Realistic flat-band model based on degenerate $p$-orbitals in two-dimensional ionic materials

Though several theoretical models have been proposed to design electronic flat-bands, the definite experimental realization in two-dimensional atomic crystal is still lacking. Here we propose a novel and realistic flat-band model based on threefold degenerate $p$-orbitals in two-dimensional ionic materials. Our theoretical analysis and first-principles calculations show that the proposed flat-band can be realized in 1T layered materials of alkali-metal chalogenides and metal-carbon group compounds. Some of the former are theoretically predicted to be stable as layered materials (e.g., K$_2$S), and some of the latter have been experimentally fabricated in previous works (e.g., Gd$_2$CCl$_2$). More interestingly, the flat-band is partially filled in the heterostructure of a K$_2$S monolayer and graphene layers. The spin polarized nearly flat-band can be realized in the ferromagnetic state of a Gd$_2$CCl$_2$ monolayer, which has been fabricated in experiments. Our theoretical model together with the material predictions provide a realistic platform for the study of flat-bands and related exotic quantum phases.