Flat-bands on partial line graphs - Systematic method for generating flat-band lattice structures

We introduce a systematic method for constructing a class of lattice structures that we call partial line graphs. In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge. This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.