Exotic vortex states and enhancement of orbital upper critical fields in an $s$-wave quasicrystalline superconductor

Quasicrystals possess long-range order without translational symmetry, giving rise to intrinsically inhomogeneous superconducting states. Using the Bogoliubov-de Gennes mean-field theory, we investigate vortex states in an $s$-wave quasicrystalline superconductor on the Ammann-Beenker tiling, with particular emphasis on the high-field regime. We find that the vortex configuration can differ qualitatively from the Abrikosov triangular lattice. In particular, at filling $\nu =0.8$, vortices preferentially penetrate weak-pairing regions centered on sites with coordination number $8$, indicating that their spatial organization is strongly influenced by the local geometry. Furthermore, we observe an enhanced upper critical field. At $\nu =0.8$, where the enhancement is particularly pronounced, the spatially averaged order parameter exhibits a plateau-like field dependence accompanied by the formation of vortex clusters. These clusters accommodate additional flux in locally weak superconducting regions, providing a microscopic interpretation of the plateau-like behavior. Moreover, the upper critical field increases upon cooling toward zero temperature without a clear sign of saturation.