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A singular flat band(SFB), a distinct class of the flat band, has been shownto exhibit various intriguing material properties characterized by a geometricquantity of the Bloch wave function called the quantum distance. We present ageneral construction scheme for a tight-binding model hosting an SFB, where thequantum distance profile can be controlled. We first introduce how to build acompact localized state(CLS), a characteristic eigenstate of the flat band,providing the flat band with a band-touching point, where a specific value ofthe maximum quantum distance is assigned. Then, we develop a scheme designing atight-binding Hamiltonian hosting an SFB starting from the obtained CLS,satisfying the desired hopping range and symmetries by applying theconstruction scheme. While the scheme can be applied to any dimensions andlattice structures, we propose several simple SFB models on the square andkagome lattices. Finally, we establish a bulk-boundary correspondence betweenthe maximum quantum distance and the boundary modes for the open boundarycondition, which can be used to detect the quantum distance via the electronicstructure of the boundary states.

General construction scheme for geometrically nontrivial flat band models