  We study the effect of carrier doping to the Mott insulator on the Penrose
tiling, aiming at clarifying the interplay between quasiperiodicity and strong
electron correlations. We numerically solve the Hubbard model on the
Penrose-tiling structure within a real-space dynamical mean-field theory, which
can deal with a singular self-energy necessary to describe the Mott insulator
and spatial inhomogeneity. We find that the strong correlation effect produces
a charge distribution unreachable by a static mean-field approximation. In a
small doping region, the spectrum shows a site-dependent gap just above the
Fermi energy, which is generated by a singularly large self-energy emergent
from the Mott physics and regarded as a real-space counterpart of the
momentum-dependent pseudogap observed in a square-lattice Hubbard model.
