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We present comparatively simple two-dimensional and three-dimensionalcheckerboard-like optical lattices possessing nontrivial topologicalproperties. By simple tuning of the parameters these lattices can have atopological insulating phase, a topological semi-metallic phase, or a trivialinsulating phase. This allows study of different topological phase transitionswithin a single cold atom system. In the topologically nontrivial phases flatbands appear at the surfaces of the system. These surface states possess shortlocalization lengths such that they are observable even in systems with smalllattice dimensions. Our proposed lattices neither need spin-orbit coupling nornon-Abelian gauge fields to reach topologically nontrivial states.

Topological flat bands in optical checkerboard-like lattices