Screening two-dimensional materials with topological flat bands

The topological flat band (TFB) has been proposed theoretically in various lattice models, to exhibit a rich spectrum of intriguing physical behaviors. However, the experimental demonstration of flat band (FB) properties has been severely hindered by the lack of materials realization. Here, by screening materials from a first-principles materials database, we identify a group of two-dimensional materials with TFBs near the Fermi level, covering some simple line-graph and generalized line-graph FB lattice models. These include the kagome sublattice of O in $\mathrm{Ti}{\mathrm{O}}₂$ yielding a spin-unpolarized TFB, and that of V in ferromagnetic ${\mathrm{V}}₃{\mathrm{F}}₈$ yielding a spin-polarized TFB. The monolayer ${\mathrm{Nb}}₃\mathrm{Te}{\mathrm{Cl}}₇$ and its counterparts from element substitution are found to be breathing-kagome-lattice crystals. The family of monolayer $\mathrm{II}{\mathrm{I}}₂\mathrm{V}{\mathrm{I}}₃$ compounds exhibit a TFB representing the coloring-triangle lattice model. $\mathrm{Re}{\mathrm{F}}₃$, $\mathrm{Mn}{\mathrm{F}}₃$, and $\mathrm{Mn}{\mathrm{Br}}₃$ are all predicted to be diatomic-kagome-lattice crystals, with TFB transitions induced by atomic substitution. Finally, $\mathrm{Hg}{\mathrm{F}}₂$, $\mathrm{Cd}{\mathrm{F}}₂$, and $\mathrm{Zn}{\mathrm{F}}₂$ are discovered to host dual TFBs in the diamond-octagon lattice. Our findings pave the way to further experimental exploration of eluding FB materials and properties.