  On the basis of the "molecular-orbital" representation which describes
generic flat-band models, we propose a systematic way to construct a class of
flat-band models with finite-range hoppings that have topological natures. In
these models, the topological natures are encoded not into the flat band itself
but into the dispersive bands touching the flat band. Such a band structure may
become a source of exotic phenomena arising from the combination of flat bands,
topology and correlations.
