star lattice (QSL). It can produce coupling double flat bands, which indicates that there exists stronger electronic correlation than in the systems with only one flat band. Moreover, we suggest some 2D carbon allotropes ( CQSL-12 and CQSL-20), made of carbon rings and dimers, to realize QSL in real materials. By calculating the band structures of the carbon materials, we find that there are indeed two coupling flat bands around the Fermi level. Hole doping leads to strong magnetism of the carbon materials. When the two flat bands are half filled, , in the cases of one- and three-hole doping, the magnetic momentums mainly distribute on the atoms of the carbon rings and dimers, respectively. Even in the case of two-hole doping, the carbon structure also shows ferromagnetic characteristics, and the total magnetic moments are larger than the former two cases.