  The disorder effects on higher-order topological phases in periodic systems
have attracted much attention. However, in aperiodic systems, such as
quasicrystalline systems, the interplay between disorder and higher-order
topology is still unclear. In this paper, we investigate the effects of
disorder on two types of second-order topological insulators, including a
quasicrystalline quadrupole insulator and a modified quantum spin Hall
insulator, in a two-dimensional Amman-Beenker tiling quasicrystalline lattice.
We demonstrate that the higher-order topological insulators are robust against
weak disorder in both models. More striking, the disorder-induced higher-order
topological insulators called higher-order topological Anderson insulators are
found at a certain region of disorder strength in both models. Our paper
extends the study of the interplay between disorder and higher-order topology
to quasicrystalline systems.
