  We numerically show that a vortex pinning occurs in superconducting
quasicrystal without impurities and defects. This vortex pinning is intrinsic
since the superconducting order parameter in quasicrystal is always
inhomogeneous due to the lack of the translational symmetry. We propose that
experiments influenced by vortex pinning effects can detect the atomic-scale
inhomogeneous superconducting order parameter in quasicrystals. We develop a
numerical method to solve the Bogoliubov-de Gennes equations and gap equations
in large systems, which is based on the localized-Krylov subspace and a sparse
modeling technique. Two two-dimensional quasicrystals, the Penrose and
Amman-Beenker tiling, are considered.
