  We study the excitonic insulating (EI) phase in the two-band Hubbard models
on the Penrose tiling. Performing the real-space mean-field calculations
systematically, we obtain the ground state phase diagrams for the vertex and
center models. We find that, in some regimes, the stable EI phase is induced by
small interband interactions. We argue that this originates from the
electron-hole pairing for the completely or nearly degenerate states, which are
characteristic of the Penrose tiling. We also study spatial distribution of the
order parameter, mapping it to the perpendicular space.
