Electrons whose energy dispersion is bound within a narrow window, i.e. "flat bands", are conjectured to exhibit a wide-range of interesting physics phenomena. Take the twisted bilayer graphene as a representative example, the flatness of the electronic bands plays a crucial role in the physics of, for example in the appearance of both the correlated insulator states and of the strong-coupling superconductivity. In this talk, I report on our recent progress in the topological flat bands. I will highlight two main results: (1) Topological flat bands with fragile band topology in 2D Line-and Split graph lattice, (2) Topological flat bands with strong band topology in 2D Line- and Split graph lattice of bipartite lattice, and (3) Catalogue of Flat Band of 3D materials.
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